0.12/0.26	% Problem    : SLH0385^1 : TPTP v8.2.0. Released v8.2.0.
0.27/0.27	% Command    : run_E %s %d THM
0.27/0.48	% Computer : n021.cluster.edu
0.27/0.48	% Model    : x86_64 x86_64
0.27/0.48	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.27/0.48	% Memory   : 8042.1875MB
0.27/0.48	% OS       : Linux 3.10.0-693.el7.x86_64
0.27/0.48	% CPULimit   : 30
0.27/0.48	% WCLimit    : 30
0.27/0.48	% DateTime   : Mon Jul  3 08:48:22 EDT 2023
0.27/0.49	% CPUTime    : 
0.40/0.61	The problem SPC is TH0_THM_EQU_NAR
0.40/0.61	Running higher-order on 1 cores theorem proving
0.40/0.61	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=1 --cpu-limit=30 /export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805
0.40/0.62	# Version: 3.0pre003-ho
0.89/1.09	# partial match(1): HSLSSMSMSSLNSSA
0.89/1.09	# Preprocessing class: HMLSSMSMSSLNSSA.
0.89/1.09	# Scheduled 1 strats onto 1 cores with 30 seconds (30 total)
0.89/1.09	# Starting ehoh_best8 with 30s (1) cores
0.89/1.09	# ehoh_best8 with pid 17163 completed with status 0
0.89/1.09	# Result found by ehoh_best8
0.89/1.09	# partial match(1): HSLSSMSMSSLNSSA
0.89/1.09	# Preprocessing class: HMLSSMSMSSLNSSA.
0.89/1.09	# Scheduled 1 strats onto 1 cores with 30 seconds (30 total)
0.89/1.09	# Starting ehoh_best8 with 30s (1) cores
0.89/1.09	# No SInE strategy applied
0.89/1.09	# Search class: HGHSM-SMLM32-MSSFFSBN
0.89/1.09	# Scheduled 6 strats onto 1 cores with 30 seconds (30 total)
0.89/1.09	# Starting full_lambda_7 with 12s (1) cores
0.89/1.09	# full_lambda_7 with pid 17216 completed with status 0
0.89/1.09	# Result found by full_lambda_7
0.89/1.09	# partial match(1): HSLSSMSMSSLNSSA
0.89/1.09	# Preprocessing class: HMLSSMSMSSLNSSA.
0.89/1.09	# Scheduled 1 strats onto 1 cores with 30 seconds (30 total)
0.89/1.09	# Starting ehoh_best8 with 30s (1) cores
0.89/1.09	# No SInE strategy applied
0.89/1.09	# Search class: HGHSM-SMLM32-MSSFFSBN
0.89/1.09	# Scheduled 6 strats onto 1 cores with 30 seconds (30 total)
0.89/1.09	# Starting full_lambda_7 with 12s (1) cores
0.89/1.09	# Preprocessing time       : 0.043 s
0.89/1.09	# Presaturation interreduction done
0.89/1.09	
0.89/1.09	# Proof found!
0.89/1.09	# SZS status Theorem
0.89/1.09	# SZS output start CNFRefutation
0.89/1.09	thf(decl_22, type, finite8272632373135393572ring_a: int > finite_mod_ring_a).
0.89/1.09	thf(decl_23, type, minus_3609261664126569004ring_a: finite_mod_ring_a > finite_mod_ring_a > finite_mod_ring_a).
0.89/1.09	thf(decl_24, type, minus_minus_int: int > int > int).
0.89/1.09	thf(decl_25, type, minus_minus_nat: nat > nat > nat).
0.89/1.09	thf(decl_26, type, minus_minus_real: real > real > real).
0.89/1.09	thf(decl_27, type, one_on2109788427901206336ring_a: finite_mod_ring_a).
0.89/1.09	thf(decl_28, type, one_one_int: int).
0.89/1.09	thf(decl_29, type, one_one_nat: nat).
0.89/1.09	thf(decl_30, type, one_one_real: real).
0.89/1.09	thf(decl_31, type, plus_p6165643967897163644ring_a: finite_mod_ring_a > finite_mod_ring_a > finite_mod_ring_a).
0.89/1.09	thf(decl_32, type, plus_plus_int: int > int > int).
0.89/1.09	thf(decl_33, type, plus_plus_nat: nat > nat > nat).
0.89/1.09	thf(decl_34, type, plus_plus_real: real > real > real).
0.89/1.09	thf(decl_35, type, times_5121417576591743744ring_a: finite_mod_ring_a > finite_mod_ring_a > finite_mod_ring_a).
0.89/1.09	thf(decl_36, type, times_times_int: int > int > int).
0.89/1.09	thf(decl_37, type, times_times_nat: nat > nat > nat).
0.89/1.09	thf(decl_38, type, times_times_real: real > real > real).
0.89/1.09	thf(decl_39, type, uminus_uminus_int: int > int).
0.89/1.09	thf(decl_40, type, uminus_uminus_real: real > real).
0.89/1.09	thf(decl_41, type, zero_z7902377541816115708ring_a: finite_mod_ring_a).
0.89/1.09	thf(decl_42, type, zero_zero_int: int).
0.89/1.09	thf(decl_43, type, zero_zero_nat: nat).
0.89/1.09	thf(decl_44, type, zero_zero_real: real).
0.89/1.09	thf(decl_45, type, groups3558780024651037881ring_a: (nat > finite_mod_ring_a) > set_nat > finite_mod_ring_a).
0.89/1.09	thf(decl_46, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_47, type, groups465414945397457501ring_a: (real > finite_mod_ring_a) > set_real > finite_mod_ring_a).
0.89/1.09	thf(decl_48, type, groups1932886352136224148al_int: (real > int) > set_real > int).
0.89/1.09	thf(decl_49, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
0.89/1.09	thf(decl_50, type, groups8097168146408367636l_real: (real > real) > set_real > real).
0.89/1.09	thf(decl_51, type, if_Finite_mod_ring_a: $o > finite_mod_ring_a > finite_mod_ring_a > finite_mod_ring_a).
0.89/1.09	thf(decl_52, type, if_int: $o > int > int > int).
0.89/1.09	thf(decl_53, type, if_nat: $o > nat > nat > nat).
0.89/1.09	thf(decl_54, type, if_real: $o > real > real > real).
0.89/1.09	thf(decl_55, type, nth_Fi694352073394265932ring_a: list_F4626807571770296779ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_56, type, ntt_a: nat > nat > nat > finite_mod_ring_a > finite_mod_ring_a > $o).
0.89/1.09	thf(decl_57, type, iNTT_a: nat > finite_mod_ring_a > list_F4626807571770296779ring_a > list_F4626807571770296779ring_a).
0.89/1.09	thf(decl_58, type, nTT_a: nat > finite_mod_ring_a > list_F4626807571770296779ring_a > list_F4626807571770296779ring_a).
0.89/1.09	thf(decl_59, type, intt_a: nat > finite_mod_ring_a > list_F4626807571770296779ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_60, type, ntt_a2: nat > finite_mod_ring_a > list_F4626807571770296779ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_61, type, semiri9180929696517417892ring_a: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_62, type, semiri1314217659103216013at_int: nat > int).
0.89/1.09	thf(decl_63, type, semiri1316708129612266289at_nat: nat > nat).
0.89/1.09	thf(decl_64, type, semiri5074537144036343181t_real: nat > real).
0.89/1.09	thf(decl_65, type, size_s7115545719440041015ring_a: list_F4626807571770296779ring_a > nat).
0.89/1.09	thf(decl_66, type, ord_less_int: int > int > $o).
0.89/1.09	thf(decl_67, type, ord_less_nat: nat > nat > $o).
0.89/1.09	thf(decl_68, type, ord_less_real: real > real > $o).
0.89/1.09	thf(decl_69, type, ord_less_eq_int: int > int > $o).
0.89/1.09	thf(decl_70, type, ord_less_eq_nat: nat > nat > $o).
0.89/1.09	thf(decl_71, type, ord_less_eq_real: real > real > $o).
0.89/1.09	thf(decl_72, type, power_6826135765519566523ring_a: finite_mod_ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_73, type, power_power_int: int > nat > int).
0.89/1.09	thf(decl_74, type, power_power_nat: nat > nat > nat).
0.89/1.09	thf(decl_75, type, power_power_real: real > nat > real).
0.89/1.09	thf(decl_76, type, preliminary_mu_a: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_77, type, preliminary_omega_a: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_78, type, modulo_modulo_int: int > int > int).
0.89/1.09	thf(decl_79, type, modulo_modulo_nat: nat > nat > nat).
0.89/1.09	thf(decl_80, type, collect_real: (real > $o) > set_real).
0.89/1.09	thf(decl_81, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
0.89/1.09	thf(decl_82, type, member_nat: nat > set_nat > $o).
0.89/1.09	thf(decl_83, type, member_real: real > set_real > $o).
0.89/1.09	thf(decl_84, type, mu: finite_mod_ring_a).
0.89/1.09	thf(decl_85, type, omega: finite_mod_ring_a).
0.89/1.09	thf(decl_86, type, i: nat).
0.89/1.09	thf(decl_87, type, j: nat).
0.89/1.09	thf(decl_88, type, k: nat).
0.89/1.09	thf(decl_89, type, n: nat).
0.89/1.09	thf(decl_90, type, numbers: list_F4626807571770296779ring_a).
0.89/1.09	thf(decl_91, type, p: nat).
0.89/1.09	thf(decl_92, type, epred1_3: (int > $o) > int > int > $o).
0.89/1.09	thf(decl_93, type, esk1_3: nat > (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_94, type, esk2_3: nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_95, type, esk3_1: (nat > $o) > nat).
0.89/1.09	thf(decl_96, type, esk4_1: (nat > $o) > nat).
0.89/1.09	thf(decl_97, type, esk5_1: (nat > $o) > nat).
0.89/1.09	thf(decl_98, type, esk6_3: set_real > (nat > real) > (real > nat) > real).
0.89/1.09	thf(decl_99, type, esk7_4: set_real > (nat > real) > (real > nat) > set_nat > real).
0.89/1.09	thf(decl_100, type, esk8_4: set_real > (nat > real) > (real > nat) > set_nat > nat).
0.89/1.09	thf(decl_101, type, esk9_4: set_real > (nat > real) > (real > nat) > set_nat > nat).
0.89/1.09	thf(decl_102, type, esk10_6: set_real > (nat > real) > (real > nat) > set_nat > (nat > finite_mod_ring_a) > (real > finite_mod_ring_a) > real).
0.89/1.09	thf(decl_103, type, esk11_3: set_real > (nat > real) > (real > nat) > real).
0.89/1.09	thf(decl_104, type, esk12_4: set_real > (nat > real) > (real > nat) > set_nat > real).
0.89/1.09	thf(decl_105, type, esk13_4: set_real > (nat > real) > (real > nat) > set_nat > nat).
0.89/1.09	thf(decl_106, type, esk14_4: set_real > (nat > real) > (real > nat) > set_nat > nat).
0.89/1.09	thf(decl_107, type, esk15_6: set_real > (nat > real) > (real > nat) > set_nat > (nat > nat) > (real > nat) > real).
0.89/1.09	thf(decl_108, type, esk16_3: set_nat > (real > nat) > (nat > real) > nat).
0.89/1.09	thf(decl_109, type, esk17_4: set_nat > (real > nat) > (nat > real) > set_real > nat).
0.89/1.09	thf(decl_110, type, esk18_4: set_nat > (real > nat) > (nat > real) > set_real > real).
0.89/1.09	thf(decl_111, type, esk19_4: set_nat > (real > nat) > (nat > real) > set_real > real).
0.89/1.09	thf(decl_112, type, esk20_6: set_nat > (real > nat) > (nat > real) > set_real > (real > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_113, type, esk21_3: set_nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_114, type, esk22_4: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_115, type, esk23_4: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_116, type, esk24_4: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_117, type, esk25_6: set_nat > (nat > nat) > (nat > nat) > set_nat > (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_118, type, esk26_3: set_nat > (real > nat) > (nat > real) > nat).
0.89/1.09	thf(decl_119, type, esk27_4: set_nat > (real > nat) > (nat > real) > set_real > nat).
0.89/1.09	thf(decl_120, type, esk28_4: set_nat > (real > nat) > (nat > real) > set_real > real).
0.89/1.09	thf(decl_121, type, esk29_4: set_nat > (real > nat) > (nat > real) > set_real > real).
0.89/1.09	thf(decl_122, type, esk30_6: set_nat > (real > nat) > (nat > real) > set_real > (real > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_123, type, esk31_3: set_nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_124, type, esk32_4: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_125, type, esk33_4: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_126, type, esk34_4: set_nat > (nat > nat) > (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_127, type, esk35_6: set_nat > (nat > nat) > (nat > nat) > set_nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_128, type, esk36_4: set_nat > (nat > real) > set_real > (real > nat) > nat).
0.89/1.09	thf(decl_129, type, esk37_6: set_nat > (nat > real) > set_real > (real > nat) > (nat > finite_mod_ring_a) > (real > finite_mod_ring_a) > real).
0.89/1.09	thf(decl_130, type, esk38_4: set_nat > (nat > real) > set_real > (real > nat) > nat).
0.89/1.09	thf(decl_131, type, esk39_6: set_nat > (nat > real) > set_real > (real > nat) > (nat > nat) > (real > nat) > real).
0.89/1.09	thf(decl_132, type, esk40_4: set_real > (real > nat) > set_nat > (nat > real) > real).
0.89/1.09	thf(decl_133, type, esk41_6: set_real > (real > nat) > set_nat > (nat > real) > (real > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_134, type, esk42_4: set_nat > (nat > nat) > set_nat > (nat > nat) > nat).
0.89/1.09	thf(decl_135, type, esk43_6: set_nat > (nat > nat) > set_nat > (nat > nat) > (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_136, type, esk44_4: set_real > (real > nat) > set_nat > (nat > real) > real).
0.89/1.09	thf(decl_137, type, esk45_6: set_real > (real > nat) > set_nat > (nat > real) > (real > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_138, type, esk46_4: set_nat > (nat > nat) > set_nat > (nat > nat) > nat).
0.89/1.09	thf(decl_139, type, esk47_6: set_nat > (nat > nat) > set_nat > (nat > nat) > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_140, type, esk48_3: set_nat > set_real > (real > nat) > nat).
0.89/1.09	thf(decl_141, type, esk49_4: set_nat > set_real > (real > nat) > real > real).
0.89/1.09	thf(decl_142, type, esk50_5: set_nat > set_real > (real > nat) > (nat > finite_mod_ring_a) > (real > finite_mod_ring_a) > real).
0.89/1.09	thf(decl_143, type, esk51_3: set_nat > set_real > (real > nat) > nat).
0.89/1.09	thf(decl_144, type, esk52_4: set_nat > set_real > (real > nat) > real > real).
0.89/1.09	thf(decl_145, type, esk53_5: set_nat > set_real > (real > nat) > (nat > nat) > (real > nat) > real).
0.89/1.09	thf(decl_146, type, esk54_3: set_real > set_nat > (nat > real) > real).
0.89/1.09	thf(decl_147, type, esk55_4: set_real > set_nat > (nat > real) > nat > nat).
0.89/1.09	thf(decl_148, type, esk56_5: set_real > set_nat > (nat > real) > (real > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_149, type, esk57_3: set_nat > set_nat > (nat > nat) > nat).
0.89/1.09	thf(decl_150, type, esk58_4: set_nat > set_nat > (nat > nat) > nat > nat).
0.89/1.09	thf(decl_151, type, esk59_5: set_nat > set_nat > (nat > nat) > (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_152, type, esk60_3: set_real > set_nat > (nat > real) > real).
0.89/1.09	thf(decl_153, type, esk61_4: set_real > set_nat > (nat > real) > nat > nat).
0.89/1.09	thf(decl_154, type, esk62_5: set_real > set_nat > (nat > real) > (real > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_155, type, esk63_3: set_nat > set_nat > (nat > nat) > nat).
0.89/1.09	thf(decl_156, type, esk64_4: set_nat > set_nat > (nat > nat) > nat > nat).
0.89/1.09	thf(decl_157, type, esk65_5: set_nat > set_nat > (nat > nat) > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_158, type, esk66_4: set_nat > set_nat > (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_159, type, esk67_4: set_nat > set_nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_160, type, esk68_2: (real > nat) > set_real > real).
0.89/1.09	thf(decl_161, type, esk69_2: (real > finite_mod_ring_a) > set_real > real).
0.89/1.09	thf(decl_162, type, esk70_2: (real > int) > set_real > real).
0.89/1.09	thf(decl_163, type, esk71_2: (real > real) > set_real > real).
0.89/1.09	thf(decl_164, type, esk72_2: (nat > finite_mod_ring_a) > set_nat > nat).
0.89/1.09	thf(decl_165, type, esk73_2: (nat > nat) > set_nat > nat).
0.89/1.09	thf(decl_166, type, esk74_2: set_nat > (nat > finite_mod_ring_a) > nat).
0.89/1.09	thf(decl_167, type, esk75_2: set_nat > (nat > nat) > nat).
0.89/1.09	thf(decl_168, type, esk76_0: finite_mod_ring_a).
0.89/1.09	thf(decl_169, type, esk77_0: finite_mod_ring_a).
0.89/1.09	thf(decl_170, type, esk78_2: nat > nat > nat).
0.89/1.09	thf(decl_171, type, esk79_2: nat > nat > nat).
0.89/1.09	thf(decl_172, type, esk80_2: (nat > $o) > nat > nat).
0.89/1.09	thf(decl_173, type, esk81_1: (nat > $o) > nat).
0.89/1.09	thf(decl_174, type, esk82_1: (nat > nat) > nat).
0.89/1.09	thf(decl_175, type, esk83_1: (nat > nat) > nat).
0.89/1.09	thf(decl_176, type, esk84_3: set_real > (real > nat) > (real > nat) > real).
0.89/1.09	thf(decl_177, type, esk85_3: set_real > (real > int) > (real > int) > real).
0.89/1.09	thf(decl_178, type, esk86_3: set_real > (real > real) > (real > real) > real).
0.89/1.09	thf(decl_179, type, esk87_3: set_nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_180, type, esk88_3: set_real > (real > nat) > (real > nat) > real).
0.89/1.09	thf(decl_181, type, esk89_3: set_nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_182, type, esk90_2: nat > nat > nat).
0.89/1.09	thf(decl_183, type, esk91_2: (nat > $o) > nat > nat).
0.89/1.09	thf(decl_184, type, esk92_2: int > int > nat).
0.89/1.09	thf(decl_185, type, esk93_1: int > nat).
0.89/1.09	thf(decl_186, type, esk94_1: int > nat).
0.89/1.09	thf(decl_187, type, esk95_2: nat > nat > nat).
0.89/1.09	thf(decl_188, type, esk96_2: nat > nat > nat).
0.89/1.09	thf(decl_189, type, esk97_2: nat > nat > nat).
0.89/1.09	thf(decl_190, type, esk98_1: (nat > nat) > nat).
0.89/1.09	thf(decl_191, type, esk99_1: (nat > nat) > nat).
0.89/1.09	thf(decl_192, type, esk100_3: (nat > $o) > nat > nat > nat).
0.89/1.09	thf(decl_193, type, esk101_3: (nat > $o) > nat > nat > nat).
0.89/1.09	thf(decl_194, type, esk102_2: (nat > $o) > nat > nat).
0.89/1.09	thf(decl_195, type, esk103_1: (nat > $o) > nat).
0.89/1.09	thf(decl_196, type, esk104_1: int > nat).
0.89/1.09	thf(decl_197, type, esk105_1: int > nat).
0.89/1.09	thf(decl_198, type, esk106_1: int > nat).
0.89/1.09	thf(decl_199, type, esk107_1: int > nat).
0.89/1.09	thf(decl_200, type, esk108_2: nat > (nat > nat) > nat).
0.89/1.09	thf(decl_201, type, esk109_2: nat > (nat > nat) > nat).
0.89/1.09	thf(decl_202, type, esk110_3: nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_203, type, esk111_3: nat > (nat > nat) > (nat > nat) > nat).
0.89/1.09	thf(decl_204, type, esk112_2: (int > $o) > int > int).
0.89/1.09	thf(decl_205, type, esk113_2: (int > $o) > int > int).
0.89/1.09	thf(decl_206, type, esk114_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_207, type, esk115_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_208, type, esk116_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_209, type, esk117_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_210, type, esk118_2: int > (int > $o) > int).
0.89/1.09	thf(decl_211, type, esk119_2: int > (int > $o) > int).
0.89/1.09	thf(decl_212, type, esk120_2: int > (int > $o) > int).
0.89/1.09	thf(decl_213, type, esk121_2: int > (int > $o) > int).
0.89/1.09	thf(decl_214, type, esk122_4: int > (int > $o) > (int > $o) > int > int).
0.89/1.09	thf(decl_215, type, esk123_3: int > (int > $o) > (int > $o) > int).
0.89/1.09	thf(decl_216, type, esk124_2: int > (int > $o) > int).
0.89/1.09	thf(decl_217, type, esk125_2: int > (int > $o) > int).
0.89/1.09	thf(decl_218, type, esk126_4: int > (int > $o) > (int > $o) > int > int).
0.89/1.09	thf(decl_219, type, esk127_3: int > (int > $o) > (int > $o) > int).
0.89/1.09	thf(decl_220, type, esk128_3: nat > nat > nat > nat).
0.89/1.09	thf(decl_221, type, esk129_3: nat > nat > nat > nat).
0.89/1.09	thf(decl_222, type, esk130_3: nat > nat > nat > nat).
0.89/1.09	thf(decl_223, type, esk131_3: nat > nat > nat > nat).
0.89/1.09	thf(decl_224, type, esk132_3: (nat > $o) > nat > nat > nat).
0.89/1.09	thf(decl_225, type, esk133_3: (nat > $o) > nat > nat > nat).
0.89/1.09	thf(decl_226, type, esk134_2: int > int > int).
0.89/1.09	thf(decl_227, type, esk135_2: nat > (nat > $o) > nat).
0.89/1.09	thf(decl_228, type, esk136_2: nat > (nat > $o) > nat).
0.89/1.09	thf(decl_229, type, esk137_2: nat > (nat > $o) > nat).
0.89/1.09	thf(decl_230, type, esk138_2: nat > (nat > $o) > nat).
0.89/1.09	thf(decl_231, type, esk139_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_232, type, esk140_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_233, type, esk141_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_234, type, esk142_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_235, type, esk143_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_236, type, esk144_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_237, type, esk145_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_238, type, esk146_1: (nat > nat > $o) > nat).
0.89/1.09	thf(decl_239, type, esk147_2: real > real > nat).
0.89/1.09	thf(decl_240, type, esk148_2: set_real > real > real).
0.89/1.09	thf(decl_241, type, esk149_1: set_real > real).
0.89/1.09	thf(decl_242, type, esk150_2: set_real > real > real).
0.89/1.09	thf(decl_243, type, esk151_2: real > real > nat).
0.89/1.09	thf(decl_244, type, esk152_2: real > real > nat).
0.89/1.09	thf(decl_245, type, esk153_2: real > real > nat).
0.89/1.09	thf(decl_246, type, esk154_3: real > real > (real > real > $o) > real).
0.89/1.09	thf(decl_247, type, esk155_3: real > real > (real > real > $o) > real).
0.89/1.09	thf(decl_248, type, esk156_3: real > real > (real > real > $o) > real).
0.89/1.09	thf(decl_249, type, esk157_3: real > real > (real > real > $o) > real).
0.89/1.09	thf(decl_250, type, esk158_4: real > real > (real > real > $o) > real > real).
0.89/1.09	thf(decl_251, type, esk159_4: real > real > (real > real > $o) > real > real).
0.89/1.09	thf(decl_252, type, esk160_2: nat > real > real).
0.89/1.09	thf(decl_253, type, esk161_2: nat > real > real).
0.89/1.09	thf(decl_254, type, esk162_1: int > nat).
0.89/1.09	thf(decl_255, type, esk163_1: int > nat).
0.89/1.09	thf(decl_256, type, esk164_1: int > nat).
0.89/1.09	thf(decl_257, type, esk165_1: int > nat).
0.89/1.09	thf(decl_258, type, esk166_1: int > nat).
0.89/1.09	thf(decl_259, type, esk167_1: int > nat).
0.89/1.09	thf(decl_260, type, esk168_1: int > nat).
0.89/1.09	thf(decl_261, type, esk169_1: int > nat).
0.89/1.09	thf(decl_262, type, esk170_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_263, type, esk171_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_264, type, esk172_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_265, type, esk173_3: int > int > (int > $o) > int).
0.89/1.09	thf(decl_266, type, esk174_2: nat > (nat > nat > finite_mod_ring_a) > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_267, type, esk175_1: (nat > nat > finite_mod_ring_a) > nat > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_268, type, esk176_2: nat > (nat > nat > nat) > nat > nat).
0.89/1.09	thf(decl_269, type, esk177_1: (nat > nat > nat) > nat > nat > nat).
0.89/1.09	thf(decl_270, type, esk178_2: finite_mod_ring_a > (nat > finite_mod_ring_a) > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_271, type, esk179_0: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_272, type, esk180_0: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_273, type, esk181_0: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_274, type, esk182_0: nat > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_275, type, esk183_0: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_276, type, esk184_0: nat > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_277, type, esk185_0: nat > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_278, type, esk186_2: nat > list_F4626807571770296779ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_279, type, esk187_2: nat > list_F4626807571770296779ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_280, type, esk188_0: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_281, type, esk189_0: nat > finite_mod_ring_a).
0.89/1.09	thf(decl_282, type, esk190_0: nat > nat).
0.89/1.09	thf(decl_283, type, epred2_1: set_real > real > $o).
0.89/1.09	thf(decl_284, type, esk191_2: (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_285, type, esk192_2: set_nat > (nat > nat > finite_mod_ring_a) > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_286, type, esk193_2: set_nat > (nat > nat > nat) > nat > nat).
0.89/1.09	thf(decl_287, type, esk194_2: (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_288, type, esk195_2: (nat > nat) > (nat > nat) > nat > nat > nat).
0.89/1.09	thf(decl_289, type, esk196_2: nat > (nat > nat) > nat > nat).
0.89/1.09	thf(decl_290, type, esk197_2: (nat > finite_mod_ring_a) > finite_mod_ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_291, type, esk198_2: (nat > nat) > nat > nat > nat).
0.89/1.09	thf(decl_292, type, esk199_3: nat > list_F4626807571770296779ring_a > finite_mod_ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_293, type, esk200_1: finite_mod_ring_a > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_294, type, esk201_2: (nat > finite_mod_ring_a) > (nat > finite_mod_ring_a) > nat > finite_mod_ring_a).
0.89/1.09	thf(decl_295, type, esk202_2: (nat > nat) > (nat > nat) > nat > nat).
0.89/1.09	thf(decl_296, type, esk203_2: (real > nat) > (real > nat) > real > nat).
0.89/1.09	thf(decl_297, type, esk204_2: (nat > nat) > (nat > nat) > nat > nat).
0.89/1.09	thf(decl_298, type, esk205_2: (nat > nat) > (nat > nat) > nat > nat).
0.89/1.09	thf(decl_299, type, esk206_0: nat).
0.89/1.09	thf(decl_300, type, esk207_0: nat).
0.89/1.09	thf(decl_301, type, esk208_0: nat).
0.89/1.09	thf(decl_302, type, esk209_0: nat).
0.89/1.09	thf(decl_303, type, esk210_0: nat).
0.89/1.09	thf(decl_304, type, esk211_0: nat).
0.89/1.09	thf(decl_305, type, esk212_0: nat).
0.89/1.09	thf(decl_306, type, esk213_0: nat).
0.89/1.09	thf(decl_307, type, esk214_0: nat).
0.89/1.09	thf(decl_308, type, esk215_0: nat).
0.89/1.09	thf(decl_309, type, esk216_0: nat).
0.89/1.09	thf(decl_310, type, esk217_0: nat).
0.89/1.09	thf(decl_311, type, esk218_0: nat).
0.89/1.09	thf(decl_312, type, esk219_0: nat).
0.89/1.09	thf(decl_313, type, esk220_0: nat).
0.89/1.09	thf(decl_314, type, esk221_0: nat).
0.89/1.09	thf(decl_315, type, esk222_0: nat).
0.89/1.09	thf(decl_316, type, esk223_0: nat).
0.89/1.09	thf(decl_317, type, esk224_0: nat).
0.89/1.09	thf(decl_318, type, esk225_0: nat).
0.89/1.09	thf(decl_319, type, esk226_0: nat).
0.89/1.09	thf(decl_320, type, esk227_0: nat).
0.89/1.09	thf(decl_321, type, esk228_0: nat).
0.89/1.09	thf(decl_322, type, esk229_0: nat).
0.89/1.09	thf(decl_323, type, esk230_0: nat).
0.89/1.09	thf(decl_324, type, esk231_0: nat).
0.89/1.09	thf(decl_325, type, esk232_0: nat).
0.89/1.09	thf(decl_326, type, esk233_0: nat).
0.89/1.09	thf(decl_327, type, esk234_0: nat).
0.89/1.09	thf(decl_328, type, esk235_0: nat).
0.89/1.09	thf(decl_329, type, esk236_0: nat).
0.89/1.09	thf(decl_330, type, esk237_0: nat).
0.89/1.09	thf(fact_366_mult_Ocommute, axiom, ((times_5121417576591743744ring_a)=(^[X547:finite_mod_ring_a, X548:finite_mod_ring_a]:(times_5121417576591743744ring_a @ X548 @ X547))), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', fact_366_mult_Ocommute)).
0.89/1.09	thf(fact_6__C02_C, axiom, ((groups3558780024651037881ring_a @ (^[X12:nat]:(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ X12) @ (minus_minus_nat @ j @ i)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (groups3558780024651037881ring_a @ (^[X12:nat]:(power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ X12) @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n)))), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', fact_6__C02_C)).
0.89/1.09	thf(fact_4__C03_C, axiom, ((groups3558780024651037881ring_a @ (^[X12:nat]:(power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ X12) @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(groups3558780024651037881ring_a @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', fact_4__C03_C)).
0.89/1.09	thf(fact_208_lambda__zero, axiom, ((^[X401:finite_mod_ring_a]:(zero_z7902377541816115708ring_a))=(times_5121417576591743744ring_a @ zero_z7902377541816115708ring_a)), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', fact_208_lambda__zero)).
0.89/1.09	thf(fact_5__092_060open_062sum_A_I_I_094_J_A_I_092_060omega_062_A_094_A_Ij_A_N_Ai_J_J_J_A_1230_O_O_060n_125_A_061_A0_092_060close_062, axiom, ((groups3558780024651037881ring_a @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(zero_z7902377541816115708ring_a)), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', fact_5__092_060open_062sum_A_I_I_094_J_A_I_092_060omega_062_A_094_A_Ij_A_N_Ai_J_J_J_A_1230_O_O_060n_125_A_061_A0_092_060close_062)).
0.89/1.09	thf(fact_7__C01_C, axiom, ((groups3558780024651037881ring_a @ (^[X12:nat]:(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X12 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X12)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(groups3558780024651037881ring_a @ (^[X12:nat]:(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ X12) @ (minus_minus_nat @ j @ i)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', fact_7__C01_C)).
0.89/1.09	thf(conj_0, conjecture, ((groups3558780024651037881ring_a @ (^[X12:nat]:(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X12 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X12)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(zero_z7902377541816115708ring_a)), file('/export/starexec/sandbox/tmp/tmp.TgAm8JhjY0/Vampire---4.8_16805', conj_0)).
0.89/1.09	thf(c_0_7, plain, ![X5183:finite_mod_ring_a, X5184:finite_mod_ring_a]:(((times_5121417576591743744ring_a @ X5183 @ X5184)=(times_5121417576591743744ring_a @ X5184 @ X5183))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_366_mult_Ocommute])])).
0.89/1.09	thf(c_0_8, plain, ((groups3558780024651037881ring_a @ (^[Z0:nat]:(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ Z0) @ (minus_minus_nat @ j @ i)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (groups3558780024651037881ring_a @ (^[Z0:nat]:(power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ Z0) @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n)))), inference(fof_simplification,[status(thm)],[fact_6__C02_C])).
0.89/1.09	thf(c_0_9, plain, ![X8480:nat]:(((esk179_0 @ X8480)=(power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ X8480) @ (minus_minus_nat @ j @ i)))), introduced(definition)).
0.89/1.09	thf(c_0_10, plain, ![X8481:nat]:(((esk180_0 @ X8481)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ X8481) @ (minus_minus_nat @ j @ i))))), introduced(definition)).
0.89/1.09	thf(c_0_11, plain, ![X6082:finite_mod_ring_a, X6083:finite_mod_ring_a]:(((times_5121417576591743744ring_a @ X6082 @ X6083)=(times_5121417576591743744ring_a @ X6083 @ X6082))), inference(variable_rename,[status(thm)],[c_0_7])).
0.89/1.09	thf(c_0_12, plain, ((groups3558780024651037881ring_a @ (^[Z0:nat]:(power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ Z0) @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(groups3558780024651037881ring_a @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), inference(fof_simplification,[status(thm)],[fact_4__C03_C])).
0.89/1.09	thf(c_0_13, plain, ![X5167:finite_mod_ring_a]:(((zero_z7902377541816115708ring_a)=(times_5121417576591743744ring_a @ zero_z7902377541816115708ring_a @ X5167))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_208_lambda__zero])])).
0.89/1.09	thf(c_0_14, plain, ((groups3558780024651037881ring_a @ esk180_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (groups3558780024651037881ring_a @ esk179_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n)))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_8]), c_0_9]), c_0_10])).
0.89/1.09	thf(c_0_15, plain, ![X2:finite_mod_ring_a, X1:finite_mod_ring_a]:(((times_5121417576591743744ring_a @ X1 @ X2)=(times_5121417576591743744ring_a @ X2 @ X1))), inference(split_conjunct,[status(thm)],[c_0_11])).
0.89/1.09	thf(c_0_16, plain, ((groups3558780024651037881ring_a @ esk179_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(groups3558780024651037881ring_a @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_12]), c_0_9])).
0.89/1.09	thf(c_0_17, plain, ((groups3558780024651037881ring_a @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ (minus_minus_nat @ j @ i))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(zero_z7902377541816115708ring_a)), inference(split_conjunct,[status(thm)],[fact_5__092_060open_062sum_A_I_I_094_J_A_I_092_060omega_062_A_094_A_Ij_A_N_Ai_J_J_J_A_1230_O_O_060n_125_A_061_A0_092_060close_062])).
0.89/1.09	thf(c_0_18, plain, ![X5819:finite_mod_ring_a]:(((zero_z7902377541816115708ring_a)=(times_5121417576591743744ring_a @ zero_z7902377541816115708ring_a @ X5819))), inference(variable_rename,[status(thm)],[c_0_13])).
0.89/1.09	thf(c_0_19, plain, ((groups3558780024651037881ring_a @ (^[Z0:nat]:(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ Z0 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ Z0)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(groups3558780024651037881ring_a @ (^[Z0:nat]:(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ (power_6826135765519566523ring_a @ omega @ Z0) @ (minus_minus_nat @ j @ i)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), inference(fof_simplification,[status(thm)],[fact_7__C01_C])).
0.89/1.09	thf(c_0_20, plain, ![X8483:nat]:(((esk181_0 @ X8483)=(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X8483 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X8483))))), introduced(definition)).
0.89/1.09	thf(c_0_21, plain, ((times_5121417576591743744ring_a @ (groups3558780024651037881ring_a @ esk179_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n)) @ (nth_Fi694352073394265932ring_a @ numbers @ j))=(groups3558780024651037881ring_a @ esk180_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), inference(rw,[status(thm)],[c_0_14, c_0_15])).
0.89/1.09	thf(c_0_22, plain, ((groups3558780024651037881ring_a @ esk179_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(zero_z7902377541816115708ring_a)), inference(rw,[status(thm)],[c_0_16, c_0_17])).
0.89/1.09	thf(c_0_23, plain, ![X1:finite_mod_ring_a]:(((zero_z7902377541816115708ring_a)=(times_5121417576591743744ring_a @ zero_z7902377541816115708ring_a @ X1))), inference(split_conjunct,[status(thm)],[c_0_18])).
0.89/1.09	thf(c_0_24, plain, ![X8573:nat, X8574:list_F4626807571770296779ring_a, X8575:nat]:(((esk186_2 @ X8575 @ X8574 @ X8573)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ X8574 @ X8573) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X8575 @ X8573))))), inference(variable_rename,[status(thm)],[])).
0.89/1.09	thf(c_0_25, plain, ![X8610:nat, X8611:finite_mod_ring_a, X8612:list_F4626807571770296779ring_a, X8613:nat]:(((esk199_3 @ X8613 @ X8612 @ X8611 @ X8610)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ X8612 @ X8610) @ (power_6826135765519566523ring_a @ X8611 @ (times_times_nat @ X8613 @ X8610))))), inference(variable_rename,[status(thm)],[])).
0.89/1.09	thf(c_0_26, plain, ![X8566:nat, X8567:nat]:(((esk182_0 @ X8567 @ X8566)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ X8566) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X8567 @ X8566))))), inference(variable_rename,[status(thm)],[])).
0.89/1.09	thf(c_0_27, negated_conjecture, ((groups3558780024651037881ring_a @ (^[Z0:nat]:(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ Z0 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ Z0)))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))!=(zero_z7902377541816115708ring_a)), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])])).
0.89/1.09	thf(c_0_28, plain, ![X8494:nat, X8495:nat]:(((esk185_0 @ X8495 @ X8494)=(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ X8495) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X8494 @ X8495))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X8494))))), introduced(definition)).
0.89/1.09	thf(c_0_29, plain, ((groups3558780024651037881ring_a @ esk181_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(groups3558780024651037881ring_a @ esk180_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_19]), c_0_10]), c_0_20])).
0.89/1.09	thf(c_0_30, plain, ((groups3558780024651037881ring_a @ esk180_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(zero_z7902377541816115708ring_a)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22]), c_0_23])).
0.89/1.09	thf(c_0_31, plain, ![X8565:nat]:(((esk181_0 @ X8565)=(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X8565 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X8565))))), inference(variable_rename,[status(thm)],[])).
0.89/1.09	thf(c_0_32, plain, ![X3:nat, X15:list_F4626807571770296779ring_a, X5:nat]:(((esk186_2 @ X3 @ X15 @ X5)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ X15 @ X5) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X3 @ X5))))), inference(split_conjunct,[status(thm)],[c_0_24])).
0.89/1.09	thf(c_0_33, plain, ![X3:nat, X1:finite_mod_ring_a, X15:list_F4626807571770296779ring_a, X5:nat]:(((esk199_3 @ X3 @ X15 @ X1 @ X5)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ X15 @ X5) @ (power_6826135765519566523ring_a @ X1 @ (times_times_nat @ X3 @ X5))))), inference(split_conjunct,[status(thm)],[c_0_25])).
0.89/1.09	thf(c_0_34, plain, ![X3:nat, X5:nat]:(((esk182_0 @ X3 @ X5)=(times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ X5) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X3 @ X5))))), inference(split_conjunct,[status(thm)],[c_0_26])).
0.89/1.09	thf(c_0_35, plain, ![X8571:nat, X8572:nat]:(((esk185_0 @ X8572 @ X8571)=(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ X8572) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X8571 @ X8572))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X8571))))), inference(variable_rename,[status(thm)],[])).
0.89/1.09	thf(c_0_36, negated_conjecture, ((groups3558780024651037881ring_a @ (esk185_0 @ j) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))!=(zero_z7902377541816115708ring_a)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_27]), c_0_28])).
0.89/1.09	thf(c_0_37, plain, ((groups3558780024651037881ring_a @ esk181_0 @ (set_or4665077453230672383an_nat @ zero_zero_nat @ n))=(zero_z7902377541816115708ring_a)), inference(rw,[status(thm)],[c_0_29, c_0_30])).
0.89/1.09	thf(c_0_38, plain, ![X3:nat]:(((esk181_0 @ X3)=(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ j) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X3 @ j))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X3))))), inference(split_conjunct,[status(thm)],[c_0_31])).
0.89/1.09	thf(c_0_39, plain, ![X3:nat, X15:list_F4626807571770296779ring_a, X5:nat]:(((esk199_3 @ X3 @ X15 @ omega @ X5)=(esk186_2 @ X3 @ X15 @ X5))), inference(rw,[status(thm)],[c_0_32, c_0_33])).
0.89/1.09	thf(c_0_40, plain, ![X3:nat, X5:nat]:(((esk186_2 @ X3 @ numbers @ X5)=(esk182_0 @ X3 @ X5))), inference(rw,[status(thm)],[c_0_34, c_0_32])).
0.89/1.09	thf(c_0_41, plain, ![X3:nat, X5:nat]:(((esk185_0 @ X3 @ X5)=(times_5121417576591743744ring_a @ (times_5121417576591743744ring_a @ (nth_Fi694352073394265932ring_a @ numbers @ X3) @ (power_6826135765519566523ring_a @ omega @ (times_times_nat @ X5 @ X3))) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X5))))), inference(split_conjunct,[status(thm)],[c_0_35])).
0.89/1.09	thf(c_0_42, plain, ((esk185_0 @ j)!=(esk181_0)), inference(ext_sup,[status(thm)],[c_0_36, c_0_37])).
0.89/1.09	thf(c_0_43, plain, ![X3:nat]:(((times_5121417576591743744ring_a @ (esk182_0 @ X3 @ j) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X3)))=(esk181_0 @ X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_33]), c_0_39]), c_0_40])).
0.89/1.09	thf(c_0_44, plain, ![X5:nat, X3:nat]:(((times_5121417576591743744ring_a @ (esk182_0 @ X3 @ X5) @ (power_6826135765519566523ring_a @ mu @ (times_times_nat @ i @ X3)))=(esk185_0 @ X5 @ X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_32]), c_0_40])).
0.89/1.09	thf(c_0_45, plain, ((esk185_0 @ j @ esk208_0)!=(esk181_0 @ esk208_0)), inference(neg_ext,[status(thm)],[c_0_42])).
0.89/1.09	thf(c_0_46, plain, ![X3:nat]:(((esk185_0 @ j @ X3)=(esk181_0 @ X3))), inference(rw,[status(thm)],[c_0_43, c_0_44])).
0.89/1.09	thf(c_0_47, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])]), ['proof']).
0.89/1.09	# SZS output end CNFRefutation
0.89/1.09	# Parsed axioms                        : 1354
0.89/1.09	# Removed by relevancy pruning/SinE    : 0
0.89/1.09	# Initial clauses                      : 2347
0.89/1.09	# Removed in clause preprocessing      : 169
0.89/1.09	# Initial clauses in saturation        : 2178
0.89/1.09	# Processed clauses                    : 2482
0.89/1.09	# ...of these trivial                  : 147
0.89/1.09	# ...subsumed                          : 423
0.89/1.09	# ...remaining for further processing  : 1912
0.89/1.09	# Other redundant clauses eliminated   : 258
0.89/1.09	# Clauses deleted for lack of memory   : 0
0.89/1.09	# Backward-subsumed                    : 6
0.89/1.09	# Backward-rewritten                   : 43
0.89/1.09	# Generated clauses                    : 453
0.89/1.09	# ...of the previous two non-redundant : 280
0.89/1.09	# ...aggressively subsumed             : 0
0.89/1.09	# Contextual simplify-reflections      : 3
0.89/1.09	# Paramodulations                      : 116
0.89/1.09	# Factorizations                       : 0
0.89/1.09	# NegExts                              : 32
0.89/1.09	# Equation resolutions                 : 260
0.89/1.09	# Propositional unsat checks           : 0
0.89/1.09	#    Propositional check models        : 0
0.89/1.09	#    Propositional check unsatisfiable : 0
0.89/1.09	#    Propositional clauses             : 0
0.89/1.09	#    Propositional clauses after purity: 0
0.89/1.09	#    Propositional unsat core size     : 0
0.89/1.09	#    Propositional preprocessing time  : 0.000
0.89/1.09	#    Propositional encoding time       : 0.000
0.89/1.09	#    Propositional solver time         : 0.000
0.89/1.09	#    Success case prop preproc time    : 0.000
0.89/1.09	#    Success case prop encoding time   : 0.000
0.89/1.09	#    Success case prop solver time     : 0.000
0.89/1.09	# Current number of processed clauses  : 167
0.89/1.09	#    Positive orientable unit clauses  : 65
0.89/1.09	#    Positive unorientable unit clauses: 3
0.89/1.09	#    Negative unit clauses             : 32
0.89/1.09	#    Non-unit-clauses                  : 67
0.89/1.09	# Current number of unprocessed clauses: 1441
0.89/1.09	# ...number of literals in the above   : 4376
0.89/1.09	# Current number of archived formulas  : 0
0.89/1.09	# Current number of archived clauses   : 1516
0.89/1.09	# Clause-clause subsumption calls (NU) : 354002
0.89/1.09	# Rec. Clause-clause subsumption calls : 121168
0.89/1.09	# Non-unit clause-clause subsumptions  : 353
0.89/1.09	# Unit Clause-clause subsumption calls : 12993
0.89/1.09	# Rewrite failures with RHS unbound    : 18
0.89/1.09	# BW rewrite match attempts            : 1546
0.89/1.09	# BW rewrite match successes           : 286
0.89/1.09	# Condensation attempts                : 0
0.89/1.09	# Condensation successes               : 0
0.89/1.09	# Termbank termtop insertions          : 280904
0.89/1.09	
0.89/1.09	# -------------------------------------------------
0.89/1.09	# User time                : 0.399 s
0.89/1.09	# System time              : 0.025 s
0.89/1.09	# Total time               : 0.423 s
0.89/1.09	# Maximum resident set size: 12124 pages
0.89/1.09	
0.89/1.09	# -------------------------------------------------
0.89/1.09	# User time                : 0.449 s
0.89/1.09	# System time              : 0.029 s
0.89/1.09	# Total time               : 0.478 s
0.89/1.09	# Maximum resident set size: 4372 pages
0.89/1.09	EOF