TSTP Solution File: ITP332_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 : n021.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 07:14:29 EDT 2024
% Result : Theorem 24.63s 3.91s
% Output : Refutation 24.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 195
% Syntax : Number of formulae : 225 ( 12 unt; 187 typ; 0 def)
% Number of atoms : 87 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 35 ~; 29 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 23 ( 20 usr; 2 ari)
% Number of type conns : 303 ( 154 >; 149 *; 0 +; 0 <<)
% Number of predicates : 59 ( 57 usr; 4 prp; 0-3 aty)
% Number of functors : 113 ( 113 usr; 13 con; 0-4 aty)
% Number of variables : 44 ( 36 !; 8 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'A_m_vec_m_vec$': $tType ).
tff(type_def_6,type,
'M$': $tType ).
tff(type_def_7,type,
'A_n_vec_set$': $tType ).
tff(type_def_8,type,
'Int_set$': $tType ).
tff(type_def_9,type,
'Int_int_fun$': $tType ).
tff(type_def_10,type,
'A_n_vec_n_vec$': $tType ).
tff(type_def_11,type,
'A_n_vec_m_vec$': $tType ).
tff(type_def_12,type,
'Nat_nat_fun$': $tType ).
tff(type_def_13,type,
'A_m_vec$': $tType ).
tff(type_def_14,type,
'Nat$': $tType ).
tff(type_def_15,type,
'N$': $tType ).
tff(type_def_16,type,
tlbool: $tType ).
tff(type_def_17,type,
'Real_real_fun$': $tType ).
tff(type_def_18,type,
'A_m_vec_n_vec$': $tType ).
tff(type_def_19,type,
'A$': $tType ).
tff(type_def_20,type,
'A_n_vec$': $tType ).
tff(type_def_21,type,
'Nat_bool_fun$': $tType ).
tff(type_def_22,type,
'Real_bool_fun$': $tType ).
tff(type_def_23,type,
'Real_set$': $tType ).
tff(type_def_24,type,
'Nat_set$': $tType ).
tff(func_def_0,type,
'interchange_rows$a': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_1,type,
'zero$f': 'A_n_vec$' ).
tff(func_def_2,type,
'column_add$b': ( 'A_n_vec_m_vec$' * 'N$' * 'N$' * 'A$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_3,type,
'matrix_vector_mult$b': ( 'A_m_vec_m_vec$' * 'A_m_vec$' ) > 'A_m_vec$' ).
tff(func_def_4,type,
'matrix_matrix_mult$c': ( 'A_n_vec_m_vec$' * 'A_m_vec_n_vec$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_5,type,
'mat$': 'A$' > 'A_n_vec_n_vec$' ).
tff(func_def_6,type,
'interchange_columns$': ( 'A_m_vec_m_vec$' * 'M$' * 'M$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_7,type,
'column$a': ( 'N$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).
tff(func_def_8,type,
'interchange_rows$b': ( 'A_n_vec_m_vec$' * 'M$' * 'M$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_9,type,
'mult_column$': ( 'A_m_vec_m_vec$' * 'M$' * 'A$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_10,type,
'norm$': $real > $real ).
tff(func_def_11,type,
'mult_column$b': ( 'A_n_vec_m_vec$' * 'N$' * 'A$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_12,type,
'zero$a': 'A_n_vec_m_vec$' ).
tff(func_def_13,type,
'matrix_vector_mult$a': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'A_n_vec$' ).
tff(func_def_14,type,
'times$c': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_15,type,
'zero$b': 'A_m_vec_m_vec$' ).
tff(func_def_16,type,
'column_add$': ( 'A_m_vec_m_vec$' * 'M$' * 'M$' * 'A$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_17,type,
'matrix_matrix_mult$d': ( 'A_m_vec_n_vec$' * 'A_m_vec_m_vec$' ) > 'A_m_vec_n_vec$' ).
tff(func_def_18,type,
'b$': 'A_n_vec_m_vec$' ).
tff(func_def_19,type,
'null_space$': 'A_n_vec_m_vec$' > 'A_n_vec_set$' ).
tff(func_def_20,type,
'less_eq$': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_21,type,
'arcosh$': $real > $real ).
tff(func_def_22,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_23,type,
'times$': ( 'A$' * 'A$' ) > 'A$' ).
tff(func_def_24,type,
'mat$a': 'A$' > 'A_m_vec_m_vec$' ).
tff(func_def_25,type,
'matrix_matrix_mult$b': ( 'A_m_vec_m_vec$' * 'A_m_vec_m_vec$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_26,type,
'vector_matrix_mult$b': ( 'A_m_vec$' * 'A_m_vec_m_vec$' ) > 'A_m_vec$' ).
tff(func_def_27,type,
'one$': 'A$' ).
tff(func_def_28,type,
'dbl_inc$': $int > $int ).
tff(func_def_29,type,
'divide$': $real > 'Real_real_fun$' ).
tff(func_def_30,type,
tltrue: tlbool ).
tff(func_def_31,type,
'row_add$a': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_32,type,
'null_space$a': 'A_n_vec_n_vec$' > 'A_n_vec_set$' ).
tff(func_def_33,type,
'matrix_matrix_mult$f': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_34,type,
'mult_column$a': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_35,type,
'artanh$': $real > $real ).
tff(func_def_36,type,
'powr$': ( $real * $real ) > $real ).
tff(func_def_37,type,
'row_add$b': ( 'A_n_vec_m_vec$' * 'M$' * 'M$' * 'A$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_38,type,
'one$a': 'Nat$' ).
tff(func_def_39,type,
'times$d': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_40,type,
'transpose$c': 'A_n_vec_m_vec$' > 'A_m_vec_n_vec$' ).
tff(func_def_41,type,
'times$e': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_42,type,
'times$a': ( $real * $real ) > $real ).
tff(func_def_43,type,
'times$b': ( $int * $int ) > $int ).
tff(func_def_44,type,
'column$': ( 'N$' * 'A_n_vec_m_vec$' ) > 'A_m_vec$' ).
tff(func_def_45,type,
'mult_row$b': ( 'A_n_vec_m_vec$' * 'M$' * 'A$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_46,type,
'divide$a': $int > 'Int_int_fun$' ).
tff(func_def_47,type,
'transpose$': 'A_m_vec_n_vec$' > 'A_n_vec_m_vec$' ).
tff(func_def_48,type,
'matrix_inv$b': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_49,type,
'row_add$': ( 'A_m_vec_m_vec$' * 'M$' * 'M$' * 'A$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_50,type,
'less$': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_51,type,
'matrix_matrix_mult$e': ( 'A_n_vec_n_vec$' * 'A_m_vec_n_vec$' ) > 'A_m_vec_n_vec$' ).
tff(func_def_52,type,
'plus$': ( 'Real_set$' * 'Real_set$' ) > 'Real_set$' ).
tff(func_def_53,type,
'zero$': 'A_n_vec_n_vec$' ).
tff(func_def_54,type,
'matrix_matrix_mult$a': ( 'A_m_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_55,type,
'interchange_rows$': ( 'A_m_vec_m_vec$' * 'M$' * 'M$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_56,type,
'fun_app$': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_57,type,
'column_add$a': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_58,type,
'interchange_columns$b': ( 'A_n_vec_m_vec$' * 'N$' * 'N$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_59,type,
'exp$': $real > $real ).
tff(func_def_60,type,
'transpose$b': 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_61,type,
'zero$c': 'A$' ).
tff(func_def_62,type,
'fun_app$d': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_63,type,
tlfalse: tlbool ).
tff(func_def_64,type,
'nat$': $int > 'Nat$' ).
tff(func_def_65,type,
'arsinh$': $real > $real ).
tff(func_def_66,type,
'mult_row$a': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_67,type,
'vector_matrix_mult$': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).
tff(func_def_68,type,
'interchange_columns$a': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_69,type,
'fun_app$c': ( 'Real_real_fun$' * $real ) > $real ).
tff(func_def_70,type,
'times$f': ( 'Real_set$' * 'Real_set$' ) > 'Real_set$' ).
tff(func_def_71,type,
'matrix_inv$a': 'A_m_vec_n_vec$' > 'A_n_vec_m_vec$' ).
tff(func_def_72,type,
'orthogonal$': $real > 'Real_bool_fun$' ).
tff(func_def_73,type,
'columnvector$a': 'A_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_74,type,
'mult_row$': ( 'A_m_vec_m_vec$' * 'M$' * 'A$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_75,type,
'transpose$a': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_76,type,
'matrix_vector_mult$': ( 'A_n_vec_m_vec$' * 'A_n_vec$' ) > 'A_m_vec$' ).
tff(func_def_77,type,
'a$': 'A_n_vec_m_vec$' ).
tff(func_def_78,type,
'matrix_matrix_mult$g': ( 'A_m_vec_n_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_79,type,
'zero$d': 'Nat$' ).
tff(func_def_80,type,
'zero$e': 'A_m_vec$' ).
tff(func_def_81,type,
'matrix_matrix_mult$': ( 'A_n_vec_m_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_m_vec$' ).
tff(func_def_82,type,
'vector_matrix_mult$a': ( 'A_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec$' ).
tff(func_def_83,type,
'columnvector$': 'A_m_vec$' > 'A_n_vec_m_vec$' ).
tff(func_def_84,type,
'ln$': $real > $real ).
tff(func_def_85,type,
'divide$b': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_86,type,
'matrix_inv$': 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_87,type,
'dbl_inc$a': $real > $real ).
tff(func_def_98,type,
sK38: $real > $real ).
tff(func_def_99,type,
sK39: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_100,type,
sK40: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_101,type,
sK41: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_102,type,
sK42: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_103,type,
sK43: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_104,type,
sK44: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_105,type,
sK45: ( $real * $real ) > $real ).
tff(func_def_106,type,
sK46: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_107,type,
sK47: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_108,type,
sK48: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_109,type,
sK49: ( $real * $real ) > $real ).
tff(func_def_110,type,
sK50: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_111,type,
sK51: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_112,type,
sK52: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_113,type,
sK53: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_114,type,
sK54: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_115,type,
sK55: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_116,type,
sK56: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_117,type,
sK57: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_118,type,
sK58: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_119,type,
sK59: ( $real * 'Real_set$' * 'Real_set$' ) > $real ).
tff(func_def_120,type,
sK60: ( $real * 'Real_set$' * 'Real_set$' ) > $real ).
tff(func_def_121,type,
sK61: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_122,type,
sK62: 'Nat_nat_fun$' > 'Nat$' ).
tff(pred_def_1,type,
'equivalent_matrices$c': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > $o ).
tff(pred_def_2,type,
'equivalent_matrices$a': ( 'A_m_vec_n_vec$' * 'A_m_vec_m_vec$' ) > $o ).
tff(pred_def_3,type,
'member$b': ( $real * 'Real_set$' ) > $o ).
tff(pred_def_4,type,
'member$a': ( 'Nat$' * 'Nat_set$' ) > $o ).
tff(pred_def_5,type,
'invertible$a': 'A_n_vec_n_vec$' > $o ).
tff(pred_def_6,type,
'equivalent_matrices$f': ( 'A_m_vec_m_vec$' * 'A_n_vec_m_vec$' ) > $o ).
tff(pred_def_7,type,
'fun_app$b': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_9,type,
'equivalent_matrices$e': ( 'A_n_vec_n_vec$' * 'A_n_vec_m_vec$' ) > $o ).
tff(pred_def_10,type,
'invertible$c': 'A_n_vec_m_vec$' > $o ).
tff(pred_def_11,type,
'equivalent_matrices$b': ( 'A_m_vec_n_vec$' * 'A_m_vec_n_vec$' ) > $o ).
tff(pred_def_12,type,
'fun_app$a': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_13,type,
'equivalent_matrices$d': ( 'A_m_vec_m_vec$' * 'A_m_vec_m_vec$' ) > $o ).
tff(pred_def_14,type,
'equivalent_matrices$': ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > $o ).
tff(pred_def_15,type,
'invertible$': 'A_m_vec_m_vec$' > $o ).
tff(pred_def_16,type,
'member$': ( $int * 'Int_set$' ) > $o ).
tff(pred_def_17,type,
'invertible$b': 'A_m_vec_n_vec$' > $o ).
tff(pred_def_22,type,
sP0: ( $int * $int ) > $o ).
tff(pred_def_23,type,
sP1: ( $int * $int ) > $o ).
tff(pred_def_24,type,
sP2: ( $int * $int ) > $o ).
tff(pred_def_25,type,
sP3: ( $int * $int ) > $o ).
tff(pred_def_26,type,
sP4: ( $int * $int ) > $o ).
tff(pred_def_27,type,
sP5: ( $int * $int ) > $o ).
tff(pred_def_28,type,
sP6: ( $int * $int ) > $o ).
tff(pred_def_29,type,
sP7: ( $int * $int ) > $o ).
tff(pred_def_30,type,
sP8: ( $real * $real ) > $o ).
tff(pred_def_31,type,
sP9: ( $real * $real ) > $o ).
tff(pred_def_32,type,
sP10: ( $real * $real ) > $o ).
tff(pred_def_33,type,
sP11: ( $real * $real ) > $o ).
tff(pred_def_34,type,
sP12: ( $real * $real ) > $o ).
tff(pred_def_35,type,
sP13: ( $real * $real ) > $o ).
tff(pred_def_36,type,
sP14: ( $int * $int ) > $o ).
tff(pred_def_37,type,
sP15: ( $int * $int ) > $o ).
tff(pred_def_38,type,
sP16: ( $int * $int ) > $o ).
tff(pred_def_39,type,
sP17: ( $int * $int ) > $o ).
tff(pred_def_40,type,
sP18: ( $real * $real ) > $o ).
tff(pred_def_41,type,
sP19: ( $real * $real ) > $o ).
tff(pred_def_42,type,
sP20: ( $real * $real ) > $o ).
tff(pred_def_43,type,
sP21: ( $real * $real ) > $o ).
tff(pred_def_44,type,
sP22: ( $real * $real ) > $o ).
tff(pred_def_45,type,
sP23: ( $real * $real ) > $o ).
tff(pred_def_46,type,
sP24: ( $real * $real ) > $o ).
tff(pred_def_47,type,
sP25: ( $real * $real ) > $o ).
tff(pred_def_48,type,
sP26: ( $int * $int * $int ) > $o ).
tff(pred_def_49,type,
sP27: ( $int * $int * $int ) > $o ).
tff(pred_def_50,type,
sP28: ( $int * $int * $int ) > $o ).
tff(pred_def_51,type,
sP29: ( $int * $int * $int ) > $o ).
tff(pred_def_52,type,
sP30: ( $real * $real * $real ) > $o ).
tff(pred_def_53,type,
sP31: ( $real * $real * $real ) > $o ).
tff(pred_def_54,type,
sP32: ( $real * $real * $real ) > $o ).
tff(pred_def_55,type,
sP33: ( $real * $real * $real ) > $o ).
tff(pred_def_56,type,
sP34: ( $int * $int * $int ) > $o ).
tff(pred_def_57,type,
sP35: ( $int * $int * $int ) > $o ).
tff(pred_def_58,type,
sP36: ( $real * $real * $real ) > $o ).
tff(pred_def_59,type,
sP37: ( $real * $real * $real ) > $o ).
tff(f157074,plain,
$false,
inference(avatar_sat_refutation,[],[f156852,f157007,f157073]) ).
tff(f157073,plain,
spl63_607,
inference(avatar_contradiction_clause,[],[f157072]) ).
tff(f157072,plain,
( $false
| spl63_607 ),
inference(subsumption_resolution,[],[f157071,f1929]) ).
tff(f1929,plain,
'equivalent_matrices$'('a$','b$'),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
'equivalent_matrices$'('a$','b$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f157071,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| spl63_607 ),
inference(resolution,[],[f156851,f2352]) ).
tff(f2352,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$a'(sK52(X0,X1))
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f1603]) ).
tff(f1603,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK51(X0,X1)),X0),sK52(X0,X1)) = X1 )
& 'invertible$a'(sK52(X0,X1))
& 'invertible$'(sK51(X0,X1)) )
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52])],[f1158,f1602]) ).
tff(f1602,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ? [X2: 'A_m_vec_m_vec$',X3: 'A_n_vec_n_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) = X1 )
& 'invertible$a'(X3)
& 'invertible$'(X2) )
=> ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK51(X0,X1)),X0),sK52(X0,X1)) = X1 )
& 'invertible$a'(sK52(X0,X1))
& 'invertible$'(sK51(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1158,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ? [X2: 'A_m_vec_m_vec$',X3: 'A_n_vec_n_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) = X1 )
& 'invertible$a'(X3)
& 'invertible$'(X2) )
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(ennf_transformation,[],[f910]) ).
tff(f910,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'equivalent_matrices$'(X0,X1)
=> ? [X2: 'A_m_vec_m_vec$',X3: 'A_n_vec_n_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) = X1 )
& 'invertible$a'(X3)
& 'invertible$'(X2) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
tff(f10,axiom,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'equivalent_matrices$'(X0,X1)
<=> ? [X2: 'A_m_vec_m_vec$',X3: 'A_n_vec_n_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) = X1 )
& 'invertible$a'(X3)
& 'invertible$'(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
tff(f156851,plain,
( ~ 'invertible$a'(sK52('a$','b$'))
| spl63_607 ),
inference(avatar_component_clause,[],[f156849]) ).
tff(f156849,plain,
( spl63_607
<=> 'invertible$a'(sK52('a$','b$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_607])]) ).
tff(f157007,plain,
spl63_606,
inference(avatar_contradiction_clause,[],[f157006]) ).
tff(f157006,plain,
( $false
| spl63_606 ),
inference(subsumption_resolution,[],[f157005,f1929]) ).
tff(f157005,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| spl63_606 ),
inference(resolution,[],[f156847,f2351]) ).
tff(f2351,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$'(sK51(X0,X1))
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f1603]) ).
tff(f156847,plain,
( ~ 'invertible$'(sK51('a$','b$'))
| spl63_606 ),
inference(avatar_component_clause,[],[f156845]) ).
tff(f156845,plain,
( spl63_606
<=> 'invertible$'(sK51('a$','b$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_606])]) ).
tff(f156852,plain,
( ~ spl63_606
| ~ spl63_607 ),
inference(avatar_split_clause,[],[f156843,f156849,f156845]) ).
tff(f156843,plain,
( ~ 'invertible$a'(sK52('a$','b$'))
| ~ 'invertible$'(sK51('a$','b$')) ),
inference(trivial_inequality_removal,[],[f156776]) ).
tff(f156776,plain,
( ( 'b$' != 'b$' )
| ~ 'invertible$a'(sK52('a$','b$'))
| ~ 'invertible$'(sK51('a$','b$')) ),
inference(superposition,[],[f3252,f55307]) ).
tff(f55307,plain,
'b$' = 'matrix_matrix_mult$a'('matrix_inv$'(sK51('a$','b$')),'matrix_matrix_mult$'('a$',sK52('a$','b$'))),
inference(resolution,[],[f3253,f1929]) ).
tff(f3253,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'(X0,X1)
| ( 'matrix_matrix_mult$a'('matrix_inv$'(sK51(X0,X1)),'matrix_matrix_mult$'(X0,sK52(X0,X1))) = X1 ) ),
inference(backward_demodulation,[],[f2353,f2701]) ).
tff(f2701,plain,
! [X2: 'A_n_vec_n_vec$',X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_m_vec$'] : ( 'matrix_matrix_mult$a'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_m_vec$',X2: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$a'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
tff(f2353,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK51(X0,X1)),X0),sK52(X0,X1)) = X1 )
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f1603]) ).
tff(f3252,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ( 'b$' != 'matrix_matrix_mult$a'('matrix_inv$'(X0),'matrix_matrix_mult$'('a$',X1)) )
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0) ),
inference(backward_demodulation,[],[f3219,f2701]) ).
tff(f3219,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(subsumption_resolution,[],[f1915,f1914]) ).
tff(f1914,plain,
~ 'thesis$',
inference(cnf_transformation,[],[f887]) ).
tff(f887,plain,
~ 'thesis$',
inference(flattening,[],[f2]) ).
tff(f2,negated_conjecture,
~ 'thesis$',
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
'thesis$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture0) ).
tff(f1915,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(cnf_transformation,[],[f912]) ).
tff(f912,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(flattening,[],[f911]) ).
tff(f911,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ( 'invertible$a'(X1)
& 'invertible$'(X0)
& ( 'b$' = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) )
=> 'thesis$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 19:20:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (5685)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.40 % (5688)WARNING: value z3 for option sas not known
% 0.13/0.40 % (5691)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)
% 0.13/0.40 % (5690)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)
% 0.13/0.40 % (5687)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.40 % (5689)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.40 % (5692)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)
% 0.13/0.40 % (5688)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)
% 0.13/0.40 % (5686)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.43 % (5687)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.43 % (5687)Terminated due to inappropriate strategy.
% 0.19/0.43 % (5687)------------------------------
% 0.19/0.43 % (5687)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.43 % (5687)Termination reason: Inappropriate
% 0.19/0.43
% 0.19/0.43 % (5687)Memory used [KB]: 1973
% 0.19/0.43 % (5687)Time elapsed: 0.030 s
% 0.19/0.43 % (5687)Instructions burned: 68 (million)
% 0.19/0.43 % (5687)------------------------------
% 0.19/0.43 % (5687)------------------------------
% 0.19/0.43 % (5689)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.43 % (5689)Terminated due to inappropriate strategy.
% 0.19/0.43 % (5689)------------------------------
% 0.19/0.43 % (5689)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.43 % (5689)Termination reason: Inappropriate
% 0.19/0.43
% 0.19/0.43 % (5689)Memory used [KB]: 1973
% 0.19/0.43 % (5689)Time elapsed: 0.031 s
% 0.19/0.43 % (5689)Instructions burned: 71 (million)
% 0.19/0.43 % (5686)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.43 % (5689)------------------------------
% 0.19/0.43 % (5689)------------------------------
% 0.19/0.43 % (5686)Terminated due to inappropriate strategy.
% 0.19/0.43 % (5686)------------------------------
% 0.19/0.43 % (5686)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.43 % (5686)Termination reason: Inappropriate
% 0.19/0.43
% 0.19/0.43 % (5686)Memory used [KB]: 1973
% 0.19/0.43 % (5686)Time elapsed: 0.030 s
% 0.19/0.43 % (5686)Instructions burned: 69 (million)
% 0.19/0.43 % (5686)------------------------------
% 0.19/0.43 % (5686)------------------------------
% 0.19/0.44 % (5695)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)
% 0.19/0.44 % (5693)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.44 % (5694)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)
% 0.19/0.47 % (5693)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.47 % (5693)Terminated due to inappropriate strategy.
% 0.19/0.47 % (5693)------------------------------
% 0.19/0.47 % (5693)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.47 % (5693)Termination reason: Inappropriate
% 0.19/0.47
% 0.19/0.47 % (5693)Memory used [KB]: 2012
% 0.19/0.47 % (5693)Time elapsed: 0.027 s
% 0.19/0.47 % (5693)Instructions burned: 64 (million)
% 0.19/0.47 % (5693)------------------------------
% 0.19/0.47 % (5693)------------------------------
% 0.19/0.48 % (5696)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)
% 24.63/3.90 % (5695)First to succeed.
% 24.63/3.90 % (5695)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5685"
% 24.63/3.91 % (5695)Refutation found. Thanks to Tanya!
% 24.63/3.91 % SZS status Theorem for theBenchmark
% 24.63/3.91 % SZS output start Proof for theBenchmark
% See solution above
% 24.63/3.91 % (5695)------------------------------
% 24.63/3.91 % (5695)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 24.63/3.91 % (5695)Termination reason: Refutation
% 24.63/3.91
% 24.63/3.91 % (5695)Memory used [KB]: 39772
% 24.63/3.91 % (5695)Time elapsed: 3.458 s
% 24.63/3.91 % (5695)Instructions burned: 10838 (million)
% 24.63/3.91 % (5685)Success in time 3.521 s
%------------------------------------------------------------------------------