%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP332_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:33:38 AM UTC 2026
% Result : Theorem 7.99s 2.31s
% Output : Refutation 9.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 94 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 49 ~; 37 |; 12 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 21 ( 19 usr; 4 prp; 0-2 aty)
% Number of functors : 93 ( 93 usr; 13 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn 47 !; 8 ?; 55 :)
% 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 > $real ).
tff(func_def_96,type,
sK0: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_97,type,
sK1: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_98,type,
sK2: ( 'A_n_vec_m_vec$' * 'A_n_vec_m_vec$' ) > 'A_m_vec_m_vec$' ).
tff(func_def_99,type,
sK3: 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
tff(func_def_100,type,
sK4: 'A_m_vec_m_vec$' > '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$' > $o ).
tff(f1,conjecture,
'thesis$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture0) ).
tff(f2,negated_conjecture,
~ 'thesis$',
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,axiom,
! [X1: 'A_n_vec_n_vec$',X0: 'A_m_vec_m_vec$'] :
( ( 'invertible$'(X0)
& 'invertible$a'(X1)
& ( 'b$' = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) )
=> 'thesis$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis1) ).
tff(f4,axiom,
'equivalent_matrices$'('a$','b$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f10,axiom,
! [X1: 'A_n_vec_m_vec$',X0: 'A_n_vec_m_vec$'] :
( ? [X3: 'A_n_vec_n_vec$',X2: 'A_m_vec_m_vec$'] :
( ( X1 = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) )
& 'invertible$a'(X3)
& 'invertible$'(X2) )
<=> 'equivalent_matrices$'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
tff(f18,axiom,
! [X2: 'A_n_vec_n_vec$',X1: 'A_n_vec_m_vec$',X0: 'A_m_vec_m_vec$'] : ( 'matrix_matrix_mult$a'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
tff(f852,plain,
~ 'thesis$',
inference(flattening,[],[f2]) ).
tff(f853,plain,
! [X0: 'A_n_vec_n_vec$',X2: 'A_m_vec_m_vec$',X1: 'A_n_vec_m_vec$'] : ( 'matrix_matrix_mult$a'(X2,'matrix_matrix_mult$'(X1,X0)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X2,X1),X0) ),
inference(rectify,[],[f18]) ).
tff(f857,plain,
! [X1: 'A_n_vec_m_vec$',X0: 'A_n_vec_m_vec$'] :
( 'equivalent_matrices$'(X0,X1)
=> ? [X3: 'A_n_vec_n_vec$',X2: 'A_m_vec_m_vec$'] :
( ( X1 = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) )
& 'invertible$a'(X3)
& 'invertible$'(X2) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
tff(f863,plain,
! [X1: 'A_n_vec_m_vec$',X0: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'(X0,X1)
| ? [X3: 'A_n_vec_n_vec$',X2: 'A_m_vec_m_vec$'] :
( ( X1 = 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X2),X0),X3) )
& 'invertible$a'(X3)
& 'invertible$'(X2) ) ),
inference(ennf_transformation,[],[f857]) ).
tff(f864,plain,
! [X1: 'A_n_vec_n_vec$',X0: 'A_m_vec_m_vec$'] :
( 'thesis$'
| ~ 'invertible$'(X0)
| ~ 'invertible$a'(X1)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f865,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ~ 'invertible$'(X0)
| 'thesis$'
| ~ 'invertible$a'(X1)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ),
inference(flattening,[],[f864]) ).
tff(f869,plain,
! [X0: 'A_n_vec_n_vec$',X1: 'A_m_vec_m_vec$',X2: 'A_n_vec_m_vec$'] : ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X1,X2),X0) = 'matrix_matrix_mult$a'(X1,'matrix_matrix_mult$'(X2,X0)) ),
inference(rectify,[],[f853]) ).
tff(f873,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'(X1,X0)
| ? [X2: 'A_n_vec_n_vec$',X3: 'A_m_vec_m_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X3),X1),X2) = X0 )
& 'invertible$a'(X2)
& 'invertible$'(X3) ) ),
inference(rectify,[],[f863]) ).
tff(f874,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'(X1,X0)
| ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK2(X0,X1)),X1),sK1(X0,X1)) = X0 )
& 'invertible$a'(sK1(X0,X1))
& 'invertible$'(sK2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1))],[f873]) ).
tff(f882,plain,
~ 'thesis$',
inference(cnf_transformation,[],[f852]) ).
tff(f885,plain,
! [X2: 'A_n_vec_m_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_m_vec_m_vec$'] : ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X1,X2),X0) = 'matrix_matrix_mult$a'(X1,'matrix_matrix_mult$'(X2,X0)) ),
inference(cnf_transformation,[],[f869]) ).
tff(f888,plain,
'equivalent_matrices$'('a$','b$'),
inference(cnf_transformation,[],[f4]) ).
tff(f889,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$'(sK2(X0,X1))
| ~ 'equivalent_matrices$'(X1,X0) ),
inference(cnf_transformation,[],[f874]) ).
tff(f890,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( 'invertible$a'(sK1(X0,X1))
| ~ 'equivalent_matrices$'(X1,X0) ),
inference(cnf_transformation,[],[f874]) ).
tff(f891,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ( 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(sK2(X0,X1)),X1),sK1(X0,X1)) = X0 )
| ~ 'equivalent_matrices$'(X1,X0) ),
inference(cnf_transformation,[],[f874]) ).
tff(f902,plain,
! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ~ 'invertible$'(X0)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) )
| 'thesis$'
| ~ 'invertible$a'(X1) ),
inference(cnf_transformation,[],[f865]) ).
tff(f904,definition,
( spl5_1
<=> ! [X0: 'A_m_vec_m_vec$',X1: 'A_n_vec_n_vec$'] :
( ~ 'invertible$'(X0)
| ~ 'invertible$a'(X1)
| ( 'b$' != 'matrix_matrix_mult$'('matrix_matrix_mult$a'('matrix_inv$'(X0),'a$'),X1) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f905,plain,
( ! [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$a'(X1) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f904]) ).
tff(f907,definition,
( spl5_2
<=> 'thesis$' ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f910,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f902,f907,f904]) ).
tff(f911,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f882,f907]) ).
tff(f965,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$'(X0) )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f905,f885]) ).
tff(f981,plain,
! [X0: 'A_n_vec_m_vec$',X1: 'A_n_vec_m_vec$'] :
( ( 'matrix_matrix_mult$a'('matrix_inv$'(sK2(X0,X1)),'matrix_matrix_mult$'(X1,sK1(X0,X1))) = X0 )
| ~ 'equivalent_matrices$'(X1,X0) ),
inference(forward_demodulation,[],[f891,f885]) ).
tff(f995,plain,
( ! [X0: 'A_n_vec_m_vec$'] :
( ~ 'invertible$a'(sK1(X0,'a$'))
| ~ 'invertible$'(sK2(X0,'a$'))
| ( 'b$' != X0 )
| ~ 'equivalent_matrices$'('a$',X0) )
| ~ spl5_1 ),
inference(superposition,[],[f965,f981]) ).
tff(f998,plain,
( ! [X0: 'A_n_vec_m_vec$'] :
( ~ 'equivalent_matrices$'('a$',X0)
| ~ 'invertible$'(sK2(X0,'a$'))
| ( 'b$' != X0 ) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f995,f890]) ).
tff(f999,plain,
( ! [X0: 'A_n_vec_m_vec$'] :
( ( 'b$' != X0 )
| ~ 'equivalent_matrices$'('a$',X0) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f998,f889]) ).
tff(f1018,plain,
( ~ 'equivalent_matrices$'('a$','b$')
| ~ spl5_1 ),
inference(equality_resolution,[],[f999]) ).
tff(f1019,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f1018,f888]) ).
tff(f1020,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f1019]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f910]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f911]) ).
cnf(s7,plain,
~ spl5_1,
inference(sat_conversion,[],[f1020]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s2,s7]) ).
tff(f1021,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP332_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 12:56:53 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/1.98 % (2324631)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.71/1.98 % (2324637)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3726258944:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.71/1.98 % (2324640)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1063706752:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.71/1.98 % (2324640)Instruction limit reached!
% 4.71/1.98 % (2324640)------------------------------
% 4.71/1.98 % (2324640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.98 % (2324640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.98 % (2324640)CaDiCaL version: 2.1.3
% 4.71/1.98 % (2324640)Termination reason: Instruction limit
% 4.71/1.98 % (2324640)Termination phase: Property scanning
% 4.71/1.98 % (2324640)Time elapsed: 0.005 s
% 4.71/1.98 % (2324640)Peak memory usage: 86 MB
% 4.71/1.98 % (2324640)Instructions burned: 4 (million)
% 4.71/1.98 % (2324636)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3530871620:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.71/1.98 % (2324642)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=21418869:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.71/1.98 % (2324641)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=6314002:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.71/1.98 % (2324639)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=87851529:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.71/1.98 % (2324638)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1363133780:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.71/1.98 % (2324639)Instruction limit reached!
% 4.71/1.98 % (2324639)------------------------------
% 4.71/1.98 % (2324639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.98 % (2324639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.98 % (2324639)CaDiCaL version: 2.1.3
% 4.71/1.98 % (2324639)Termination reason: Instruction limit
% 4.71/1.98 % (2324639)Termination phase: Property scanning
% 4.71/1.98 % (2324639)Time elapsed: 0.007 s
% 4.71/1.98 % (2324639)Peak memory usage: 86 MB
% 4.71/1.98 % (2324639)Instructions burned: 7 (million)
% 4.71/1.98 % (2324636)Instruction limit reached!
% 4.71/1.98 % (2324636)------------------------------
% 4.71/1.98 % (2324636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.98 % (2324636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.98 % (2324636)CaDiCaL version: 2.1.3
% 4.71/1.98 % (2324636)Termination reason: Instruction limit
% 4.71/1.98 % (2324636)Termination phase: Property scanning
% 4.71/1.98 % (2324636)Time elapsed: 0.012 s
% 4.71/1.98 % (2324636)Peak memory usage: 85 MB
% 4.71/1.98 % (2324636)Instructions burned: 12 (million)
% 4.71/1.98 % (2324642)Instruction limit reached!
% 4.71/1.98 % (2324642)------------------------------
% 4.71/1.98 % (2324642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.98 % (2324642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.98 % (2324642)CaDiCaL version: 2.1.3
% 4.71/1.98 % (2324642)Termination reason: Instruction limit
% 4.71/1.98 % (2324642)Termination phase: Property scanning
% 4.71/1.98 % (2324642)Time elapsed: 0.031 s
% 4.71/1.98 % (2324642)Peak memory usage: 88 MB
% 4.71/1.98 % (2324642)Instructions burned: 33 (million)
% 4.71/1.98 % (2324641)Instruction limit reached!
% 4.71/1.98 % (2324641)------------------------------
% 4.71/1.98 % (2324641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.98 % (2324641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.98 % (2324641)CaDiCaL version: 2.1.3
% 4.71/1.98 % (2324641)Termination reason: Instruction limit
% 4.71/1.98 % (2324641)Termination phase: Saturation
% 4.71/1.98 % (2324641)Time elapsed: 0.069 s
% 4.71/1.98 % (2324641)Peak memory usage: 106 MB
% 4.71/1.98 % (2324641)Instructions burned: 46 (million)
% 4.71/1.98 % (2324645)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=420142272:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 4.71/1.98 % (2324645)Instruction limit reached!
% 4.71/1.98 % (2324645)------------------------------
% 7.81/2.28 % (2324645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.28 % (2324645)CaDiCaL version: 2.1.3
% 7.81/2.28 % (2324645)Termination reason: Instruction limit
% 7.81/2.28 % (2324645)Termination phase: Preprocessing 1
% 7.81/2.28 % (2324645)Time elapsed: 0.015 s
% 7.81/2.28 % (2324645)Peak memory usage: 86 MB
% 7.81/2.28 % (2324645)Instructions burned: 14 (million)
% 7.81/2.28 % (2324651)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3545257644:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 7.81/2.28 % (2324651)Instruction limit reached!
% 7.81/2.28 % (2324651)------------------------------
% 7.81/2.28 % (2324651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.28 % (2324651)CaDiCaL version: 2.1.3
% 7.81/2.28 % (2324651)Termination reason: Instruction limit
% 7.81/2.28 % (2324651)Termination phase: Property scanning
% 7.81/2.28 % (2324651)Time elapsed: 0.015 s
% 7.81/2.28 % (2324651)Peak memory usage: 88 MB
% 7.81/2.28 % (2324651)Instructions burned: 31 (million)
% 7.81/2.28 % (2324638)Instruction limit reached!
% 7.81/2.28 % (2324638)------------------------------
% 7.81/2.28 % (2324638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.28 % (2324638)CaDiCaL version: 2.1.3
% 7.81/2.28 % (2324638)Termination reason: Instruction limit
% 7.81/2.28 % (2324638)Termination phase: Saturation
% 7.81/2.28 % (2324638)Time elapsed: 0.264 s
% 7.81/2.28 % (2324638)Peak memory usage: 118 MB
% 7.81/2.28 % (2324638)Instructions burned: 201 (million)
% 7.81/2.28 % (2324652)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2597950906:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 7.81/2.28 % (2324637)Instruction limit reached!
% 7.81/2.28 % (2324637)------------------------------
% 7.81/2.28 % (2324637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.28 % (2324637)CaDiCaL version: 2.1.3
% 7.81/2.28 % (2324637)Termination reason: Instruction limit
% 7.81/2.28 % (2324637)Termination phase: Saturation
% 7.81/2.28 % (2324637)Time elapsed: 0.357 s
% 7.81/2.28 % (2324637)Peak memory usage: 119 MB
% 7.81/2.28 % (2324637)Instructions burned: 308 (million)
% 7.81/2.28 % (2324653)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1933726816:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 7.81/2.28 % (2324652)Instruction limit reached!
% 7.81/2.28 % (2324652)------------------------------
% 7.81/2.28 % (2324652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.28 % (2324652)CaDiCaL version: 2.1.3
% 7.81/2.28 % (2324652)Termination reason: Instruction limit
% 7.81/2.28 % (2324652)Termination phase: Preprocessing 3
% 7.81/2.28 % (2324652)Time elapsed: 0.018 s
% 7.81/2.28 % (2324652)Peak memory usage: 87 MB
% 7.81/2.28 % (2324652)Instructions burned: 16 (million)
% 7.81/2.28 % (2324653)Instruction limit reached!
% 7.81/2.28 % (2324653)------------------------------
% 7.81/2.28 % (2324653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.28 % (2324653)CaDiCaL version: 2.1.3
% 7.81/2.28 % (2324653)Termination reason: Instruction limit
% 7.81/2.28 % (2324653)Termination phase: Preprocessing 3
% 7.81/2.28 % (2324653)Time elapsed: 0.025 s
% 7.81/2.28 % (2324653)Peak memory usage: 88 MB
% 7.81/2.28 % (2324653)Instructions burned: 25 (million)
% 7.81/2.28 % (2324654)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=3470748198:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 7.81/2.28 % (2324654)Instruction limit reached!
% 7.81/2.28 % (2324654)------------------------------
% 7.81/2.28 % (2324654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.28 % (2324654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324654)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324654)Termination reason: Instruction limit
% 7.99/2.31 % (2324654)Termination phase: Clausification
% 7.99/2.31 % (2324654)Time elapsed: 0.029 s
% 7.99/2.31 % (2324654)Peak memory usage: 88 MB
% 7.99/2.31 % (2324654)Instructions burned: 27 (million)
% 7.99/2.31 % (2324658)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=1705005805:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2994 on theBenchmark for (2994ds/2Mi)
% 7.99/2.31 % (2324658)Instruction limit reached!
% 7.99/2.31 % (2324658)------------------------------
% 7.99/2.31 % (2324658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324658)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324658)Termination reason: Instruction limit
% 7.99/2.31 % (2324658)Termination phase: Property scanning
% 7.99/2.31 % (2324658)Time elapsed: 0.003 s
% 7.99/2.31 % (2324658)Peak memory usage: 86 MB
% 7.99/2.31 % (2324658)Instructions burned: 3 (million)
% 7.99/2.31 % (2324657)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2564394452:i=85:gtgl=4:rtra=on:gtg=exists_sym_2995 on theBenchmark for (2995ds/85Mi)
% 7.99/2.31 % (2324659)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2614715330:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 7.99/2.31 % (2324659)First to succeed.
% 7.99/2.31 % (2324659)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2324631"
% 7.99/2.31 % (2324661)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=2642012781:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 7.99/2.31 % (2324657)Instruction limit reached!
% 7.99/2.31 % (2324657)------------------------------
% 7.99/2.31 % (2324657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324657)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324657)Termination reason: Instruction limit
% 7.99/2.31 % (2324657)Termination phase: Saturation
% 7.99/2.31 % (2324657)Time elapsed: 0.082 s
% 7.99/2.31 % (2324657)Peak memory usage: 90 MB
% 7.99/2.31 % (2324657)Instructions burned: 85 (million)
% 7.99/2.31 % (2324661)Instruction limit reached!
% 7.99/2.31 % (2324661)------------------------------
% 7.99/2.31 % (2324661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324661)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324661)Termination reason: Instruction limit
% 7.99/2.31 % (2324661)Termination phase: Property scanning
% 7.99/2.31 % (2324661)Time elapsed: 0.007 s
% 7.99/2.31 % (2324661)Peak memory usage: 86 MB
% 7.99/2.31 % (2324661)Instructions burned: 7 (million)
% 7.99/2.31 % (2324663)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=1409367968:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2994 on theBenchmark for (2994ds/66Mi)
% 7.99/2.31 % (2324664)lrs+10_1_thi=all:si=on:fd=off:random_seed=3069086296:i=53:rtra=on:gtg=all_2993 on theBenchmark for (2993ds/53Mi)
% 7.99/2.31 % (2324668)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=2603533253:st=3:i=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/2Mi)
% 7.99/2.31 % (2324668)Instruction limit reached!
% 7.99/2.31 % (2324668)------------------------------
% 7.99/2.31 % (2324668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324668)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324668)Termination reason: Instruction limit
% 7.99/2.31 % (2324668)Termination phase: Property scanning
% 7.99/2.31 % (2324668)Time elapsed: 0.003 s
% 7.99/2.31 % (2324668)Peak memory usage: 86 MB
% 7.99/2.31 % (2324668)Instructions burned: 4 (million)
% 7.99/2.31 % (2324666)ott+1011_1_to=kbo:plsq=on:drc=off:si=on:plsqr=32,1:sp=const_frequency:sos=all:uwa=one_side_interpreted:sac=on:random_seed=1528785455:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/8Mi)
% 7.99/2.31 % (2324666)Instruction limit reached!
% 7.99/2.31 % (2324666)------------------------------
% 7.99/2.31 % (2324666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324666)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324666)Termination reason: Instruction limit
% 7.99/2.31 % (2324666)Termination phase: shuffling
% 7.99/2.31 % (2324666)Time elapsed: 0.009 s
% 7.99/2.31 % (2324666)Peak memory usage: 86 MB
% 7.99/2.31 % (2324666)Instructions burned: 8 (million)
% 7.99/2.31 % (2324664)Instruction limit reached!
% 7.99/2.31 % (2324664)------------------------------
% 7.99/2.31 % (2324664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324664)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324664)Termination reason: Instruction limit
% 7.99/2.31 % (2324664)Termination phase: Equality resolution with deletion
% 7.99/2.31 % (2324664)Time elapsed: 0.050 s
% 7.99/2.31 % (2324664)Peak memory usage: 88 MB
% 7.99/2.31 % (2324664)Instructions burned: 53 (million)
% 7.99/2.31 % (2324663)Instruction limit reached!
% 7.99/2.31 % (2324663)------------------------------
% 7.99/2.31 % (2324663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324663)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324663)Termination reason: Instruction limit
% 7.99/2.31 % (2324663)Termination phase: Saturation
% 7.99/2.31 % (2324663)Time elapsed: 0.117 s
% 7.99/2.31 % (2324663)Peak memory usage: 131 MB
% 7.99/2.31 % (2324663)Instructions burned: 66 (million)
% 7.99/2.31 % (2324672)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=2883912145:i=2:doe=on:canc=force:asg=cautious:rtra=on_2991 on theBenchmark for (2991ds/2Mi)
% 7.99/2.31 % (2324672)Instruction limit reached!
% 7.99/2.31 % (2324672)------------------------------
% 7.99/2.31 % (2324672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324672)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324672)Termination reason: Instruction limit
% 7.99/2.31 % (2324672)Termination phase: Property scanning
% 7.99/2.31 % (2324672)Time elapsed: 0.002 s
% 7.99/2.31 % (2324672)Peak memory usage: 86 MB
% 7.99/2.31 % (2324672)Instructions burned: 3 (million)
% 7.99/2.31 % (2324673)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=4132115190:i=127:doe=on:rtra=on_2991 on theBenchmark for (2991ds/127Mi)
% 7.99/2.31 % (2324677)dis+10_1_si=on:random_seed=1255301073:i=10:ep=R:rtra=on_2991 on theBenchmark for (2991ds/10Mi)
% 7.99/2.31 % (2324677)Instruction limit reached!
% 7.99/2.31 % (2324677)------------------------------
% 7.99/2.31 % (2324677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324677)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324677)Termination reason: Instruction limit
% 7.99/2.31 % (2324677)Termination phase: Property scanning
% 7.99/2.31 % (2324677)Time elapsed: 0.011 s
% 7.99/2.31 % (2324677)Peak memory usage: 86 MB
% 7.99/2.31 % (2324677)Instructions burned: 11 (million)
% 7.99/2.31 % (2324680)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=4152364667:avsq=on:i=35:doe=on:thsqd=64:nm=64:fsr=off:thsqc=32:rtra=on:tac=light:ss=included:thsq=on:ev=off:sgt=32_2990 on theBenchmark for (2990ds/35Mi)
% 7.99/2.31 % (2324679)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=3131147674:i=26:canc=cautious:av=off:rtra=on_2990 on theBenchmark for (2990ds/26Mi)
% 7.99/2.31 % (2324679)Instruction limit reached!
% 7.99/2.31 % (2324679)------------------------------
% 7.99/2.31 % (2324679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324679)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324679)Termination reason: Instruction limit
% 7.99/2.31 % (2324679)Termination phase: Preprocessing 3
% 7.99/2.31 % (2324679)Time elapsed: 0.027 s
% 7.99/2.31 % (2324679)Peak memory usage: 88 MB
% 7.99/2.31 % (2324679)Instructions burned: 26 (million)
% 7.99/2.31 % (2324680)Instruction limit reached!
% 7.99/2.31 % (2324680)------------------------------
% 7.99/2.31 % (2324680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324680)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324680)Termination reason: Instruction limit
% 7.99/2.31 % (2324680)Termination phase: Property scanning
% 7.99/2.31 % (2324680)Time elapsed: 0.035 s
% 7.99/2.31 % (2324680)Peak memory usage: 88 MB
% 7.99/2.31 % (2324680)Instructions burned: 37 (million)
% 7.99/2.31 % (2324683)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=2453199530:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2989 on theBenchmark for (2989ds/8Mi)
% 7.99/2.31 % (2324683)Instruction limit reached!
% 7.99/2.31 % (2324683)------------------------------
% 7.99/2.31 % (2324683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324683)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324683)Termination reason: Instruction limit
% 7.99/2.31 % (2324683)Termination phase: Property scanning
% 7.99/2.31 % (2324683)Time elapsed: 0.004 s
% 7.99/2.31 % (2324683)Peak memory usage: 86 MB
% 7.99/2.31 % (2324683)Instructions burned: 9 (million)
% 7.99/2.31 % (2324681)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=1582738914:i=2:fsr=off:rtra=on:inst=on_2990 on theBenchmark for (2990ds/2Mi)
% 7.99/2.31 % (2324681)Instruction limit reached!
% 7.99/2.31 % (2324681)------------------------------
% 7.99/2.31 % (2324681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.99/2.31 % (2324681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.99/2.31 % (2324681)CaDiCaL version: 2.1.3
% 7.99/2.31 % (2324681)Termination reason: Instruction limit
% 7.99/2.31 % (2324681)Termination phase: Property scanning
% 7.99/2.31 % (2324681)Time elapsed: 0.004 s
% 7.99/2.31 % (2324681)Peak memory usage: 86 MB
% 7.99/2.31 % (2324681)Instructions burned: 2 (million)
% 7.99/2.31 % (2324659)Refutation found. Thanks to Tanya!
% 7.99/2.31 % SZS status Theorem for theBenchmark
% 7.99/2.31 % SZS output start Proof for theBenchmark
% See solution above
% 9.27/2.54 % (2324659)------------------------------
% 9.27/2.54 % (2324659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.54 % (2324659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.54 % (2324659)CaDiCaL version: 2.1.3
% 9.27/2.54 % (2324659)Termination reason: Refutation
% 9.27/2.54 % (2324659)Time elapsed: 0.022 s
% 9.27/2.54 % (2324659)Peak memory usage: 91 MB
% 9.27/2.54 % (2324659)Instructions burned: 17 (million)
% 9.27/2.54 % (2324659)------------------------------
% 9.27/2.54 % (2324659)------------------------------
% 9.27/2.54 % (2324631)Success in time 1.233 s
% 9.27/2.54 % Vampire exiting
%------------------------------------------------------------------------------