%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP034^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 : Wed Sep 30 08:10:26 AM UTC 2026
% Result : Theorem 1.69s 0.54s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 105 ( 55 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 375 ( 27 ~; 12 |; 7 &; 327 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 148 ( 145 usr; 11 con; 0-4 aty)
% Number of variables : 10 ( 0 sgn 0 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
binary1439146945Tree_a: $tType ).
thf(type_def_6,type,
set_a: $tType ).
thf(type_def_7,type,
int: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(type_def_9,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_1,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(func_def_2,type,
binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_3,type,
binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
thf(func_def_4,type,
binary1804682569move_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_5,type,
binary339557810e_rm_a: ( a > int ) > binary1439146945Tree_a > a ).
thf(func_def_6,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(func_def_7,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(func_def_8,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(func_def_9,type,
binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_10,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_11,type,
sup_sup_o: $o > $o > $o ).
thf(func_def_12,type,
sup_sup_int: int > int > int ).
thf(func_def_13,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_14,type,
bot_bot_a_o: a > $o ).
thf(func_def_15,type,
bot_bot_o: $o ).
thf(func_def_16,type,
bot_bot_set_a: set_a ).
thf(func_def_17,type,
ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_18,type,
ord_less_int: int > int > $o ).
thf(func_def_19,type,
ord_less_set_a: set_a > set_a > $o ).
thf(func_def_20,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_21,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_22,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_23,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_24,type,
insert_a: a > set_a > set_a ).
thf(func_def_25,type,
the_elem_a: set_a > a ).
thf(func_def_26,type,
member_a: a > set_a > $o ).
thf(func_def_27,type,
h: a > int ).
thf(func_def_28,type,
l: a ).
thf(func_def_29,type,
t1: binary1439146945Tree_a ).
thf(func_def_30,type,
t2: binary1439146945Tree_a ).
thf(func_def_31,type,
x: a ).
thf(func_def_35,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
sP0: ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_48,type,
sP1: ( binary1439146945Tree_a > $o ) > $o ).
thf(func_def_49,type,
sP2: ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_50,type,
sP3: ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_51,type,
sP4: ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_52,type,
sP5: int > int > ( int > $o ) > $o ).
thf(func_def_53,type,
sP6: int > int > ( int > $o ) > $o ).
thf(func_def_54,type,
sP7: set_a > set_a > set_a > $o ).
thf(func_def_55,type,
sP8: ( int > int > int ) > $o ).
thf(func_def_56,type,
sP9: ( ( a > $o ) > ( a > $o ) > a > $o ) > $o ).
thf(func_def_57,type,
sP10: ( set_a > set_a > set_a ) > $o ).
thf(func_def_58,type,
sK11: int > int ).
thf(func_def_59,type,
sK12: int > int ).
thf(func_def_60,type,
sK13: int > int ).
thf(func_def_61,type,
sK14: int > int ).
thf(func_def_62,type,
sK15: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_63,type,
sK16: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_64,type,
sK17: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_65,type,
sK18: binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_66,type,
sK19: binary1439146945Tree_a > a ).
thf(func_def_67,type,
sK20: binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_68,type,
sK21: ( binary1439146945Tree_a > $o ) > binary1439146945Tree_a ).
thf(func_def_69,type,
sK22: ( binary1439146945Tree_a > $o ) > a ).
thf(func_def_70,type,
sK23: ( binary1439146945Tree_a > $o ) > binary1439146945Tree_a ).
thf(func_def_71,type,
sK24: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_72,type,
sK25: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_73,type,
sK26: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_74,type,
sK27: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_75,type,
sK28: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_76,type,
sK29: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_77,type,
sK30: int > int ).
thf(func_def_78,type,
sK31: int > int ).
thf(func_def_79,type,
sK32: int > int ).
thf(func_def_80,type,
sK33: int > int ).
thf(func_def_81,type,
sK34: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_82,type,
sK35: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_83,type,
sK36: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_84,type,
sK37: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_85,type,
sK38: int > int > ( int > $o ) > int ).
thf(func_def_86,type,
sK39: int > int > ( int > $o ) > int ).
thf(func_def_87,type,
sK40: int > int ).
thf(func_def_88,type,
sK41: int > int ).
thf(func_def_89,type,
sK42: int > int ).
thf(func_def_90,type,
sK43: int > int ).
thf(func_def_91,type,
sK44: set_a > set_a > a ).
thf(func_def_92,type,
sK45: set_a > a ).
thf(func_def_93,type,
sK46: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_94,type,
sK47: set_a > a > set_a ).
thf(func_def_95,type,
sK48: set_a > a > set_a ).
thf(func_def_96,type,
sK49: set_a > set_a > set_a > set_a ).
thf(func_def_97,type,
sK50: set_a > set_a > set_a > set_a ).
thf(func_def_98,type,
sK51: ( int > int > int ) > int ).
thf(func_def_99,type,
sK52: ( int > int > int ) > int ).
thf(func_def_100,type,
sK53: ( int > int > int ) > int ).
thf(func_def_101,type,
sK54: ( int > int > int ) > int ).
thf(func_def_102,type,
sK55: ( int > int > int ) > int ).
thf(func_def_103,type,
sK56: ( int > int > int ) > int ).
thf(func_def_104,type,
sK57: ( int > int > int ) > int ).
thf(func_def_105,type,
sK58: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_106,type,
sK59: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_107,type,
sK60: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_108,type,
sK61: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_109,type,
sK62: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_110,type,
sK63: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_111,type,
sK64: ( ( a > $o ) > ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_112,type,
sK65: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_113,type,
sK66: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_114,type,
sK67: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_115,type,
sK68: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_116,type,
sK69: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_117,type,
sK70: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_118,type,
sK71: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_119,type,
sK72: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_120,type,
sK73: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_121,type,
sK74: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_122,type,
sK75: ( set_a > a > $o ) > set_a ).
thf(func_def_123,type,
sK76: ( set_a > a > $o ) > set_a ).
thf(func_def_124,type,
sK77: ( int > a > $o ) > int ).
thf(func_def_125,type,
sK78: ( int > a > $o ) > int ).
thf(func_def_126,type,
sK79: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_127,type,
sK80: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_128,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
sK81: set_a > ( a > $o ) > a ).
thf(func_def_130,type,
sK82: set_a > ( a > $o ) > a ).
thf(func_def_131,type,
sK83: set_a > set_a > ( a > $o ) > a ).
thf(func_def_132,type,
sK84: set_a > set_a > ( a > $o ) > a ).
thf(func_def_133,type,
sK85: set_a > set_a > ( a > $o ) > a ).
thf(func_def_134,type,
sK86: set_a > set_a > ( a > $o ) > a ).
thf(func_def_135,type,
sK87: set_a > ( a > $o ) > a ).
thf(func_def_136,type,
sK88: set_a > ( a > $o ) > a ).
thf(func_def_137,type,
sK89: set_a > a > set_a > a > set_a ).
thf(func_def_138,type,
sK90: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_139,type,
sK91: set_a > a ).
thf(func_def_140,type,
sK92: ( a > $o ) > a ).
thf(func_def_141,type,
sK93: ( a > $o ) > a ).
thf(func_def_142,type,
sK94: set_a > a ).
thf(func_def_143,type,
sK95: a > binary1439146945Tree_a > ( a > int ) > a ).
thf(func_def_144,type,
sK96: binary1439146945Tree_a > ( a > int ) > a > a ).
thf(f1,axiom,
ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_hLess) ).
thf(f2,axiom,
( ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= ( binary339557810e_rm_a @ h @ t2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rm__res) ).
thf(f331,axiom,
( ord_less_int
= ( ^ [X0: int,X1: int] :
( ( X1 != X0 )
& ( X1
= ( sup_sup_int @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_sup_Ostrict__order__iff) ).
thf(f353,conjecture,
ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f354,negated_conjecture,
~ ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f355,plain,
ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ),
inference(rectify,[],[f1]) ).
thf(f356,plain,
( ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) )
= $true ),
inference(fool_elimination,[],[f355]) ).
thf(f819,plain,
( ord_less_int
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(fool_elimination,[],[f331]) ).
thf(f859,plain,
~ ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ),
inference(rectify,[],[f354]) ).
thf(f860,plain,
( ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
!= $true ),
inference(fool_elimination,[],[f859]) ).
thf(f894,plain,
( ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
!= $true ),
inference(flattening,[],[f860]) ).
thf(f1199,plain,
( ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) )
= $true ),
inference(cnf_transformation,[],[f356]) ).
thf(f1200,plain,
( ( binary339557810e_rm_a @ h @ t2 )
= ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f1586,plain,
( ord_less_int
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(cnf_transformation,[],[f819]) ).
thf(f1614,plain,
( ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f894]) ).
thf(f1621,plain,
( $true
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) )
@ ( h @ l )
@ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ),
inference(definition_unfolding,[],[f1199,f1586]) ).
thf(f1959,plain,
( $true
!= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) )
@ ( h @ l )
@ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ),
inference(definition_unfolding,[],[f1614,f1586]) ).
thf(f1978,plain,
( $true
!= ( ( ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
& ( ( h @ l )
!= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1959]) ).
thf(f1979,plain,
( ( $false
= ( ( h @ l )
!= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) )
| ( $false
= ( ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1978]) ).
thf(f1980,plain,
( ( $true
= ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) )
| ( $false
= ( ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f1979]) ).
thf(f1981,plain,
( ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
| ( $false
= ( ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f1980]) ).
thf(f1982,plain,
( ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
| ( ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) )
!= ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) ) ) ),
inference(equality_proxy_clausification,[],[f1981]) ).
thf(f4187,plain,
( $true
= ( ( ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) @ ( h @ l ) )
= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) )
& ( ( h @ l )
!= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1621]) ).
thf(f4188,plain,
( $true
= ( ( h @ l )
!= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ),
inference(and_proxy_clausification,[],[f4187]) ).
thf(f4189,plain,
( $true
= ( ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) @ ( h @ l ) )
= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ),
inference(and_proxy_clausification,[],[f4187]) ).
thf(f4190,plain,
( ( h @ ( binary339557810e_rm_a @ h @ t2 ) )
= ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) @ ( h @ l ) ) ),
inference(equality_proxy_clausification,[],[f4189]) ).
thf(f4191,plain,
( $false
= ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ),
inference(not_proxy_clausification,[],[f4188]) ).
thf(f4192,plain,
( ( h @ l )
!= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ),
inference(equality_proxy_clausification,[],[f4191]) ).
thf(f4194,definition,
( spl97_1
<=> ( ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) )
= ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) ) ) ),
introduced(definition,[new_symbols(definition,[spl97_1])],[avatar_definition]) ).
thf(f4196,plain,
( ( ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) )
!= ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) @ ( h @ l ) ) )
| spl97_1 ),
inference(avatar_component_clause,[],[f4194]) ).
thf(f4198,definition,
( spl97_2
<=> ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl97_2])],[avatar_definition]) ).
thf(f4200,plain,
( ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) )
| ~ spl97_2 ),
inference(avatar_component_clause,[],[f4198]) ).
thf(f4201,plain,
( ~ spl97_1
| spl97_2 ),
inference(avatar_split_clause,[],[f1982,f4198,f4194]) ).
thf(f4266,plain,
( ( ( h @ l )
= ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) )
| ~ spl97_2 ),
inference(forward_demodulation,[],[f4200,f1200]) ).
thf(f4267,plain,
( $false
| ~ spl97_2 ),
inference(forward_subsumption_resolution,[],[f4266,f4192]) ).
thf(f4268,plain,
~ spl97_2,
inference(avatar_contradiction_clause,[],[f4267]) ).
thf(f4269,plain,
( ( ( h @ ( binary339557810e_rm_a @ h @ t2 ) )
!= ( sup_sup_int @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) @ ( h @ l ) ) )
| spl97_1 ),
inference(forward_demodulation,[],[f4196,f1200]) ).
thf(f4271,plain,
( $false
| spl97_1 ),
inference(forward_subsumption_resolution,[],[f4269,f4190]) ).
thf(f4272,plain,
spl97_1,
inference(avatar_contradiction_clause,[],[f4271]) ).
cnf(s1,plain,
( ~ spl97_1
| spl97_2 ),
inference(sat_conversion,[],[f4201]) ).
cnf(s9,plain,
~ spl97_2,
inference(sat_conversion,[],[f4268]) ).
cnf(s10,plain,
spl97_1,
inference(sat_conversion,[],[f4272]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s9,s10]) ).
thf(f4273,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP034^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:41:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 1.69/0.54 % (2969124)Will run a generic schedule for satisfiability detection.
% 1.69/0.54 % (2969134)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3935567287:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.69/0.54 % (2969130)% WARNING: option uhcvi not known.
% 1.69/0.54 % (2969130)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2760245040:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.69/0.54 % (2969129)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2167733723_2999 on theBenchmark for (2999ds/0Mi)
% 1.69/0.54 % (2969131)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2114581585:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.69/0.54 % (2969132)dis+10_1_sil=32000:sp=arity:random_seed=3854910843:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.69/0.54 % (2969133)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4022412614:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.69/0.54 % (2969130)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.69/0.54 % (2969133)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.69/0.54 % (2969135)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3902580337:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.69/0.54 % (2969134)Instruction limit reached!
% 1.69/0.54 % (2969134)------------------------------
% 1.69/0.54 % (2969134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969134)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969134)Termination reason: Instruction limit
% 1.69/0.54 % (2969134)Termination phase: Property scanning
% 1.69/0.54 % (2969134)Time elapsed: 0.029 s
% 1.69/0.54 % (2969134)Peak memory usage: 11 MB
% 1.69/0.54 % (2969134)Instructions burned: 131 (million)
% 1.69/0.54 % (2969143)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=253229257:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.69/0.54 % (2969132)Instruction limit reached!
% 1.69/0.54 % (2969132)------------------------------
% 1.69/0.54 % (2969132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969132)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969132)Termination reason: Instruction limit
% 1.69/0.54 % (2969132)Termination phase: Property scanning
% 1.69/0.54 % (2969132)Time elapsed: 0.043 s
% 1.69/0.54 % (2969132)Peak memory usage: 11 MB
% 1.69/0.54 % (2969132)Instructions burned: 104 (million)
% 1.69/0.54 % (2969133)Instruction limit reached!
% 1.69/0.54 % (2969133)------------------------------
% 1.69/0.54 % (2969133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969133)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969133)Termination reason: Instruction limit
% 1.69/0.54 % (2969133)Termination phase: Property scanning
% 1.69/0.54 % (2969133)Time elapsed: 0.048 s
% 1.69/0.54 % (2969133)Peak memory usage: 11 MB
% 1.69/0.54 % (2969133)Instructions burned: 117 (million)
% 1.69/0.54 % Exception at run slice level
% 1.69/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.69/0.54 % (2969130)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.69/0.54 % (2969145)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4121782863:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.69/0.54 % Exception at run slice level
% 1.69/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.69/0.54 % (2969146)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=711285983:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.69/0.54 % (2969149)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2270705825:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.69/0.54 % (2969147)ott-21_1_sil=16000:fs=off:random_seed=1873574925:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.69/0.54 % (2969146)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.69/0.54 % (2969145)Instruction limit reached!
% 1.69/0.54 % (2969145)------------------------------
% 1.69/0.54 % (2969145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969145)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969145)Termination reason: Instruction limit
% 1.69/0.54 % (2969145)Termination phase: Property scanning
% 1.69/0.54 % (2969145)Time elapsed: 0.053 s
% 1.69/0.54 % (2969145)Peak memory usage: 11 MB
% 1.69/0.54 % (2969145)Instructions burned: 131 (million)
% 1.69/0.54 % (2969135)Instruction limit reached!
% 1.69/0.54 % (2969135)------------------------------
% 1.69/0.54 % (2969135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969135)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969135)Termination reason: Instruction limit
% 1.69/0.54 % (2969135)Termination phase: Saturation
% 1.69/0.54 % (2969135)Time elapsed: 0.108 s
% 1.69/0.54 % (2969135)Peak memory usage: 12 MB
% 1.69/0.54 % (2969135)Instructions burned: 159 (million)
% 1.69/0.54 % (2969146)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.69/0.54 % (2969153)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2061105457:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.69/0.54 % (2969154)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2592318863:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.69/0.54 % (2969147)Instruction limit reached!
% 1.69/0.54 % (2969147)------------------------------
% 1.69/0.54 % (2969147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969147)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969147)Termination reason: Instruction limit
% 1.69/0.54 % (2969147)Termination phase: Saturation
% 1.69/0.54 % (2969147)Time elapsed: 0.074 s
% 1.69/0.54 % (2969147)Peak memory usage: 12 MB
% 1.69/0.54 % (2969147)Instructions burned: 181 (million)
% 1.69/0.54 % (2969157)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1636979748:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.69/0.54 % (2969149)Instruction limit reached!
% 1.69/0.54 % (2969149)------------------------------
% 1.69/0.54 % (2969149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969149)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969149)Termination reason: Instruction limit
% 1.69/0.54 % (2969149)Termination phase: Saturation
% 1.69/0.54 % (2969149)Time elapsed: 0.120 s
% 1.69/0.54 % (2969149)Peak memory usage: 15 MB
% 1.69/0.54 % (2969149)Instructions burned: 481 (million)
% 1.69/0.54 % (2969159)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=445672178:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.69/0.54 % Exception at run slice level
% 1.69/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.69/0.54 % (2969159)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.69/0.54 % Exception at run slice level
% 1.69/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.69/0.54 % (2969161)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3685514546:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.69/0.54 % (2969162)fmb+10_1_sil=64000:random_seed=890616320:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 1.69/0.54 % (2969161)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.69/0.54 % (2969159) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2969124-2969159"...
% 1.69/0.54 % (2969162)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.69/0.54 % (2969159)...printing done.
% 1.69/0.54 % (2969159)Refutation found. Thanks to Tanya!
% 1.69/0.54 % SZS status Theorem for theBenchmark
% 1.69/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 1.69/0.54 % (2969159)------------------------------
% 1.69/0.54 % (2969159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.54 % (2969159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.54 % (2969159)CaDiCaL version: 2.1.3
% 1.69/0.54 % (2969159)Termination reason: Refutation
% 1.69/0.54 % (2969159)Time elapsed: 0.073 s
% 1.69/0.54 % (2969159)Peak memory usage: 16 MB
% 1.69/0.54 % (2969159)Instructions burned: 317 (million)
% 1.69/0.54 % (2969124)Success in time 0.326 s
% 1.69/0.54 % Vampire exiting
%------------------------------------------------------------------------------