%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP332_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:39:23 AM UTC 2026
% Result : Theorem 1.41s 0.71s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 18 unt; 0 typ; 4 def)
% Number of atoms : 105 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 50 ~; 41 |; 8 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 23 ( 20 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 21 usr; 6 prp; 0-2 aty)
% Number of functors : 113 ( 113 usr; 13 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 34 !; 6 ?; 40 :)
% 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$' ).
tff(func_def_101,type,
sK3: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_102,type,
sK4: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_103,type,
sK5: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_104,type,
sK6: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_105,type,
sK7: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_106,type,
sK8: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_107,type,
sK9: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_108,type,
sK10: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_109,type,
sK11: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_110,type,
sK12: ( $real * 'Real_set$' * 'Real_set$' ) > $real ).
tff(func_def_111,type,
sK13: ( $real * 'Real_set$' * 'Real_set$' ) > $real ).
tff(func_def_112,type,
sK14: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_113,type,
sK15: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_114,type,
sK16: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_115,type,
sK17: $real > $real ).
tff(func_def_116,type,
sK18: ( $real * $real ) > $real ).
tff(func_def_117,type,
sK19: ( $real * $real ) > $real ).
tff(func_def_118,type,
sK20: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_119,type,
sK21: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_120,type,
sK22: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_121,type,
sK23: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_122,type,
sK24: 'Nat_bool_fun$' > '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$' > $o ).
tff(f1,conjecture,
'thesis$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture0) ).
tff(f2,negated_conjecture,
~ 'thesis$',
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,axiom,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ( ( 'b$' = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) )
& 'invertible$'(X0)
& 'invertible$a'(X1) )
=> 'thesis$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis1) ).
tff(f4,axiom,
'equivalent_matrices$'('a$','b$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
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$'] :
( 'invertible$'(X2)
& 'invertible$a'(X3)
& ( X1 = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
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$a'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
tff(f887,plain,
~ 'thesis$',
inference(flattening,[],[f2]) ).
tff(f889,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$'] :
( 'invertible$'(X2)
& 'invertible$a'(X3)
& ( X1 = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
tff(f890,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) )
| ~ 'invertible$'(X0)
| ~ 'invertible$a'(X1) ),
inference(ennf_transformation,[],[f3]) ).
tff(f891,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( 'thesis$'
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) )
| ~ 'invertible$'(X0)
| ~ 'invertible$a'(X1) ),
inference(flattening,[],[f890]) ).
tff(f892,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ? [X2: 'A_m_vec_m_vec$',X3: 'A_n_vec_n_vec$'] :
( 'invertible$'(X2)
& 'invertible$a'(X3)
& ( X1 = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) ) )
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(ennf_transformation,[],[f889]) ).
tff(f1414,plain,
~ 'thesis$',
inference(cnf_transformation,[],[f887]) ).
tff(f1415,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) )
| 'thesis$' ),
inference(cnf_transformation,[],[f891]) ).
tff(f1416,plain,
'equivalent_matrices$'('a$','b$'),
inference(cnf_transformation,[],[f4]) ).
tff(f1417,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'(X0,X1)
| ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK0(X0,X1)),X0),sK1(X0,X1)) = X1 ) ),
inference(cnf_transformation,[],[f892]) ).
tff(f1418,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,[],[f892]) ).
tff(f1419,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$'(sK0(X0,X1))
| ~ 'equivalent_matrices$'(X0,X1) ),
inference(cnf_transformation,[],[f892]) ).
tff(f1426,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$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f18]) ).
tff(f2637,definition,
( spl25_8
<=> 'thesis$' ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
tff(f2639,plain,
( 'thesis$'
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f2637]) ).
tff(f2641,definition,
( spl25_9
<=> ! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_9])],[avatar_definition]) ).
tff(f2642,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$'),X1) ) )
| ~ spl25_9 ),
inference(avatar_component_clause,[],[f2641]) ).
tff(f2643,plain,
( spl25_8
| spl25_9 ),
inference(avatar_split_clause,[],[f1415,f2641,f2637]) ).
tff(f2648,plain,
( ! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ( 'b$' != 'matrix_matrix_mult$a'('matrix_inv$'(X0),'matrix_matrix_mult$'('a$',X1)) )
| ~ 'invertible$a'(X1)
| ~ 'invertible$'(X0) )
| ~ spl25_9 ),
inference(forward_demodulation,[],[f2642,f1426]) ).
tff(f2652,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,[],[f1417,f1426]) ).
tff(f2653,plain,
'b$' = 'matrix_matrix_mult$a'('matrix_inv$'(sK0('a$','b$')),'matrix_matrix_mult$'('a$',sK1('a$','b$'))),
inference(resolution,[],[f2652,f1416]) ).
tff(f2654,plain,
( ( 'b$' != 'b$' )
| ~ 'invertible$a'(sK1('a$','b$'))
| ~ 'invertible$'(sK0('a$','b$'))
| ~ spl25_9 ),
inference(superposition,[],[f2648,f2653]) ).
tff(f2656,plain,
( ~ 'invertible$a'(sK1('a$','b$'))
| ~ 'invertible$'(sK0('a$','b$'))
| ~ spl25_9 ),
inference(trivial_inequality_removal,[],[f2654]) ).
tff(f2658,definition,
( spl25_10
<=> 'invertible$'(sK0('a$','b$')) ),
introduced(definition,[new_symbols(definition,[spl25_10])],[avatar_definition]) ).
tff(f2660,plain,
( ~ 'invertible$'(sK0('a$','b$'))
| spl25_10 ),
inference(avatar_component_clause,[],[f2658]) ).
tff(f2662,definition,
( spl25_11
<=> 'invertible$a'(sK1('a$','b$')) ),
introduced(definition,[new_symbols(definition,[spl25_11])],[avatar_definition]) ).
tff(f2664,plain,
( ~ 'invertible$a'(sK1('a$','b$'))
| spl25_11 ),
inference(avatar_component_clause,[],[f2662]) ).
tff(f2665,plain,
( ~ spl25_10
| ~ spl25_11
| ~ spl25_9 ),
inference(avatar_split_clause,[],[f2656,f2641,f2662,f2658]) ).
tff(f2666,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| spl25_11 ),
inference(resolution,[],[f2664,f1418]) ).
tff(f2667,plain,
( $false
| spl25_11 ),
inference(forward_subsumption_resolution,[],[f2666,f1416]) ).
tff(f2668,plain,
spl25_11,
inference(avatar_contradiction_clause,[],[f2667]) ).
tff(f2669,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| spl25_10 ),
inference(resolution,[],[f2660,f1419]) ).
tff(f2670,plain,
( $false
| spl25_10 ),
inference(forward_subsumption_resolution,[],[f2669,f1416]) ).
tff(f2671,plain,
spl25_10,
inference(avatar_contradiction_clause,[],[f2670]) ).
tff(f2672,plain,
( $false
| ~ spl25_8 ),
inference(forward_subsumption_resolution,[],[f2639,f1414]) ).
tff(f2673,plain,
~ spl25_8,
inference(avatar_contradiction_clause,[],[f2672]) ).
cnf(s5,plain,
( spl25_8
| spl25_9 ),
inference(sat_conversion,[],[f2643]) ).
cnf(s6,plain,
( ~ spl25_9
| ~ spl25_10
| ~ spl25_11 ),
inference(sat_conversion,[],[f2665]) ).
cnf(s7,plain,
spl25_11,
inference(sat_conversion,[],[f2668]) ).
cnf(s8,plain,
spl25_10,
inference(sat_conversion,[],[f2671]) ).
cnf(s9,plain,
~ spl25_8,
inference(sat_conversion,[],[f2673]) ).
cnf(s10,plain,
~ spl25_9,
inference(rat,[],[s6,s7,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s5,s10,s9]) ).
tff(f2674,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP332_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 % Computer : n001.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 13:00:30 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.47 Running first-order model finding
% 0.22/0.47 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.41/0.71 % (3547802)Will run a generic schedule for satisfiability detection.
% 1.41/0.71 % (3547807)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2333116222_2999 on theBenchmark for (2999ds/0Mi)
% 1.41/0.71 % (3547809)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2030772200:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.41/0.71 % (3547808)% WARNING: option uhcvi not known.
% 1.41/0.71 % (3547812)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3027229629:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.41/0.71 % (3547810)dis+10_1_sil=32000:sp=arity:random_seed=1332307878:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.41/0.71 % (3547813)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3464493805:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.41/0.71 % (3547808)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3733642556:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.41/0.71 % (3547811)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3309730997:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.41/0.71 % (3547807)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.41/0.71 % (3547807)Terminated due to inappropriate strategy.
% 1.41/0.71 % (3547807)------------------------------
% 1.41/0.71 % (3547807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547807)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547807)Termination reason: Inappropriate
% 1.41/0.71 % (3547807)Time elapsed: 0.024 s
% 1.41/0.71 % (3547807)Peak memory usage: 12 MB
% 1.41/0.71 % (3547807)Instructions burned: 51 (million)
% 1.41/0.71 % (3547807)------------------------------
% 1.41/0.71 % (3547807)------------------------------
% 1.41/0.71 % (3547821)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2843225867:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.41/0.71 % (3547821)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.41/0.71 % (3547821)Terminated due to inappropriate strategy.
% 1.41/0.71 % (3547821)------------------------------
% 1.41/0.71 % (3547821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547821)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547821)Termination reason: Inappropriate
% 1.41/0.71 % (3547821)Time elapsed: 0.025 s
% 1.41/0.71 % (3547821)Peak memory usage: 12 MB
% 1.41/0.71 % (3547821)Instructions burned: 51 (million)
% 1.41/0.71 % (3547821)------------------------------
% 1.41/0.71 % (3547821)------------------------------
% 1.41/0.71 % (3547823)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=429542688:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.41/0.71 % (3547810)Instruction limit reached!
% 1.41/0.71 % (3547810)------------------------------
% 1.41/0.71 % (3547810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547810)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547810)Termination reason: Instruction limit
% 1.41/0.71 % (3547810)Termination phase: Saturation
% 1.41/0.71 % (3547810)Time elapsed: 0.099 s
% 1.41/0.71 % (3547810)Peak memory usage: 13 MB
% 1.41/0.71 % (3547810)Instructions burned: 104 (million)
% 1.41/0.71 % (3547811)Instruction limit reached!
% 1.41/0.71 % (3547811)------------------------------
% 1.41/0.71 % (3547811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547811)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547811)Termination reason: Instruction limit
% 1.41/0.71 % (3547811)Termination phase: Saturation
% 1.41/0.71 % (3547811)Time elapsed: 0.111 s
% 1.41/0.71 % (3547811)Peak memory usage: 14 MB
% 1.41/0.71 % (3547811)Instructions burned: 116 (million)
% 1.41/0.71 % (3547812)Instruction limit reached!
% 1.41/0.71 % (3547812)------------------------------
% 1.41/0.71 % (3547812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547812)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547812)Termination reason: Instruction limit
% 1.41/0.71 % (3547812)Termination phase: Saturation
% 1.41/0.71 % (3547812)Time elapsed: 0.123 s
% 1.41/0.71 % (3547812)Peak memory usage: 14 MB
% 1.41/0.71 % (3547812)Instructions burned: 131 (million)
% 1.41/0.71 % (3547825)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=383948209:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.41/0.71 % (3547826)ott-21_1_sil=16000:fs=off:random_seed=2819986118:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.41/0.71 % (3547823)Instruction limit reached!
% 1.41/0.71 % (3547823)------------------------------
% 1.41/0.71 % (3547823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547823)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547823)Termination reason: Instruction limit
% 1.41/0.71 % (3547823)Termination phase: Saturation
% 1.41/0.71 % (3547823)Time elapsed: 0.070 s
% 1.41/0.71 % (3547823)Peak memory usage: 14 MB
% 1.41/0.71 % (3547823)Instructions burned: 132 (million)
% 1.41/0.71 % (3547827)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2438744847:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.41/0.71 % (3547813)Instruction limit reached!
% 1.41/0.71 % (3547813)------------------------------
% 1.41/0.71 % (3547813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.71 % (3547813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.71 % (3547813)CaDiCaL version: 2.1.3
% 1.41/0.71 % (3547813)Termination reason: Instruction limit
% 1.41/0.71 % (3547813)Termination phase: Saturation
% 1.41/0.71 % (3547813)Time elapsed: 0.163 s
% 1.41/0.71 % (3547813)Peak memory usage: 14 MB
% 1.41/0.71 % (3547813)Instructions burned: 159 (million)
% 1.41/0.71 % (3547825) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3547802-3547825"...
% 1.41/0.71 % (3547825)...printing done.
% 1.41/0.71 % (3547825)Refutation found. Thanks to Tanya!
% 1.41/0.71 % SZS status Theorem for theBenchmark
% 1.41/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.72 % (3547825)------------------------------
% 1.41/0.72 % (3547825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.72 % (3547825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.72 % (3547825)CaDiCaL version: 2.1.3
% 1.41/0.72 % (3547825)Termination reason: Refutation
% 1.41/0.72 % (3547825)Time elapsed: 0.040 s
% 1.41/0.72 % (3547825)Peak memory usage: 15 MB
% 1.41/0.72 % (3547825)Instructions burned: 65 (million)
% 1.41/0.72 % (3547802)Success in time 0.235 s
% 1.41/0.72 % Vampire exiting
%------------------------------------------------------------------------------