TSTP Solution File: ITP332_1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.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 06:55:54 EDT 2024
% Result : Theorem 0.64s 0.83s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 137
% Syntax : Number of formulae : 167 ( 12 unt; 129 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 : 179 ( 96 >; 83 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 4 prp; 0-2 aty)
% Number of functors : 93 ( 93 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 > $real ).
tff(func_def_98,type,
sK0: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_99,type,
sK1: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_100,type,
sK2: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_101,type,
sK3: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_102,type,
sK4: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(pred_def_1,type,
'equivalent_matrices$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(f1212,plain,
$false,
inference(avatar_sat_refutation,[],[f1167,f1180,f1211]) ).
tff(f1211,plain,
spl5_6,
inference(avatar_contradiction_clause,[],[f1210]) ).
tff(f1210,plain,
( $false
| spl5_6 ),
inference(subsumption_resolution,[],[f1209,f924]) ).
tff(f924,plain,
'equivalent_matrices$'('a$','b$'),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
'equivalent_matrices$'('a$','b$'),
file('/export/starexec/sandbox2/tmp/tmp.cxqHHWXNQy/Vampire---4.8_26910',axiom2) ).
tff(f1209,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| spl5_6 ),
inference(resolution,[],[f1166,f930]) ).
tff(f930,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$a'(sK1(X0,X1))
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f907]) ).
tff(f907,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK0(X0,X1)),X0),sK1(X0,X1)) = X1 )
& 'invertible$a'(sK1(X0,X1))
& 'invertible$'(sK0(X0,X1)) )
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f895,f906]) ).
tff(f906,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$a'('matrix_inv$'(sK0(X0,X1)),X0),sK1(X0,X1)) = X1 )
& 'invertible$a'(sK1(X0,X1))
& 'invertible$'(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f895,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,[],[f888]) ).
tff(f888,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/tmp/tmp.cxqHHWXNQy/Vampire---4.8_26910',axiom8) ).
tff(f1166,plain,
( ~ 'invertible$a'(sK1('a$','b$'))
| spl5_6 ),
inference(avatar_component_clause,[],[f1164]) ).
tff(f1164,plain,
( spl5_6
<=> 'invertible$a'(sK1('a$','b$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
tff(f1180,plain,
spl5_5,
inference(avatar_contradiction_clause,[],[f1179]) ).
tff(f1179,plain,
( $false
| spl5_5 ),
inference(subsumption_resolution,[],[f1178,f924]) ).
tff(f1178,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| spl5_5 ),
inference(resolution,[],[f1162,f929]) ).
tff(f929,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$'(sK0(X0,X1))
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f907]) ).
tff(f1162,plain,
( ~ 'invertible$'(sK0('a$','b$'))
| spl5_5 ),
inference(avatar_component_clause,[],[f1160]) ).
tff(f1160,plain,
( spl5_5
<=> 'invertible$'(sK0('a$','b$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
tff(f1167,plain,
( ~ spl5_5
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f1158,f1164,f1160]) ).
tff(f1158,plain,
( ~ 'invertible$a'(sK1('a$','b$'))
| ~ 'invertible$'(sK0('a$','b$')) ),
inference(trivial_inequality_removal,[],[f1153]) ).
tff(f1153,plain,
( ( 'b$' != 'b$' )
| ~ 'invertible$a'(sK1('a$','b$'))
| ~ 'invertible$'(sK0('a$','b$')) ),
inference(superposition,[],[f958,f1079]) ).
tff(f1079,plain,
'b$' = 'matrix_matrix_mult$a'('matrix_inv$'(sK0('a$','b$')),'matrix_matrix_mult$'('a$',sK1('a$','b$'))),
inference(resolution,[],[f959,f924]) ).
tff(f959,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'(X0,X1)
| ( 'matrix_matrix_mult$a'('matrix_inv$'(sK0(X0,X1)),'matrix_matrix_mult$'(X0,sK1(X0,X1))) = X1 ) ),
inference(forward_demodulation,[],[f931,f925]) ).
tff(f925,plain,
! [X2: 'A_n_vec_n_vec$',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$a'(X0,X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.cxqHHWXNQy/Vampire---4.8_26910',axiom16) ).
tff(f931,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK0(X0,X1)),X0),sK1(X0,X1)) = X1 )
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f907]) ).
tff(f958,plain,
! [X0: 'A_m_vec_m_vec$',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,[],[f957,f925]) ).
tff(f957,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$'),X1) ) ),
inference(subsumption_resolution,[],[f923,f922]) ).
tff(f922,plain,
~ 'thesis$',
inference(cnf_transformation,[],[f887]) ).
tff(f887,plain,
~ 'thesis$',
inference(flattening,[],[f2]) ).
tff(f2,negated_conjecture,
~ 'thesis$',
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
'thesis$',
file('/export/starexec/sandbox2/tmp/tmp.cxqHHWXNQy/Vampire---4.8_26910',conjecture0) ).
tff(f923,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(cnf_transformation,[],[f890]) ).
tff(f890,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(flattening,[],[f889]) ).
tff(f889,plain,
! [X0: 'A_m_vec_m_vec$',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/tmp/tmp.cxqHHWXNQy/Vampire---4.8_26910',hypothesis1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.09/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 19:20:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TF0_THM_EQU_ARI problem
% 0.15/0.37 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.cxqHHWXNQy/Vampire---4.8_26910
% 0.64/0.81 % (27263)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.64/0.81 % (27256)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.64/0.81 % (27258)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.64/0.81 % (27259)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.64/0.81 % (27257)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.64/0.81 % (27260)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.64/0.81 % (27261)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.64/0.81 % (27262)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.64/0.82 % (27263)Refutation not found, incomplete strategy% (27263)------------------------------
% 0.64/0.82 % (27263)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.82 % (27263)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.82
% 0.64/0.82 % (27263)Memory used [KB]: 1566
% 0.64/0.82 % (27263)Time elapsed: 0.007 s
% 0.64/0.82 % (27263)Instructions burned: 25 (million)
% 0.64/0.82 % (27263)------------------------------
% 0.64/0.82 % (27263)------------------------------
% 0.64/0.82 % (27264)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.64/0.82 % (27259)Refutation not found, incomplete strategy% (27259)------------------------------
% 0.64/0.82 % (27259)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.82 % (27259)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.82
% 0.64/0.82 % (27259)Memory used [KB]: 1553
% 0.64/0.82 % (27259)Time elapsed: 0.012 s
% 0.64/0.82 % (27259)Instructions burned: 24 (million)
% 0.64/0.82 % (27259)------------------------------
% 0.64/0.82 % (27259)------------------------------
% 0.64/0.82 % (27261)Refutation not found, incomplete strategy% (27261)------------------------------
% 0.64/0.82 % (27261)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.82 % (27261)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.82
% 0.64/0.82 % (27261)Memory used [KB]: 1565
% 0.64/0.82 % (27261)Time elapsed: 0.012 s
% 0.64/0.82 % (27261)Instructions burned: 25 (million)
% 0.64/0.82 % (27261)------------------------------
% 0.64/0.82 % (27261)------------------------------
% 0.64/0.82 % (27262)Refutation not found, incomplete strategy% (27262)------------------------------
% 0.64/0.82 % (27262)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.82 % (27262)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.82
% 0.64/0.82 % (27262)Memory used [KB]: 1597
% 0.64/0.82 % (27262)Time elapsed: 0.015 s
% 0.64/0.82 % (27262)Instructions burned: 30 (million)
% 0.64/0.82 % (27262)------------------------------
% 0.64/0.82 % (27262)------------------------------
% 0.64/0.83 % (27256)Refutation not found, incomplete strategy% (27256)------------------------------
% 0.64/0.83 % (27256)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.83 % (27256)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.83
% 0.64/0.83 % (27256)Memory used [KB]: 1630
% 0.64/0.83 % (27256)Time elapsed: 0.017 s
% 0.64/0.83 % (27256)Instructions burned: 33 (million)
% 0.64/0.83 % (27265)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.64/0.83 % (27260)Instruction limit reached!
% 0.64/0.83 % (27260)------------------------------
% 0.64/0.83 % (27260)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.83 % (27260)Termination reason: Unknown
% 0.64/0.83 % (27260)Termination phase: Preprocessing 3
% 0.64/0.83
% 0.64/0.83 % (27260)Memory used [KB]: 1949
% 0.64/0.83 % (27260)Time elapsed: 0.017 s
% 0.64/0.83 % (27260)Instructions burned: 36 (million)
% 0.64/0.83 % (27260)------------------------------
% 0.64/0.83 % (27260)------------------------------
% 0.64/0.83 % (27256)------------------------------
% 0.64/0.83 % (27256)------------------------------
% 0.64/0.83 % (27266)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.64/0.83 % (27267)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.64/0.83 % (27268)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.64/0.83 % (27269)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.64/0.83 % (27258)First to succeed.
% 0.64/0.83 % (27264)Instruction limit reached!
% 0.64/0.83 % (27264)------------------------------
% 0.64/0.83 % (27264)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.83 % (27264)Termination reason: Unknown
% 0.64/0.83 % (27264)Termination phase: Property scanning
% 0.64/0.83
% 0.64/0.83 % (27264)Memory used [KB]: 2131
% 0.64/0.83 % (27264)Time elapsed: 0.014 s
% 0.64/0.83 % (27264)Instructions burned: 55 (million)
% 0.64/0.83 % (27264)------------------------------
% 0.64/0.83 % (27264)------------------------------
% 0.64/0.83 % (27258)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27091"
% 0.64/0.83 % (27257)Instruction limit reached!
% 0.64/0.83 % (27257)------------------------------
% 0.64/0.83 % (27257)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.83 % (27257)Termination reason: Unknown
% 0.64/0.83 % (27257)Termination phase: Property scanning
% 0.64/0.83
% 0.64/0.83 % (27257)Memory used [KB]: 2131
% 0.64/0.83 % (27257)Time elapsed: 0.024 s
% 0.64/0.83 % (27257)Instructions burned: 53 (million)
% 0.64/0.83 % (27257)------------------------------
% 0.64/0.83 % (27257)------------------------------
% 0.64/0.83 % (27258)Refutation found. Thanks to Tanya!
% 0.64/0.83 % SZS status Theorem for Vampire---4
% 0.64/0.83 % SZS output start Proof for Vampire---4
% See solution above
% 0.64/0.83 % (27258)------------------------------
% 0.64/0.83 % (27258)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.64/0.83 % (27258)Termination reason: Refutation
% 0.64/0.83
% 0.64/0.83 % (27258)Memory used [KB]: 1741
% 0.64/0.83 % (27258)Time elapsed: 0.023 s
% 0.64/0.83 % (27258)Instructions burned: 42 (million)
% 0.64/0.83 % (27091)Success in time 0.446 s
% 0.64/0.83 % Vampire---4.8 exiting
%------------------------------------------------------------------------------