TSTP Solution File: ITP320_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:14:23 EDT 2024
% Result : Theorem 7.68s 1.53s
% Output : Refutation 7.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 295
% Syntax : Number of formulae : 327 ( 28 unt; 283 typ; 0 def)
% Number of atoms : 69 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 31 ~; 19 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 25 ( 0 atm; 4 fun; 21 num; 0 var)
% Number of types : 43 ( 40 usr; 2 ari)
% Number of type conns : 315 ( 212 >; 103 *; 0 +; 0 <<)
% Number of predicates : 33 ( 31 usr; 3 prp; 0-3 aty)
% Number of functors : 217 ( 214 usr; 33 con; 0-3 aty)
% Number of variables : 29 ( 28 !; 1 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_bool_fun$': $tType ).
tff(type_def_6,type,
'Rows_rows_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_8,type,
'Rows_rows_vec$': $tType ).
tff(type_def_9,type,
'Real_cols_vec_rows_vec$': $tType ).
tff(type_def_10,type,
'Rows_rows_vec_rows_vec$': $tType ).
tff(type_def_11,type,
'Rows$': $tType ).
tff(type_def_12,type,
'Int_rows_vec$': $tType ).
tff(type_def_13,type,
'Rows_a_cols_vec_fun$': $tType ).
tff(type_def_14,type,
'Int_rows_vec_rows_vec$': $tType ).
tff(type_def_15,type,
'Cols_cols_vec_rows_vec$': $tType ).
tff(type_def_16,type,
'Nat_nat_fun$': $tType ).
tff(type_def_17,type,
'Nat$': $tType ).
tff(type_def_18,type,
'Real_rows_vec$': $tType ).
tff(type_def_19,type,
'Rows_cols_vec_rows_vec$': $tType ).
tff(type_def_20,type,
'A_rows_vec$': $tType ).
tff(type_def_21,type,
'Cols_rows_vec$': $tType ).
tff(type_def_22,type,
tlbool: $tType ).
tff(type_def_23,type,
'Real_rows_vec_cols_vec$': $tType ).
tff(type_def_24,type,
'Rows_bool_fun$': $tType ).
tff(type_def_25,type,
'Int_cols_vec$': $tType ).
tff(type_def_26,type,
'A_cols_vec_rows_vec$': $tType ).
tff(type_def_27,type,
'Real_cols_vec$': $tType ).
tff(type_def_28,type,
'Rows_cols_vec$': $tType ).
tff(type_def_29,type,
'Nat_real_fun$': $tType ).
tff(type_def_30,type,
'A_cols_vec$': $tType ).
tff(type_def_31,type,
'A$': $tType ).
tff(type_def_32,type,
'Real_rows_vec_rows_vec$': $tType ).
tff(type_def_33,type,
'Cols_rows_vec_rows_vec$': $tType ).
tff(type_def_34,type,
'A_a_fun$': $tType ).
tff(type_def_35,type,
'Cols$': $tType ).
tff(type_def_36,type,
'Nat_rows_fun$': $tType ).
tff(type_def_37,type,
'A_rows_vec_rows_vec$': $tType ).
tff(type_def_38,type,
'Nat_bool_fun$': $tType ).
tff(type_def_39,type,
'Real_bool_fun$': $tType ).
tff(type_def_40,type,
'Cols_a_fun$': $tType ).
tff(type_def_41,type,
'Real_set$': $tType ).
tff(type_def_42,type,
'Nat_int_fun$': $tType ).
tff(type_def_43,type,
'Cols_cols_vec$': $tType ).
tff(type_def_44,type,
'Int_cols_vec_rows_vec$': $tType ).
tff(func_def_0,type,
'column$d': ( 'Rows$' * 'Cols_rows_vec_rows_vec$' ) > 'Cols_rows_vec$' ).
tff(func_def_1,type,
'one$e': 'Nat$' ).
tff(func_def_2,type,
'one$c': 'Rows$' ).
tff(func_def_3,type,
'column$b': ( 'Rows$' * 'Int_rows_vec_rows_vec$' ) > 'Int_rows_vec$' ).
tff(func_def_4,type,
'zero$k': 'Nat$' ).
tff(func_def_5,type,
'vec_nth$c': ( 'Real_rows_vec_rows_vec$' * 'Rows$' ) > 'Real_rows_vec$' ).
tff(func_def_6,type,
'column$h': ( 'Cols$' * 'Rows_cols_vec_rows_vec$' ) > 'Rows_rows_vec$' ).
tff(func_def_7,type,
'column$': ( 'Cols$' * 'A_cols_vec_rows_vec$' ) > 'A_rows_vec$' ).
tff(func_def_8,type,
'fun_app$d': ( 'Rows_rows_bool_fun_fun$' * 'Rows$' ) > 'Rows_bool_fun$' ).
tff(func_def_9,type,
'axis$': ( 'Cols$' * 'A$' ) > 'A_cols_vec$' ).
tff(func_def_10,type,
'vec_nth$b': ( 'Real_rows_vec$' * 'Rows$' ) > $real ).
tff(func_def_11,type,
'vec_nth$s': ( 'Cols_cols_vec_rows_vec$' * 'Rows$' ) > 'Cols_cols_vec$' ).
tff(func_def_12,type,
'one$a': 'A$' ).
tff(func_def_13,type,
'vec_nth$e': ( 'Int_rows_vec_rows_vec$' * 'Rows$' ) > 'Int_rows_vec$' ).
tff(func_def_14,type,
'vec_nth$': 'A_cols_vec$' > 'Cols_a_fun$' ).
tff(func_def_15,type,
'vec_nth$n': ( 'Int_cols_vec$' * 'Cols$' ) > $int ).
tff(func_def_16,type,
'to_nat$a': 'Rows$' > 'Nat$' ).
tff(func_def_17,type,
'dbl_inc$b': 'Rows$' > 'Rows$' ).
tff(func_def_18,type,
'zero$h': 'Real_cols_vec$' ).
tff(func_def_19,type,
'less$a': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_20,type,
'zero$b': 'A_rows_vec$' ).
tff(func_def_21,type,
'arcosh$': $real > $real ).
tff(func_def_22,type,
'column$f': ( 'Cols$' * 'Real_cols_vec_rows_vec$' ) > 'Real_rows_vec$' ).
tff(func_def_23,type,
'fun_app$l': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_24,type,
'power$b': $real > 'Nat_real_fun$' ).
tff(func_def_25,type,
'less_eq$a': 'Rows_rows_bool_fun_fun$' ).
tff(func_def_26,type,
'vec_nth$k': ( 'A_rows_vec_rows_vec$' * 'Rows$' ) > 'A_rows_vec$' ).
tff(func_def_27,type,
'zero$': 'Rows$' ).
tff(func_def_28,type,
'column$a': ( 'Rows$' * 'Real_rows_vec_rows_vec$' ) > 'Real_rows_vec$' ).
tff(func_def_29,type,
'fun_app$e': ( 'Cols_a_fun$' * 'Cols$' ) > 'A$' ).
tff(func_def_30,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_31,type,
'dbl_inc$a': $int > $int ).
tff(func_def_32,type,
'vec_nth$o': ( 'Int_cols_vec_rows_vec$' * 'Rows$' ) > 'Int_cols_vec$' ).
tff(func_def_33,type,
'zero$e': 'Int_rows_vec$' ).
tff(func_def_34,type,
'dbl_inc$c': 'Cols$' > 'Cols$' ).
tff(func_def_35,type,
'column$g': ( 'Cols$' * 'Int_cols_vec_rows_vec$' ) > 'Int_rows_vec$' ).
tff(func_def_36,type,
'column$j': ( 'Rows$' * 'Real_rows_vec_cols_vec$' ) > 'Real_cols_vec$' ).
tff(func_def_37,type,
'of_nat$a': 'Nat_real_fun$' ).
tff(func_def_38,type,
tltrue: tlbool ).
tff(func_def_39,type,
'dbl_inc$': $real > $real ).
tff(func_def_40,type,
'ncols$': 'A_cols_vec_rows_vec$' > 'Nat$' ).
tff(func_def_41,type,
'vec_nth$g': ( 'Rows_rows_vec_rows_vec$' * 'Rows$' ) > 'Rows_rows_vec$' ).
tff(func_def_42,type,
'to_nat$': 'Cols$' > 'Nat$' ).
tff(func_def_43,type,
'one$d': 'Cols$' ).
tff(func_def_44,type,
'uu$': 'Real_set$' > 'Real_bool_fun$' ).
tff(func_def_45,type,
'a$': 'A_cols_vec_rows_vec$' ).
tff(func_def_46,type,
'fun_app$f': ( 'Rows_a_cols_vec_fun$' * 'Rows$' ) > 'A_cols_vec$' ).
tff(func_def_47,type,
'artanh$': $real > $real ).
tff(func_def_48,type,
'powr$': ( $real * $real ) > $real ).
tff(func_def_49,type,
'vec_nth$t': ( 'Real_rows_vec_cols_vec$' * 'Cols$' ) > 'Real_rows_vec$' ).
tff(func_def_50,type,
'vec$': 'A$' > 'A_cols_vec$' ).
tff(func_def_51,type,
'zero$d': 'Real_rows_vec$' ).
tff(func_def_52,type,
'vec_nth$l': ( 'Real_cols_vec$' * 'Cols$' ) > $real ).
tff(func_def_53,type,
'uub$': $real > 'Real_bool_fun$' ).
tff(func_def_54,type,
'one$b': 'A_cols_vec_rows_vec$' ).
tff(func_def_55,type,
'zero$a': 'Cols$' ).
tff(func_def_56,type,
'power$a': $int > 'Nat_int_fun$' ).
tff(func_def_57,type,
'vec_nth$p': ( 'Rows_cols_vec$' * 'Cols$' ) > 'Rows$' ).
tff(func_def_58,type,
'uminus$a': 'Cols$' > 'Cols$' ).
tff(func_def_59,type,
'zero$j': 'A_cols_vec_rows_vec$' ).
tff(func_def_60,type,
'fun_app$i': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_61,type,
'vec_nth$r': ( 'Cols_cols_vec$' * 'Cols$' ) > 'Cols$' ).
tff(func_def_62,type,
'column$e': ( 'Rows$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec$' ).
tff(func_def_63,type,
'map_matrix$': ( 'A_a_fun$' * 'A_cols_vec_rows_vec$' ) > 'A_cols_vec_rows_vec$' ).
tff(func_def_64,type,
'from_nat$': 'Nat_rows_fun$' ).
tff(func_def_65,type,
'of_nat$b': 'Nat_nat_fun$' ).
tff(func_def_66,type,
'from_nat$a': 'Nat$' > 'Cols$' ).
tff(func_def_67,type,
'fun_app$h': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_68,type,
'fun_app$g': ( 'A_a_fun$' * 'A$' ) > 'A$' ).
tff(func_def_69,type,
'vec_nth$a': 'A_cols_vec_rows_vec$' > 'Rows_a_cols_vec_fun$' ).
tff(func_def_70,type,
'fun_app$j': ( 'Nat_rows_fun$' * 'Nat$' ) > 'Rows$' ).
tff(func_def_71,type,
'less_eq$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_72,type,
'zero$f': 'Rows_rows_vec$' ).
tff(func_def_73,type,
'zero$c': 'A$' ).
tff(func_def_74,type,
'vec_nth$m': ( 'Real_cols_vec_rows_vec$' * 'Rows$' ) > 'Real_cols_vec$' ).
tff(func_def_75,type,
'i$': 'Rows$' ).
tff(func_def_76,type,
tlfalse: tlbool ).
tff(func_def_77,type,
'nat$': $int > 'Nat$' ).
tff(func_def_78,type,
'arsinh$': $real > $real ).
tff(func_def_79,type,
'less$': 'Rows_rows_bool_fun_fun$' ).
tff(func_def_80,type,
'vec_nth$i': ( 'Cols_rows_vec_rows_vec$' * 'Rows$' ) > 'Cols_rows_vec$' ).
tff(func_def_81,type,
'vec$a': 'A_cols_vec$' > 'A_cols_vec_rows_vec$' ).
tff(func_def_82,type,
'column$c': ( 'Rows$' * 'Rows_rows_vec_rows_vec$' ) > 'Rows_rows_vec$' ).
tff(func_def_83,type,
'uua$': $int > 'Int_bool_fun$' ).
tff(func_def_84,type,
'zero$g': 'Cols_rows_vec$' ).
tff(func_def_85,type,
'axis$a': ( 'Rows$' * 'A_cols_vec$' ) > 'A_cols_vec_rows_vec$' ).
tff(func_def_86,type,
'zero$i': 'A_cols_vec$' ).
tff(func_def_87,type,
'fun_app$k': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_88,type,
'reduced_row_echelon_form_upt_k$': 'A_cols_vec_rows_vec$' > 'Nat_bool_fun$' ).
tff(func_def_89,type,
'vec_nth$j': ( 'A_rows_vec$' * 'Rows$' ) > 'A$' ).
tff(func_def_90,type,
'vec_nth$d': ( 'Int_rows_vec$' * 'Rows$' ) > $int ).
tff(func_def_91,type,
'vec_nth$q': ( 'Rows_cols_vec_rows_vec$' * 'Rows$' ) > 'Rows_cols_vec$' ).
tff(func_def_92,type,
'vec_nth$h': ( 'Cols_rows_vec$' * 'Rows$' ) > 'Cols$' ).
tff(func_def_93,type,
'column$i': ( 'Cols$' * 'Cols_cols_vec_rows_vec$' ) > 'Cols_rows_vec$' ).
tff(func_def_94,type,
'vec_nth$f': ( 'Rows_rows_vec$' * 'Rows$' ) > 'Rows$' ).
tff(func_def_95,type,
'ln$': $real > $real ).
tff(func_def_96,type,
'collect$': 'Real_bool_fun$' > 'Real_set$' ).
tff(func_def_97,type,
'power$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_98,type,
'uminus$': 'Rows$' > 'Rows$' ).
tff(func_def_99,type,
'one$': 'A_cols_vec$' ).
tff(func_def_108,type,
sK10: 'Rows$' ).
tff(func_def_109,type,
sK11: $int > 'Nat$' ).
tff(func_def_110,type,
sK12: $int > 'Nat$' ).
tff(func_def_111,type,
sK13: $int > 'Nat$' ).
tff(func_def_112,type,
sK14: 'Nat$' > 'Nat$' ).
tff(func_def_113,type,
sK15: 'Nat$' > 'Nat$' ).
tff(func_def_114,type,
sK16: $int > 'Nat$' ).
tff(func_def_115,type,
sK17: $int > 'Nat$' ).
tff(func_def_116,type,
sK18: $int > 'Nat$' ).
tff(func_def_117,type,
sK19: $int > 'Nat$' ).
tff(func_def_118,type,
sK20: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_119,type,
sK21: $int > 'Nat$' ).
tff(func_def_120,type,
sK22: $int > 'Nat$' ).
tff(func_def_121,type,
sK23: 'Nat$' > 'Nat$' ).
tff(func_def_122,type,
sK24: 'Nat$' > 'Nat$' ).
tff(func_def_123,type,
sK25: $int > 'Nat$' ).
tff(func_def_124,type,
sK26: $int > 'Nat$' ).
tff(func_def_125,type,
sK27: $int > 'Nat$' ).
tff(func_def_126,type,
sK28: $int > 'Nat$' ).
tff(func_def_127,type,
sK29: $int > 'Nat$' ).
tff(func_def_128,type,
sK30: $int > 'Nat$' ).
tff(func_def_129,type,
sK31: 'Real_set$' > $real ).
tff(func_def_130,type,
sK32: ( 'Real_set$' * $real ) > $real ).
tff(func_def_131,type,
sK33: ( 'Real_set$' * $real ) > $real ).
tff(func_def_132,type,
sK34: 'Nat$' > 'Nat$' ).
tff(func_def_133,type,
sK35: 'Nat_bool_fun$' > $int ).
tff(func_def_134,type,
sK36: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_135,type,
sK37: 'Rows_bool_fun$' > 'Rows$' ).
tff(func_def_136,type,
sK38: ( 'Rows_bool_fun$' * 'Rows$' ) > 'Rows$' ).
tff(func_def_137,type,
sK39: 'Rows_bool_fun$' > 'Rows$' ).
tff(func_def_138,type,
sK40: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_139,type,
sK41: 'Nat_bool_fun$' > $int ).
tff(func_def_140,type,
sK42: $real > 'Nat$' ).
tff(func_def_141,type,
sK43: $real > 'Nat$' ).
tff(func_def_142,type,
sK44: ( $real * $real ) > 'Nat$' ).
tff(func_def_143,type,
sK45: ( $real * 'Nat$' ) > $real ).
tff(func_def_144,type,
sK46: 'Nat$' > 'Nat$' ).
tff(func_def_145,type,
sK47: ( $real * $real ) > 'Nat$' ).
tff(func_def_146,type,
sK48: ( $real * $real ) > $real ).
tff(func_def_147,type,
sK49: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_148,type,
sK50: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_149,type,
sK51: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_150,type,
sK52: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_151,type,
sK53: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_152,type,
sK54: ( 'Nat$' * $real ) > $real ).
tff(func_def_153,type,
sK55: ( 'Nat$' * $real ) > $real ).
tff(func_def_154,type,
sK56: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_155,type,
sK57: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_156,type,
sK58: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_157,type,
sK59: 'Int_bool_fun$' > 'Nat$' ).
tff(func_def_158,type,
sK60: 'Int_bool_fun$' > 'Nat$' ).
tff(func_def_159,type,
sK61: ( 'Nat$' * 'A_cols_vec_rows_vec$' ) > 'Rows$' ).
tff(func_def_160,type,
sK62: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_161,type,
sK63: 'Rows_bool_fun$' > 'Rows$' ).
tff(func_def_162,type,
sK64: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_163,type,
sK65: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_164,type,
sK66: ( 'A_cols_vec$' * 'A_cols_vec$' ) > 'Cols$' ).
tff(func_def_165,type,
sK67: ( 'A_cols_vec_rows_vec$' * 'A_cols_vec_rows_vec$' ) > 'Rows$' ).
tff(func_def_166,type,
sK68: ( 'Rows$' * 'A_cols_vec_rows_vec$' ) > 'Cols$' ).
tff(func_def_167,type,
sK69: ( 'Nat_bool_fun$' * $int ) > 'Nat$' ).
tff(func_def_168,type,
sK70: ( 'Rows$' * 'A_cols_vec_rows_vec$' ) > 'Cols$' ).
tff(func_def_169,type,
sK71: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_170,type,
sK72: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_171,type,
sK73: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_172,type,
sK74: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_173,type,
sK75: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_174,type,
sK76: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_175,type,
sK77: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_176,type,
sK78: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_177,type,
sK79: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_178,type,
sK80: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_179,type,
sK81: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_180,type,
sK82: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_181,type,
sK83: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_182,type,
sK84: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_183,type,
sK85: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_184,type,
sK86: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_185,type,
sK87: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_186,type,
sK88: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_187,type,
sK89: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_188,type,
sK90: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_189,type,
sK91: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_190,type,
sK92: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_191,type,
sK93: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_192,type,
sK94: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_193,type,
sK95: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_194,type,
sK96: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_195,type,
sK97: ( 'Nat$' * 'A_cols_vec_rows_vec$' ) > 'Rows$' ).
tff(func_def_196,type,
sK98: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_197,type,
sK99: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_198,type,
sK100: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_199,type,
sK101: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_200,type,
sK102: 'Nat_real_fun$' > 'Nat$' ).
tff(func_def_201,type,
sK103: 'Nat_real_fun$' > 'Nat$' ).
tff(func_def_202,type,
sK104: 'Nat_real_fun$' > 'Nat$' ).
tff(func_def_203,type,
sK105: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_204,type,
sK106: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_205,type,
sK107: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_206,type,
sK108: 'Nat_rows_fun$' > 'Nat$' ).
tff(func_def_207,type,
sK109: 'Nat_rows_fun$' > 'Nat$' ).
tff(func_def_208,type,
sK110: ( 'Nat$' * 'Nat_real_fun$' ) > 'Nat$' ).
tff(func_def_209,type,
sK111: ( 'Nat$' * 'Nat_real_fun$' * 'Nat_real_fun$' ) > 'Nat$' ).
tff(func_def_210,type,
sK112: 'Rows_rows_bool_fun_fun$' > 'Rows$' ).
tff(func_def_211,type,
sK113: 'Rows_rows_bool_fun_fun$' > 'Rows$' ).
tff(func_def_212,type,
sK114: 'Rows_rows_bool_fun_fun$' > 'Rows$' ).
tff(func_def_213,type,
sK115: 'Rows_rows_bool_fun_fun$' > 'Rows$' ).
tff(func_def_214,type,
sK116: 'Rows_rows_bool_fun_fun$' > 'Rows$' ).
tff(func_def_215,type,
sK117: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_216,type,
sK118: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_217,type,
sK119: 'Nat_real_fun$' > 'Nat$' ).
tff(func_def_218,type,
sK120: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_219,type,
sK121: 'Nat_rows_fun$' > 'Nat$' ).
tff(func_def_220,type,
sK122: 'Nat_rows_fun$' > 'Nat$' ).
tff(func_def_221,type,
sK123: ( 'Rows$' * 'Nat$' * 'A_cols_vec_rows_vec$' ) > 'Cols$' ).
tff(pred_def_1,type,
'reduced_row_echelon_form$f': 'Real_cols_vec_rows_vec$' > $o ).
tff(pred_def_2,type,
'reduced_row_echelon_form$g': 'Int_cols_vec_rows_vec$' > $o ).
tff(pred_def_3,type,
'is_zero_row_upt_k$': ( 'Rows$' * 'Nat$' * 'A_cols_vec_rows_vec$' ) > $o ).
tff(pred_def_4,type,
'fun_app$c': ( 'Rows_bool_fun$' * 'Rows$' ) > $o ).
tff(pred_def_5,type,
'fun_app$a': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_6,type,
'reduced_row_echelon_form$e': 'A_rows_vec_rows_vec$' > $o ).
tff(pred_def_7,type,
'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_8,type,
'reduced_row_echelon_form$h': 'Rows_cols_vec_rows_vec$' > $o ).
tff(pred_def_9,type,
'is_zero_row$': ( 'Rows$' * 'A_cols_vec_rows_vec$' ) > $o ).
tff(pred_def_10,type,
'fun_app$b': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_11,type,
'reduced_row_echelon_form$j': 'Real_rows_vec_cols_vec$' > $o ).
tff(pred_def_12,type,
'less_eq$b': ( 'Cols$' * 'Cols$' ) > $o ).
tff(pred_def_13,type,
'member$': ( $real * 'Real_set$' ) > $o ).
tff(pred_def_14,type,
'reduced_row_echelon_form$': 'A_cols_vec_rows_vec$' > $o ).
tff(pred_def_15,type,
'reduced_row_echelon_form$b': 'Int_rows_vec_rows_vec$' > $o ).
tff(pred_def_16,type,
'reduced_row_echelon_form$i': 'Cols_cols_vec_rows_vec$' > $o ).
tff(pred_def_17,type,
'reduced_row_echelon_form$a': 'Real_rows_vec_rows_vec$' > $o ).
tff(pred_def_18,type,
'reduced_row_echelon_form$d': 'Cols_rows_vec_rows_vec$' > $o ).
tff(pred_def_19,type,
'reduced_row_echelon_form$c': 'Rows_rows_vec_rows_vec$' > $o ).
tff(pred_def_24,type,
sP0: 'Real_set$' > $o ).
tff(pred_def_25,type,
sP1: ( 'Nat_bool_fun$' * $int ) > $o ).
tff(pred_def_26,type,
sP2: ( 'Nat$' * $int ) > $o ).
tff(pred_def_27,type,
sP3: ( 'Nat$' * $int ) > $o ).
tff(pred_def_28,type,
sP4: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_29,type,
sP5: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_30,type,
sP6: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_31,type,
sP7: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_32,type,
sP8: 'Nat_nat_bool_fun_fun$' > $o ).
tff(pred_def_33,type,
sP9: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(f50409,plain,
$false,
inference(avatar_sat_refutation,[],[f19466,f30142,f50408]) ).
tff(f50408,plain,
~ spl124_95,
inference(avatar_contradiction_clause,[],[f50407]) ).
tff(f50407,plain,
( $false
| ~ spl124_95 ),
inference(subsumption_resolution,[],[f50397,f5085]) ).
tff(f5085,plain,
'is_zero_row_upt_k$'('zero$','one$e','a$'),
inference(backward_demodulation,[],[f1873,f5072]) ).
tff(f5072,plain,
'nat$'(1) = 'one$e',
inference(superposition,[],[f1915,f5054]) ).
tff(f5054,plain,
1 = 'fun_app$h'('of_nat$','one$e'),
inference(superposition,[],[f2886,f3087]) ).
tff(f3087,plain,
! [X0: 'Nat$'] : ( 'one$e' = 'fun_app$l'('power$'(X0),'to_nat$'('zero$a')) ),
inference(backward_demodulation,[],[f1923,f3081]) ).
tff(f3081,plain,
'nat$'(0) = 'to_nat$'('zero$a'),
inference(superposition,[],[f1915,f1880]) ).
tff(f1880,plain,
0 = 'fun_app$h'('of_nat$','to_nat$'('zero$a')),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
0 = 'fun_app$h'('of_nat$','to_nat$'('zero$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
tff(f1923,plain,
! [X0: 'Nat$'] : ( 'one$e' = 'fun_app$l'('power$'(X0),'nat$'(0)) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,axiom,
! [X0: 'Nat$'] : ( 'one$e' = 'fun_app$l'('power$'(X0),'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).
tff(f2886,plain,
! [X0: 'Nat$'] : ( 1 = 'fun_app$h'('of_nat$','fun_app$l'('power$'('nat$'(1)),X0)) ),
inference(evaluation,[],[f1946]) ).
tff(f1946,plain,
! [X0: 'Nat$'] : ( $sum(0,1) = 'fun_app$h'('of_nat$','fun_app$l'('power$'('nat$'($sum(0,1))),X0)) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,axiom,
! [X0: 'Nat$'] : ( $sum(0,1) = 'fun_app$h'('of_nat$','fun_app$l'('power$'('nat$'($sum(0,1))),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom150) ).
tff(f1915,plain,
! [X0: 'Nat$'] : ( 'nat$'('fun_app$h'('of_nat$',X0)) = X0 ),
inference(cnf_transformation,[],[f616]) ).
tff(f616,axiom,
! [X0: 'Nat$'] : ( 'nat$'('fun_app$h'('of_nat$',X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).
tff(f1873,plain,
'is_zero_row_upt_k$'('zero$','nat$'(1),'a$'),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
'is_zero_row_upt_k$'('zero$','nat$'(1),'a$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f50397,plain,
( ~ 'is_zero_row_upt_k$'('zero$','one$e','a$')
| ~ spl124_95 ),
inference(resolution,[],[f19465,f1872]) ).
tff(f1872,plain,
'fun_app$c'('fun_app$d'('less$','zero$'),'i$'),
inference(cnf_transformation,[],[f10]) ).
tff(f10,axiom,
'fun_app$c'('fun_app$d'('less$','zero$'),'i$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
tff(f19465,plain,
( ! [X0: 'Rows$'] :
( ~ 'fun_app$c'('fun_app$d'('less$',X0),'i$')
| ~ 'is_zero_row_upt_k$'(X0,'one$e','a$') )
| ~ spl124_95 ),
inference(avatar_component_clause,[],[f19464]) ).
tff(f19464,plain,
( spl124_95
<=> ! [X0: 'Rows$'] :
( ~ 'fun_app$c'('fun_app$d'('less$',X0),'i$')
| ~ 'is_zero_row_upt_k$'(X0,'one$e','a$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl124_95])]) ).
tff(f30142,plain,
spl124_94,
inference(avatar_contradiction_clause,[],[f30141]) ).
tff(f30141,plain,
( $false
| spl124_94 ),
inference(subsumption_resolution,[],[f30117,f1808]) ).
tff(f1808,plain,
'reduced_row_echelon_form$'('a$'),
inference(cnf_transformation,[],[f817]) ).
tff(f817,plain,
'reduced_row_echelon_form$'('a$'),
inference(flattening,[],[f5]) ).
tff(f5,negated_conjecture,
~ ~ 'reduced_row_echelon_form$'('a$'),
inference(negated_conjecture,[],[f4]) ).
tff(f4,conjecture,
~ 'reduced_row_echelon_form$'('a$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture3) ).
tff(f30117,plain,
( ~ 'reduced_row_echelon_form$'('a$')
| spl124_94 ),
inference(resolution,[],[f19462,f2184]) ).
tff(f2184,plain,
! [X0: 'A_cols_vec_rows_vec$',X1: 'Nat$'] :
( 'fun_app$b'('reduced_row_echelon_form_upt_k$'(X0),X1)
| ~ 'reduced_row_echelon_form$'(X0) ),
inference(cnf_transformation,[],[f974]) ).
tff(f974,plain,
! [X0: 'A_cols_vec_rows_vec$',X1: 'Nat$'] :
( 'fun_app$b'('reduced_row_echelon_form_upt_k$'(X0),X1)
| ~ 'reduced_row_echelon_form$'(X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: 'A_cols_vec_rows_vec$',X1: 'Nat$'] :
( 'reduced_row_echelon_form$'(X0)
=> 'fun_app$b'('reduced_row_echelon_form_upt_k$'(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
tff(f19462,plain,
( ~ 'fun_app$b'('reduced_row_echelon_form_upt_k$'('a$'),'one$e')
| spl124_94 ),
inference(avatar_component_clause,[],[f19460]) ).
tff(f19460,plain,
( spl124_94
<=> 'fun_app$b'('reduced_row_echelon_form_upt_k$'('a$'),'one$e') ),
introduced(avatar_definition,[new_symbols(naming,[spl124_94])]) ).
tff(f19466,plain,
( ~ spl124_94
| spl124_95 ),
inference(avatar_split_clause,[],[f19448,f19464,f19460]) ).
tff(f19448,plain,
! [X0: 'Rows$'] :
( ~ 'fun_app$c'('fun_app$d'('less$',X0),'i$')
| ~ 'is_zero_row_upt_k$'(X0,'one$e','a$')
| ~ 'fun_app$b'('reduced_row_echelon_form_upt_k$'('a$'),'one$e') ),
inference(resolution,[],[f2219,f5084]) ).
tff(f5084,plain,
~ 'is_zero_row_upt_k$'('i$','one$e','a$'),
inference(backward_demodulation,[],[f1869,f5072]) ).
tff(f1869,plain,
~ 'is_zero_row_upt_k$'('i$','nat$'(1),'a$'),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
~ 'is_zero_row_upt_k$'('i$','nat$'(1),'a$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(f2219,plain,
! [X2: 'Rows$',X3: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Nat$'] :
( 'is_zero_row_upt_k$'(X3,X1,X0)
| ~ 'fun_app$c'('fun_app$d'('less$',X2),X3)
| ~ 'is_zero_row_upt_k$'(X2,X1,X0)
| ~ 'fun_app$b'('reduced_row_echelon_form_upt_k$'(X0),X1) ),
inference(cnf_transformation,[],[f1001]) ).
tff(f1001,plain,
! [X0: 'A_cols_vec_rows_vec$',X1: 'Nat$'] :
( ! [X2: 'Rows$'] :
( ! [X3: 'Rows$'] :
( 'is_zero_row_upt_k$'(X3,X1,X0)
| ~ 'fun_app$c'('fun_app$d'('less$',X2),X3) )
| ~ 'is_zero_row_upt_k$'(X2,X1,X0) )
| ~ 'fun_app$b'('reduced_row_echelon_form_upt_k$'(X0),X1) ),
inference(ennf_transformation,[],[f20]) ).
tff(f20,axiom,
! [X0: 'A_cols_vec_rows_vec$',X1: 'Nat$'] :
( 'fun_app$b'('reduced_row_echelon_form_upt_k$'(X0),X1)
=> ! [X2: 'Rows$'] :
( 'is_zero_row_upt_k$'(X2,X1,X0)
=> ~ ? [X3: 'Rows$'] :
( ~ 'is_zero_row_upt_k$'(X3,X1,X0)
& 'fun_app$c'('fun_app$d'('less$',X2),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 18:59:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (10371)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (10391)WARNING: value z3 for option sas not known
% 0.21/0.41 % (10389)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.41 % (10392)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.41 % (10390)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.41 % (10391)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.41 % (10395)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.41 % (10396)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.41 % (10393)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.44 % (10389)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.44 % (10389)Terminated due to inappropriate strategy.
% 0.21/0.44 % (10389)------------------------------
% 0.21/0.44 % (10389)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44 % (10389)Termination reason: Inappropriate
% 0.21/0.44
% 0.21/0.44 % (10389)Memory used [KB]: 2056
% 0.21/0.44 % (10389)Time elapsed: 0.031 s
% 0.21/0.44 % (10389)Instructions burned: 70 (million)
% 0.21/0.44 % (10390)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.44 % (10390)Terminated due to inappropriate strategy.
% 0.21/0.44 % (10390)------------------------------
% 0.21/0.44 % (10390)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44 % (10390)Termination reason: Inappropriate
% 0.21/0.44
% 0.21/0.44 % (10390)Memory used [KB]: 2056
% 0.21/0.44 % (10390)Time elapsed: 0.031 s
% 0.21/0.44 % (10390)Instructions burned: 70 (million)
% 0.21/0.44 % (10392)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.44 % (10392)Terminated due to inappropriate strategy.
% 0.21/0.44 % (10392)------------------------------
% 0.21/0.44 % (10392)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44 % (10392)Termination reason: Inappropriate
% 0.21/0.44
% 0.21/0.44 % (10392)Memory used [KB]: 2056
% 0.21/0.44 % (10392)Time elapsed: 0.031 s
% 0.21/0.44 % (10392)Instructions burned: 71 (million)
% 0.21/0.44 % (10389)------------------------------
% 0.21/0.44 % (10389)------------------------------
% 0.21/0.44 % (10390)------------------------------
% 0.21/0.44 % (10390)------------------------------
% 0.21/0.44 % (10392)------------------------------
% 0.21/0.44 % (10392)------------------------------
% 0.21/0.46 % (10414)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.46 % (10415)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.46 % (10416)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.49 % (10414)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.49 % (10414)Terminated due to inappropriate strategy.
% 0.21/0.49 % (10414)------------------------------
% 0.21/0.49 % (10414)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.49 % (10414)Termination reason: Inappropriate
% 0.21/0.49
% 0.21/0.49 % (10414)Memory used [KB]: 1982
% 0.21/0.49 % (10414)Time elapsed: 0.030 s
% 0.21/0.49 % (10414)Instructions burned: 70 (million)
% 0.21/0.49 % (10414)------------------------------
% 0.21/0.49 % (10414)------------------------------
% 0.21/0.50 % (10440)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 7.68/1.53 % (10416)First to succeed.
% 7.68/1.53 % (10416)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10371"
% 7.68/1.53 % (10416)Refutation found. Thanks to Tanya!
% 7.68/1.53 % SZS status Theorem for theBenchmark
% 7.68/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 7.68/1.53 % (10416)------------------------------
% 7.68/1.53 % (10416)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.68/1.53 % (10416)Termination reason: Refutation
% 7.68/1.53
% 7.68/1.53 % (10416)Memory used [KB]: 13478
% 7.68/1.53 % (10416)Time elapsed: 1.071 s
% 7.68/1.53 % (10416)Instructions burned: 3317 (million)
% 7.68/1.53 % (10371)Success in time 1.157 s
%------------------------------------------------------------------------------