%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP345_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:33:40 AM UTC 2026
% Result : Theorem 4.08s 1.59s
% Output : Refutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 85 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 39 ~; 31 |; 1 &)
% ( 4 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 52 ( 26 atm; 0 fun; 26 num; 0 var)
% Number of types : 49 ( 46 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 21 usr; 3 prp; 0-3 aty)
% Number of functors : 137 ( 136 usr; 42 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Nat_set_set$': $tType ).
tff(type_def_6,type,
'Real_real_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'Int_bool_fun$': $tType ).
tff(type_def_8,type,
'A_rows_vec_a_rows_vec_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'A_rows_vec_a_rows_vec_fun$': $tType ).
tff(type_def_10,type,
'A_n_vec_real_fun$': $tType ).
tff(type_def_11,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_12,type,
'A_a_rows_vec_a_rows_vec_fun_fun$': $tType ).
tff(type_def_13,type,
'Rows$': $tType ).
tff(type_def_14,type,
'Int_real_fun$': $tType ).
tff(type_def_15,type,
'A_n_vec_set$': $tType ).
tff(type_def_16,type,
'Int_set$': $tType ).
tff(type_def_17,type,
'Int_int_fun$': $tType ).
tff(type_def_18,type,
'A_rows_vec_set$': $tType ).
tff(type_def_19,type,
'Real_set_bool_fun$': $tType ).
tff(type_def_20,type,
'A_n_vec_a_n_vec_bool_fun_fun$': $tType ).
tff(type_def_21,type,
'Nat_nat_fun$': $tType ).
tff(type_def_22,type,
'Nat$': $tType ).
tff(type_def_23,type,
'A_a_n_vec_a_n_vec_fun_fun$': $tType ).
tff(type_def_24,type,
'A_n_vec_set_bool_fun$': $tType ).
tff(type_def_25,type,
'A_rows_vec$': $tType ).
tff(type_def_26,type,
'A_n_vec_rows_vec$': $tType ).
tff(type_def_27,type,
tlbool: $tType ).
tff(type_def_28,type,
'Real_real_fun$': $tType ).
tff(type_def_29,type,
'Nat_real_fun$': $tType ).
tff(type_def_30,type,
'Nat_set_bool_fun$': $tType ).
tff(type_def_31,type,
'A_n_vec_set_set$': $tType ).
tff(type_def_32,type,
'Real_real_real_fun_fun$': $tType ).
tff(type_def_33,type,
'Real_int_fun$': $tType ).
tff(type_def_34,type,
'A$': $tType ).
tff(type_def_35,type,
'A_rows_vec_bool_fun$': $tType ).
tff(type_def_36,type,
'A_n_vec$': $tType ).
tff(type_def_37,type,
'Real_set_nat_fun$': $tType ).
tff(type_def_38,type,
'Int_set_bool_fun$': $tType ).
tff(type_def_39,type,
'A_n_vec_a_n_vec_fun$': $tType ).
tff(type_def_40,type,
'A_rows_vec_rows_vec$': $tType ).
tff(type_def_41,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_42,type,
'A_n_vec_int_fun$': $tType ).
tff(type_def_43,type,
'Nat_bool_fun$': $tType ).
tff(type_def_44,type,
'Real_bool_fun$': $tType ).
tff(type_def_45,type,
'Real_set$': $tType ).
tff(type_def_46,type,
'A_n_vec_bool_fun$': $tType ).
tff(type_def_47,type,
'Nat_set$': $tType ).
tff(type_def_48,type,
'A_rows_vec_set_nat_fun$': $tType ).
tff(type_def_49,type,
'Nat_int_fun$': $tType ).
tff(type_def_50,type,
'A_n_vec_set_nat_fun$': $tType ).
tff(func_def_0,type,
'fun_app$ab': ( 'A_n_vec_real_fun$' * 'A_n_vec$' ) > $real ).
tff(func_def_1,type,
'fun_app$u': ( 'Real_real_bool_fun_fun$' * $real ) > 'Real_bool_fun$' ).
tff(func_def_2,type,
'a$': 'A_n_vec_rows_vec$' ).
tff(func_def_3,type,
'times$b': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_4,type,
'fun_app$r': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_5,type,
'collect$a': 'A_rows_vec_bool_fun$' > 'A_rows_vec_set$' ).
tff(func_def_6,type,
'fun_app$x': ( 'A_n_vec_int_fun$' * 'A_n_vec$' ) > $int ).
tff(func_def_7,type,
'bot$': 'A_rows_vec_set$' ).
tff(func_def_8,type,
'insert$b': ( 'Nat$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_9,type,
'insert$c': ( $int * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_10,type,
'fun_app$m': ( 'A_rows_vec_a_rows_vec_fun$' * 'A_rows_vec$' ) > 'A_rows_vec$' ).
tff(func_def_11,type,
'bot$f': 'A_n_vec_set_set$' ).
tff(func_def_12,type,
'dim$': 'A_a_n_vec_a_n_vec_fun_fun$' > 'A_n_vec_set_nat_fun$' ).
tff(func_def_13,type,
'fun_app$s': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_14,type,
'card$a': 'Nat_set$' > 'Nat$' ).
tff(func_def_15,type,
'zero$a': 'A_n_vec$' ).
tff(func_def_16,type,
'times$f': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_17,type,
'enumerate$': 'Nat_set$' > 'Nat_nat_fun$' ).
tff(func_def_18,type,
'fun_app$l': ( 'A_rows_vec_set_nat_fun$' * 'A_rows_vec_set$' ) > 'Nat$' ).
tff(func_def_19,type,
'less_eq$c': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_20,type,
'member$c': 'Nat$' > 'Nat_set_bool_fun$' ).
tff(func_def_21,type,
'card$': 'A_n_vec_set$' > 'Nat$' ).
tff(func_def_22,type,
'fun_app$w': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_23,type,
'fun_app$aa': ( 'Real_real_fun$' * $real ) > $real ).
tff(func_def_24,type,
'card$b': 'Real_set$' > 'Nat$' ).
tff(func_def_25,type,
'collect$d': 'Nat_bool_fun$' > 'Nat_set$' ).
tff(func_def_26,type,
'uuc$': 'Real_set$' > 'Real_bool_fun$' ).
tff(func_def_27,type,
'vector_scalar_mult$a': 'A_a_rows_vec_a_rows_vec_fun_fun$' ).
tff(func_def_28,type,
'uua$': 'A_rows_vec_set$' > 'A_rows_vec_bool_fun$' ).
tff(func_def_29,type,
'of_nat$a': 'Nat_nat_fun$' ).
tff(func_def_30,type,
'fun_app$o': ( 'A_n_vec_a_n_vec_fun$' * 'A_n_vec$' ) > 'A_n_vec$' ).
tff(func_def_31,type,
'fun_app$z': ( 'Int_real_fun$' * $int ) > $real ).
tff(func_def_32,type,
'less$d': 'Nat_set$' > 'Nat_set_bool_fun$' ).
tff(func_def_33,type,
'fun_app$j': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_34,type,
'one$c': 'Nat$' ).
tff(func_def_35,type,
'finite$': 'A_n_vec_set_bool_fun$' ).
tff(func_def_36,type,
'arg_min_on$a': ( 'Nat_int_fun$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_37,type,
'member$b': $real > 'Real_set_bool_fun$' ).
tff(func_def_38,type,
'is_solution$a': ( 'A_n_vec$' * 'A_n_vec_rows_vec$' ) > 'A_rows_vec_bool_fun$' ).
tff(func_def_39,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_40,type,
'uud$': 'Nat_set$' > 'Nat_bool_fun$' ).
tff(func_def_41,type,
'fun_app$a': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_42,type,
'one$': 'A$' ).
tff(func_def_43,type,
'zero$': 'A_rows_vec$' ).
tff(func_def_44,type,
'arg_min_on$': ( 'A_n_vec_int_fun$' * 'A_n_vec_set$' ) > 'A_n_vec$' ).
tff(func_def_45,type,
'null_space$': 'A_rows_vec_rows_vec$' > 'A_rows_vec_set$' ).
tff(func_def_46,type,
'null_space$a': 'A_n_vec_rows_vec$' > 'A_n_vec_set$' ).
tff(func_def_47,type,
'vec$': 'A$' > 'A_rows_vec$' ).
tff(func_def_48,type,
'less$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_49,type,
'of_nat$d': 'Nat$' > 'A$' ).
tff(func_def_50,type,
'fun_app$ad': ( 'Real_real_real_fun_fun$' * $real ) > 'Real_real_fun$' ).
tff(func_def_51,type,
'times$': 'Real_real_real_fun_fun$' ).
tff(func_def_52,type,
'less_eq$d': 'Real_set$' > 'Real_set_bool_fun$' ).
tff(func_def_53,type,
tltrue: tlbool ).
tff(func_def_54,type,
'uu$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
tff(func_def_55,type,
'zero$d': 'A_rows_vec_set$' ).
tff(func_def_56,type,
'finite$d': 'Nat_set_bool_fun$' ).
tff(func_def_57,type,
'of_nat$c': 'Nat$' > 'A_rows_vec$' ).
tff(func_def_58,type,
'dim$b': 'Real_real_real_fun_fun$' > 'Real_set_nat_fun$' ).
tff(func_def_59,type,
'zero$f': 'Int_set$' ).
tff(func_def_60,type,
'finite$b': 'Int_set_bool_fun$' ).
tff(func_def_61,type,
'less_eq$a': 'A_n_vec_set$' > 'A_n_vec_set_bool_fun$' ).
tff(func_def_62,type,
'bot$a': 'A_n_vec_set$' ).
tff(func_def_63,type,
'axis$': ( 'Rows$' * 'A$' ) > 'A_rows_vec$' ).
tff(func_def_64,type,
'insert$d': ( $real * 'Real_set$' ) > 'Real_set$' ).
tff(func_def_65,type,
'times$d': ( 'A$' * 'A$' ) > 'A$' ).
tff(func_def_66,type,
'solution_set$a': ( 'A_rows_vec_rows_vec$' * 'A_rows_vec$' ) > 'A_rows_vec_set$' ).
tff(func_def_67,type,
'fun_app$t': ( 'A_rows_vec_a_rows_vec_bool_fun_fun$' * 'A_rows_vec$' ) > 'A_rows_vec_bool_fun$' ).
tff(func_def_68,type,
'arg_min_on$c': ( 'Nat_real_fun$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_69,type,
'one$a': 'Int_set$' ).
tff(func_def_70,type,
'less_eq$b': 'Nat_set$' > 'Nat_set_bool_fun$' ).
tff(func_def_71,type,
'fun_app$ac': ( 'Real_set_nat_fun$' * 'Real_set$' ) > 'Nat$' ).
tff(func_def_72,type,
'collect$b': 'Int_bool_fun$' > 'Int_set$' ).
tff(func_def_73,type,
'bot$g': 'Nat$' ).
tff(func_def_74,type,
'collect$': 'A_n_vec_bool_fun$' > 'A_n_vec_set$' ).
tff(func_def_75,type,
'bot$e': 'Nat_set_set$' ).
tff(func_def_76,type,
'vector_scalar_mult$': 'A_a_n_vec_a_n_vec_fun_fun$' ).
tff(func_def_77,type,
'fun_app$n': ( 'A_a_rows_vec_a_rows_vec_fun_fun$' * 'A$' ) > 'A_rows_vec_a_rows_vec_fun$' ).
tff(func_def_78,type,
'inconsistent$': 'A_n_vec_rows_vec$' > 'A_rows_vec_bool_fun$' ).
tff(func_def_79,type,
'zero$e': 'Real_set$' ).
tff(func_def_80,type,
'is_singleton$': 'Nat_set_bool_fun$' ).
tff(func_def_81,type,
'insert$': ( 'A_rows_vec$' * 'A_rows_vec_set$' ) > 'A_rows_vec_set$' ).
tff(func_def_82,type,
'bot$h': 'Nat_bool_fun$' ).
tff(func_def_83,type,
'bot$c': 'Int_set$' ).
tff(func_def_84,type,
'is_solution$': ( 'A_rows_vec$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec_bool_fun$' ).
tff(func_def_85,type,
'one$b': 'A_rows_vec$' ).
tff(func_def_86,type,
'fun_app$v': ( 'A_n_vec_a_n_vec_bool_fun_fun$' * 'A_n_vec$' ) > 'A_n_vec_bool_fun$' ).
tff(func_def_87,type,
'less$b': 'Real_set$' > 'Real_set_bool_fun$' ).
tff(func_def_88,type,
tlfalse: tlbool ).
tff(func_def_89,type,
'nat$': $int > 'Nat$' ).
tff(func_def_90,type,
'finite$c': 'Real_set_bool_fun$' ).
tff(func_def_91,type,
'times$c': ( 'A_rows_vec$' * 'A_rows_vec$' ) > 'A_rows_vec$' ).
tff(func_def_92,type,
'fun_app$y': ( 'Real_int_fun$' * $real ) > $int ).
tff(func_def_93,type,
'zero$b': 'A$' ).
tff(func_def_94,type,
'less$a': 'Int_set$' > 'Int_set_bool_fun$' ).
tff(func_def_95,type,
'consistent$': 'A_rows_vec_rows_vec$' > 'A_rows_vec_bool_fun$' ).
tff(func_def_96,type,
'arg_min_on$b': ( 'A_n_vec_real_fun$' * 'A_n_vec_set$' ) > 'A_n_vec$' ).
tff(func_def_97,type,
'fun_app$k': ( 'A_n_vec_set_nat_fun$' * 'A_n_vec_set$' ) > 'Nat$' ).
tff(func_def_98,type,
'uue$': 'Int_int_bool_fun_fun$' ).
tff(func_def_99,type,
'insert$a': ( 'A_n_vec$' * 'A_n_vec_set$' ) > 'A_n_vec_set$' ).
tff(func_def_100,type,
'times$e': ( 'A_n_vec_set$' * 'A_n_vec_set$' ) > 'A_n_vec_set$' ).
tff(func_def_101,type,
'solution_set$': ( 'A_n_vec_rows_vec$' * 'A_rows_vec$' ) > 'A_n_vec_set$' ).
tff(func_def_102,type,
'fun_app$p': ( 'A_a_n_vec_a_n_vec_fun_fun$' * 'A$' ) > 'A_n_vec_a_n_vec_fun$' ).
tff(func_def_103,type,
'collect$c': 'Real_bool_fun$' > 'Real_set$' ).
tff(func_def_104,type,
'fun_app$q': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_105,type,
'times$a': $int > 'Int_int_fun$' ).
tff(func_def_106,type,
'less$c': 'A_n_vec_set$' > 'A_n_vec_set_bool_fun$' ).
tff(func_def_107,type,
'of_nat$b': 'Nat_real_fun$' ).
tff(func_def_108,type,
'consistent$a': 'A_n_vec_rows_vec$' > 'A_rows_vec_bool_fun$' ).
tff(func_def_109,type,
'member$a': 'A_n_vec$' > 'A_n_vec_set_bool_fun$' ).
tff(func_def_110,type,
'bot$d': 'Nat_set$' ).
tff(func_def_111,type,
'uub$': 'Int_set$' > 'Int_bool_fun$' ).
tff(func_def_112,type,
'bot$b': 'Real_set$' ).
tff(func_def_113,type,
'member$d': $int > 'Int_set_bool_fun$' ).
tff(func_def_114,type,
'dim$a': 'A_a_rows_vec_a_rows_vec_fun_fun$' > 'A_rows_vec_set_nat_fun$' ).
tff(func_def_115,type,
'zero$c': 'Nat$' ).
tff(func_def_122,type,
sK3: $int > $int ).
tff(func_def_123,type,
sK4: $int > $int ).
tff(func_def_124,type,
sK5: 'A_n_vec_set$' > 'A_n_vec_set$' ).
tff(func_def_125,type,
sK6: 'A_n_vec_set$' > 'A_n_vec$' ).
tff(func_def_126,type,
sK7: 'A_n_vec_set$' > 'A_n_vec_set$' ).
tff(func_def_127,type,
sK8: 'A_n_vec_set$' > 'A_n_vec$' ).
tff(func_def_128,type,
sK9: 'A_n_vec_set_bool_fun$' > 'A_n_vec_set$' ).
tff(func_def_129,type,
sK10: 'A_n_vec_set_bool_fun$' > 'A_n_vec$' ).
tff(func_def_130,type,
sK11: $int > 'Nat$' ).
tff(func_def_131,type,
sK12: $int > 'Nat$' ).
tff(func_def_132,type,
sK13: 'A_n_vec_set_bool_fun$' > 'A_n_vec_set$' ).
tff(func_def_133,type,
sK14: 'A_n_vec_set_bool_fun$' > 'A_n_vec$' ).
tff(func_def_134,type,
sK15: 'A_n_vec_set_bool_fun$' > 'A_n_vec_set$' ).
tff(func_def_135,type,
sK16: 'A_n_vec_set_bool_fun$' > 'A_n_vec$' ).
tff(func_def_136,type,
sK17: 'A_n_vec_set_bool_fun$' > 'A_n_vec_set$' ).
tff(func_def_137,type,
sK18: 'A_n_vec_set_bool_fun$' > 'A_n_vec$' ).
tff(func_def_138,type,
sF19: 'A_n_vec_set_nat_fun$' ).
tff(func_def_139,type,
sF20: 'A_n_vec_set$' ).
tff(func_def_140,type,
sF21: 'Nat$' ).
tff(func_def_141,type,
sF22: $int ).
tff(pred_def_1,type,
'fun_app$i': ( 'Int_set_bool_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_2,type,
'member$f': ( 'A_n_vec_set$' * 'A_n_vec_set_set$' ) > $o ).
tff(pred_def_3,type,
'finite$a': 'A_rows_vec_set$' > $o ).
tff(pred_def_4,type,
'member$': ( 'A_rows_vec$' * 'A_rows_vec_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$g': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_6,type,
'fun_app$b': ( 'A_rows_vec_bool_fun$' * 'A_rows_vec$' ) > $o ).
tff(pred_def_7,type,
'fun_app$': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_8,type,
'finite$f': 'A_n_vec_set_set$' > $o ).
tff(pred_def_9,type,
'fun_app$c': ( 'A_n_vec_bool_fun$' * 'A_n_vec$' ) > $o ).
tff(pred_def_10,type,
'less_eq$': ( 'A_rows_vec_set$' * 'A_rows_vec_set$' ) > $o ).
tff(pred_def_11,type,
'member$e': ( 'Nat_set$' * 'Nat_set_set$' ) > $o ).
tff(pred_def_12,type,
'fun_app$d': ( 'A_n_vec_set_bool_fun$' * 'A_n_vec_set$' ) > $o ).
tff(pred_def_13,type,
'fun_app$h': ( 'Nat_set_bool_fun$' * 'Nat_set$' ) > $o ).
tff(pred_def_14,type,
'fun_app$f': ( 'Real_set_bool_fun$' * 'Real_set$' ) > $o ).
tff(pred_def_15,type,
'fun_app$e': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_16,type,
'finite$e': 'Nat_set_set$' > $o ).
tff(pred_def_21,type,
sP0: ( $int * $int * $int ) > $o ).
tff(pred_def_22,type,
sP1: ( $int * $int * $int ) > $o ).
tff(pred_def_23,type,
sP2: ( $int * $int * $int ) > $o ).
tff(f7,conjecture,
( $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$'))))
<=> ~ 'fun_app$d'('finite$','solution_set$'('a$','zero$')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture6) ).
tff(f8,negated_conjecture,
~ ( $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$'))))
<=> ~ 'fun_app$d'('finite$','solution_set$'('a$','zero$')) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f12,axiom,
! [X0: 'A_n_vec_rows_vec$'] :
( $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'(X0,'zero$'))))
=> ~ 'fun_app$d'('finite$','solution_set$'(X0,'zero$')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
tff(f14,axiom,
! [X0: 'A_n_vec_rows_vec$'] :
( ~ 'fun_app$d'('finite$','solution_set$'(X0,'zero$'))
=> $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'(X0,'zero$')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
tff(f965,plain,
! [X0: 'A_n_vec_rows_vec$'] :
( $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'(X0,'zero$'))))
| 'fun_app$d'('finite$','solution_set$'(X0,'zero$')) ),
inference(ennf_transformation,[],[f14]) ).
tff(f1021,plain,
( ~ 'fun_app$d'('finite$','solution_set$'('a$','zero$'))
<~> $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$')))) ),
inference(ennf_transformation,[],[f8]) ).
tff(f1035,plain,
! [X0: 'A_n_vec_rows_vec$'] :
( ~ 'fun_app$d'('finite$','solution_set$'(X0,'zero$'))
| ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'(X0,'zero$')))) ),
inference(ennf_transformation,[],[f12]) ).
tff(f1154,plain,
( ( ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$'))))
| 'fun_app$d'('finite$','solution_set$'('a$','zero$')) )
& ( $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$'))))
| ~ 'fun_app$d'('finite$','solution_set$'('a$','zero$')) ) ),
inference(nnf_transformation,[],[f1021]) ).
tff(f1233,plain,
! [X0: 'A_n_vec_rows_vec$'] :
( 'fun_app$d'('finite$','solution_set$'(X0,'zero$'))
| $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'(X0,'zero$')))) ),
inference(cnf_transformation,[],[f965]) ).
tff(f1376,plain,
( $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$'))))
| ~ 'fun_app$d'('finite$','solution_set$'('a$','zero$')) ),
inference(cnf_transformation,[],[f1154]) ).
tff(f1377,plain,
( ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'('a$','zero$'))))
| 'fun_app$d'('finite$','solution_set$'('a$','zero$')) ),
inference(cnf_transformation,[],[f1154]) ).
tff(f1512,plain,
! [X0: 'A_n_vec_rows_vec$'] :
( ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'('dim$'('vector_scalar_mult$'),'solution_set$'(X0,'zero$'))))
| ~ 'fun_app$d'('finite$','solution_set$'(X0,'zero$')) ),
inference(cnf_transformation,[],[f1035]) ).
tff(f1584,definition,
sF19 = 'dim$'('vector_scalar_mult$'),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
tff(f1585,plain,
'dim$'('vector_scalar_mult$') = sF19,
inference(reorient_equations,[],[f1584]) ).
tff(f1586,definition,
sF20 = 'solution_set$'('a$','zero$'),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
tff(f1587,plain,
'solution_set$'('a$','zero$') = sF20,
inference(reorient_equations,[],[f1586]) ).
tff(f1588,definition,
sF21 = 'fun_app$k'(sF19,sF20),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
tff(f1589,definition,
sF22 = 'fun_app$j'('of_nat$',sF21),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
tff(f1590,plain,
( 'fun_app$d'('finite$',sF20)
| ~ $less(0,sF22) ),
inference(definition_folding,[],[f1377,f1587,f1589,f1588,f1587,f1585]) ).
tff(f1591,plain,
( $less(0,sF22)
| ~ 'fun_app$d'('finite$',sF20) ),
inference(definition_folding,[],[f1376,f1587,f1589,f1588,f1587,f1585]) ).
tff(f1595,definition,
( spl23_1
<=> 'fun_app$d'('finite$',sF20) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
tff(f1596,plain,
( 'fun_app$d'('finite$',sF20)
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f1595]) ).
tff(f1599,definition,
( spl23_2
<=> $less(0,sF22) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
tff(f1601,plain,
( $less(0,sF22)
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f1599]) ).
tff(f1602,plain,
( ~ spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f1591,f1599,f1595]) ).
tff(f1603,plain,
( ~ spl23_2
| spl23_1 ),
inference(avatar_split_clause,[],[f1590,f1595,f1599]) ).
tff(f2195,plain,
! [X0: 'A_n_vec_rows_vec$'] :
( $less(0,'fun_app$j'('of_nat$','fun_app$k'(sF19,'solution_set$'(X0,'zero$'))))
| 'fun_app$d'('finite$','solution_set$'(X0,'zero$')) ),
inference(forward_demodulation,[],[f1233,f1585]) ).
tff(f2219,plain,
( 'fun_app$d'('finite$',sF20)
| $less(0,'fun_app$j'('of_nat$','fun_app$k'(sF19,sF20))) ),
inference(superposition,[],[f2195,f1587]) ).
tff(f2235,plain,
( $less(0,'fun_app$j'('of_nat$',sF21))
| 'fun_app$d'('finite$',sF20) ),
inference(forward_demodulation,[],[f2219,f1588]) ).
tff(f2242,plain,
( $less(0,sF22)
| 'fun_app$d'('finite$',sF20) ),
inference(forward_demodulation,[],[f2235,f1589]) ).
tff(f2243,plain,
( spl23_2
| spl23_1 ),
inference(avatar_split_clause,[],[f2242,f1595,f1599]) ).
tff(f2268,plain,
! [X0: 'A_n_vec_rows_vec$'] :
( ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'(sF19,'solution_set$'(X0,'zero$'))))
| ~ 'fun_app$d'('finite$','solution_set$'(X0,'zero$')) ),
inference(forward_demodulation,[],[f1512,f1585]) ).
tff(f2275,plain,
( ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'(sF19,sF20)))
| ~ 'fun_app$d'('finite$',sF20) ),
inference(superposition,[],[f2268,f1587]) ).
tff(f2277,plain,
( ~ $less(0,'fun_app$j'('of_nat$','fun_app$k'(sF19,sF20)))
| ~ spl23_1 ),
inference(forward_subsumption_resolution,[],[f2275,f1596]) ).
tff(f2278,plain,
( ~ $less(0,'fun_app$j'('of_nat$',sF21))
| ~ spl23_1 ),
inference(forward_demodulation,[],[f2277,f1588]) ).
tff(f2279,plain,
( ~ $less(0,sF22)
| ~ spl23_1 ),
inference(forward_demodulation,[],[f2278,f1589]) ).
tff(f2280,plain,
( $false
| ~ spl23_1
| ~ spl23_2 ),
inference(forward_subsumption_resolution,[],[f2279,f1601]) ).
tff(f2281,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(avatar_contradiction_clause,[],[f2280]) ).
cnf(s1,plain,
( ~ spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f1602]) ).
cnf(s2,plain,
( spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f1603]) ).
cnf(s26,plain,
( spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f2243]) ).
cnf(s28,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f2281]) ).
cnf(s31,plain,
spl23_1,
inference(rat,[],[s2,s26]) ).
cnf(s32,plain,
~ spl23_2,
inference(rat,[],[s28,s31]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s32,s31]) ).
tff(f2282,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP345_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 12:54:46 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/1.46 % (3963625)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.15/1.46 % (3963731)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=52288155:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.15/1.46 % (3963731)Instruction limit reached!
% 3.15/1.46 % (3963731)------------------------------
% 3.15/1.46 % (3963731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.46 % (3963731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.46 % (3963731)CaDiCaL version: 2.1.3
% 3.15/1.46 % (3963731)Termination reason: Instruction limit
% 3.15/1.46 % (3963731)Termination phase: Including theory axioms
% 3.15/1.46 % (3963731)Time elapsed: 0.004 s
% 3.15/1.46 % (3963731)Peak memory usage: 86 MB
% 3.15/1.46 % (3963731)Instructions burned: 15 (million)
% 3.15/1.46 % (3963733)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2222435088:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.15/1.46 % (3963734)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3352426557:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.15/1.46 % (3963737)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3307075779:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.15/1.46 % (3963735)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3314538099:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.15/1.46 % (3963736)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2259043112:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.15/1.46 % (3963732)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2703174219:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.15/1.46 % (3963735)Instruction limit reached!
% 3.15/1.46 % (3963735)------------------------------
% 3.15/1.46 % (3963735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.46 % (3963735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.46 % (3963735)CaDiCaL version: 2.1.3
% 3.15/1.46 % (3963735)Termination reason: Instruction limit
% 3.15/1.46 % (3963735)Termination phase: Property scanning
% 3.15/1.46 % (3963735)Time elapsed: 0.003 s
% 3.15/1.46 % (3963735)Peak memory usage: 85 MB
% 3.15/1.46 % (3963735)Instructions burned: 5 (million)
% 3.15/1.46 % (3963734)Instruction limit reached!
% 3.15/1.46 % (3963734)------------------------------
% 3.15/1.46 % (3963734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.46 % (3963734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.46 % (3963734)CaDiCaL version: 2.1.3
% 3.15/1.46 % (3963734)Termination reason: Instruction limit
% 3.15/1.46 % (3963734)Termination phase: Property scanning
% 3.15/1.46 % (3963734)Time elapsed: 0.004 s
% 3.15/1.46 % (3963734)Peak memory usage: 85 MB
% 3.15/1.46 % (3963734)Instructions burned: 7 (million)
% 3.15/1.46 % (3963737)Instruction limit reached!
% 3.15/1.46 % (3963737)------------------------------
% 3.15/1.46 % (3963737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.46 % (3963737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.46 % (3963737)CaDiCaL version: 2.1.3
% 3.15/1.46 % (3963737)Termination reason: Instruction limit
% 3.15/1.46 % (3963737)Termination phase: Property scanning
% 3.15/1.46 % (3963737)Time elapsed: 0.022 s
% 3.15/1.46 % (3963737)Peak memory usage: 88 MB
% 3.15/1.46 % (3963737)Instructions burned: 34 (million)
% 3.15/1.46 % (3963736)Instruction limit reached!
% 3.15/1.46 % (3963736)------------------------------
% 3.15/1.46 % (3963736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.46 % (3963736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.46 % (3963736)CaDiCaL version: 2.1.3
% 3.15/1.46 % (3963736)Termination reason: Instruction limit
% 3.15/1.46 % (3963736)Termination phase: Property scanning
% 3.15/1.46 % (3963736)Time elapsed: 0.033 s
% 3.15/1.46 % (3963736)Peak memory usage: 88 MB
% 3.15/1.46 % (3963736)Instructions burned: 46 (million)
% 3.15/1.46 % (3963740)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4049170873:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.15/1.46 % (3963740)Instruction limit reached!
% 3.15/1.46 % (3963740)------------------------------
% 4.08/1.59 % (3963740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963740)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963740)Termination reason: Instruction limit
% 4.08/1.59 % (3963740)Termination phase: shuffling
% 4.08/1.59 % (3963740)Time elapsed: 0.005 s
% 4.08/1.59 % (3963740)Peak memory usage: 86 MB
% 4.08/1.59 % (3963740)Instructions burned: 16 (million)
% 4.08/1.59 % (3963755)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=1707299247:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 4.08/1.59 % (3963755)Instruction limit reached!
% 4.08/1.59 % (3963755)------------------------------
% 4.08/1.59 % (3963755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963755)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963755)Termination reason: Instruction limit
% 4.08/1.59 % (3963755)Termination phase: Preprocessing 3
% 4.08/1.59 % (3963755)Time elapsed: 0.018 s
% 4.08/1.59 % (3963755)Peak memory usage: 87 MB
% 4.08/1.59 % (3963755)Instructions burned: 30 (million)
% 4.08/1.59 % (3963761)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3893877182:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 4.08/1.59 % (3963733)Instruction limit reached!
% 4.08/1.59 % (3963733)------------------------------
% 4.08/1.59 % (3963733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963733)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963733)Termination reason: Instruction limit
% 4.08/1.59 % (3963733)Termination phase: Saturation
% 4.08/1.59 % (3963733)Time elapsed: 0.174 s
% 4.08/1.59 % (3963733)Peak memory usage: 119 MB
% 4.08/1.59 % (3963733)Instructions burned: 203 (million)
% 4.08/1.59 % (3963761)Instruction limit reached!
% 4.08/1.59 % (3963761)------------------------------
% 4.08/1.59 % (3963761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963761)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963761)Termination reason: Instruction limit
% 4.08/1.59 % (3963761)Termination phase: Preprocessing 3
% 4.08/1.59 % (3963761)Time elapsed: 0.015 s
% 4.08/1.59 % (3963761)Peak memory usage: 87 MB
% 4.08/1.59 % (3963761)Instructions burned: 24 (million)
% 4.08/1.59 % (3963758)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1912560886:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.08/1.59 % (3963762)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=1798321245:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 4.08/1.59 % (3963758)Instruction limit reached!
% 4.08/1.59 % (3963758)------------------------------
% 4.08/1.59 % (3963758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963758)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963758)Termination reason: Instruction limit
% 4.08/1.59 % (3963758)Termination phase: Preprocessing 3
% 4.08/1.59 % (3963758)Time elapsed: 0.016 s
% 4.08/1.59 % (3963758)Peak memory usage: 87 MB
% 4.08/1.59 % (3963758)Instructions burned: 17 (million)
% 4.08/1.59 % (3963762)Instruction limit reached!
% 4.08/1.59 % (3963762)------------------------------
% 4.08/1.59 % (3963762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963762)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963762)Termination reason: Instruction limit
% 4.08/1.59 % (3963762)Termination phase: Preprocessing 3
% 4.08/1.59 % (3963762)Time elapsed: 0.016 s
% 4.08/1.59 % (3963762)Peak memory usage: 87 MB
% 4.08/1.59 % (3963762)Instructions burned: 27 (million)
% 4.08/1.59 % (3963764)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1801725609:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 4.08/1.59 % (3963764)Instruction limit reached!
% 4.08/1.59 % (3963764)------------------------------
% 4.08/1.59 % (3963764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963764)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963764)Termination reason: Instruction limit
% 4.08/1.59 % (3963764)Termination phase: Saturation
% 4.08/1.59 % (3963764)Time elapsed: 0.024 s
% 4.08/1.59 % (3963764)Peak memory usage: 90 MB
% 4.08/1.59 % (3963764)Instructions burned: 86 (million)
% 4.08/1.59 % (3963732)Instruction limit reached!
% 4.08/1.59 % (3963732)------------------------------
% 4.08/1.59 % (3963732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963732)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963732)Termination reason: Instruction limit
% 4.08/1.59 % (3963732)Termination phase: Saturation
% 4.08/1.59 % (3963732)Time elapsed: 0.252 s
% 4.08/1.59 % (3963732)Peak memory usage: 119 MB
% 4.08/1.59 % (3963732)Instructions burned: 308 (million)
% 4.08/1.59 % (3963767)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=281285832:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 4.08/1.59 % (3963771)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=3585060287:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 4.08/1.59 % (3963769)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2862753181:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 4.08/1.59 % (3963767)Instruction limit reached!
% 4.08/1.59 % (3963767)------------------------------
% 4.08/1.59 % (3963767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963767)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963767)Termination reason: Instruction limit
% 4.08/1.59 % (3963767)Termination phase: Property scanning
% 4.08/1.59 % (3963771)Instruction limit reached!
% 4.08/1.59 % (3963771)------------------------------
% 4.08/1.59 % (3963771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963767)Time elapsed: 0.003 s
% 4.08/1.59 % (3963767)Peak memory usage: 85 MB
% 4.08/1.59 % (3963771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963767)Instructions burned: 3 (million)
% 4.08/1.59 % (3963771)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963771)Termination reason: Instruction limit
% 4.08/1.59 % (3963771)Termination phase: Property scanning
% 4.08/1.59 % (3963771)Time elapsed: 0.003 s
% 4.08/1.59 % (3963771)Peak memory usage: 85 MB
% 4.08/1.59 % (3963771)Instructions burned: 4 (million)
% 4.08/1.59 % (3963772)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=3967063037:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2996 on theBenchmark for (2996ds/66Mi)
% 4.08/1.59 % (3963775)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=1759304615:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2995 on theBenchmark for (2995ds/8Mi)
% 4.08/1.59 % (3963775)Instruction limit reached!
% 4.08/1.59 % (3963775)------------------------------
% 4.08/1.59 % (3963775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963775)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963775)Termination reason: Instruction limit
% 4.08/1.59 % (3963775)Termination phase: Property scanning
% 4.08/1.59 % (3963775)Time elapsed: 0.003 s
% 4.08/1.59 % (3963775)Peak memory usage: 86 MB
% 4.08/1.59 % (3963775)Instructions burned: 12 (million)
% 4.08/1.59 % (3963769)First to succeed.
% 4.08/1.59 % (3963773)lrs+10_1_thi=all:si=on:fd=off:random_seed=4151242887:i=53:rtra=on:gtg=all_2995 on theBenchmark for (2995ds/53Mi)
% 4.08/1.59 % (3963769)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3963625"
% 4.08/1.59 % (3963773)Instruction limit reached!
% 4.08/1.59 % (3963773)------------------------------
% 4.08/1.59 % (3963773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963773)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963773)Termination reason: Instruction limit
% 4.08/1.59 % (3963773)Termination phase: Property scanning
% 4.08/1.59 % (3963773)Time elapsed: 0.030 s
% 4.08/1.59 % (3963773)Peak memory usage: 88 MB
% 4.08/1.59 % (3963773)Instructions burned: 55 (million)
% 4.08/1.59 % (3963776)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=2497661718:st=3:i=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/2Mi)
% 4.08/1.59 % (3963772)Instruction limit reached!
% 4.08/1.59 % (3963772)------------------------------
% 4.08/1.59 % (3963772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963772)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963772)Termination reason: Instruction limit
% 4.08/1.59 % (3963772)Termination phase: Saturation
% 4.08/1.59 % (3963772)Time elapsed: 0.061 s
% 4.08/1.59 % (3963772)Peak memory usage: 117 MB
% 4.08/1.59 % (3963772)Instructions burned: 66 (million)
% 4.08/1.59 % (3963776)Instruction limit reached!
% 4.08/1.59 % (3963776)------------------------------
% 4.08/1.59 % (3963776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963776)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963776)Termination reason: Instruction limit
% 4.08/1.59 % (3963776)Termination phase: shuffling
% 4.08/1.59 % (3963776)Time elapsed: 0.002 s
% 4.08/1.59 % (3963776)Peak memory usage: 85 MB
% 4.08/1.59 % (3963776)Instructions burned: 2 (million)
% 4.08/1.59 % (3963781)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=1501984204:i=127:doe=on:rtra=on_2994 on theBenchmark for (2994ds/127Mi)
% 4.08/1.59 % (3963780)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=1606096754:i=2:doe=on:canc=force:asg=cautious:rtra=on_2994 on theBenchmark for (2994ds/2Mi)
% 4.08/1.59 % (3963780)Instruction limit reached!
% 4.08/1.59 % (3963780)------------------------------
% 4.08/1.59 % (3963780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.59 % (3963780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.59 % (3963780)CaDiCaL version: 2.1.3
% 4.08/1.59 % (3963780)Termination reason: Instruction limit
% 4.08/1.59 % (3963780)Termination phase: Property scanning
% 4.08/1.59 % (3963780)Time elapsed: 0.003 s
% 4.08/1.59 % (3963780)Peak memory usage: 85 MB
% 4.08/1.59 % (3963780)Instructions burned: 4 (million)
% 4.08/1.59 % (3963784)dis+10_1_si=on:random_seed=3122688573:i=10:ep=R:rtra=on_2994 on theBenchmark for (2994ds/10Mi)
% 4.08/1.59 % (3963769)Refutation found. Thanks to Tanya!
% 4.08/1.59 % SZS status Theorem for theBenchmark
% 4.08/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.48/1.86 % (3963769)------------------------------
% 5.48/1.86 % (3963769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.48/1.86 % (3963769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.48/1.86 % (3963769)CaDiCaL version: 2.1.3
% 5.48/1.86 % (3963769)Termination reason: Refutation
% 5.48/1.86 % (3963769)Time elapsed: 0.034 s
% 5.48/1.86 % (3963769)Peak memory usage: 91 MB
% 5.48/1.86 % (3963769)Instructions burned: 51 (million)
% 5.48/1.86 % (3963769)------------------------------
% 5.48/1.86 % (3963769)------------------------------
% 5.48/1.86 % (3963625)Success in time 0.708 s
% 5.48/1.86 % Vampire exiting
%------------------------------------------------------------------------------