%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV458^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:39:32 AM UTC 2026
% Result : Theorem 2.99s 0.68s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 146 ( 21 unt; 0 typ; 8 def)
% Number of atoms : 868 ( 189 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 967 ( 131 ~; 201 |; 0 &; 623 @)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 12 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 4 sgn 139 !; 4 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK1: sK0 > $o ).
thf(func_def_9,type,
sK2: sK0 > $o ).
thf(func_def_10,type,
sK3: sK0 > $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK5: sK0 ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK7:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK8: ( sK0 > $o ) > sK0 ).
thf(func_def_20,type,
sK9:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
sK10: ( sK0 > $o ) > sK0 ).
thf(func_def_22,type,
sK11: ( sK0 > $o ) > sK0 ).
thf(func_def_23,type,
sK12:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_24,type,
sK13: ( sK0 > $o ) > sK0 ).
thf(func_def_25,type,
sK14: ( sK0 > $o ) > sK0 ).
thf(func_def_26,type,
sK15: ( sK0 > $o ) > sK0 ).
thf(func_def_27,type,
sK16:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_28,type,
sK17:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_29,type,
sK18:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > X0 ) ).
thf(func_def_30,type,
sK19:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > X0 ) ).
thf(func_def_31,type,
sK20:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > X0 ) ).
thf(func_def_32,type,
sK21:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_33,type,
sK22:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_34,type,
sK23:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > sK0 ) ).
thf(func_def_35,type,
sK24:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_36,type,
sK25:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_37,type,
sK26:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_38,type,
sK27: ( sK0 > $o ) > sK0 ).
thf(func_def_39,type,
sK28:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_40,type,
sK29:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_41,type,
sK30: ( sK0 > $o ) > sK0 ).
thf(func_def_42,type,
sK31: ( sK0 > $o ) > sK0 ).
thf(func_def_43,type,
sK32:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_44,type,
sK33: ( sK0 > $o ) > sK0 ).
thf(func_def_45,type,
sK34: ( sK0 > $o ) > sK0 ).
thf(func_def_46,type,
sK35:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_47,type,
sK36: ( sK0 > $o ) > sK0 ).
thf(func_def_48,type,
sK37: ( sK0 > $o ) > sK0 ).
thf(func_def_49,type,
sK38:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > $o ) > ( X0 > sK0 > sK0 ) > X0 ) ).
thf(func_def_50,type,
sK39:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > $o ) > ( X0 > sK0 > sK0 ) > X0 ) ).
thf(func_def_51,type,
sK40:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > $o ) > ( X0 > sK0 > $o ) > X0 ) ).
thf(func_def_52,type,
sK41:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > $o ) > ( X0 > sK0 > $o ) > X0 ) ).
thf(func_def_53,type,
sK42:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_54,type,
sK43:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_55,type,
sK44:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_56,type,
sK45:
!>[X0: $tType] : ( ( X0 > sK0 ) > ( X0 > sK0 > sK0 ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_57,type,
sK46:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_58,type,
sK47:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_59,type,
sK48:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_60,type,
sK49:
!>[X0: $tType] : ( ( X0 > sK0 > $o ) > ( X0 > sK0 > $o ) > ( X0 > $o ) > sK0 ) ).
thf(func_def_61,type,
sK50: ( sK0 > $o ) > sK0 ).
thf(func_def_62,type,
sK51: ( sK0 > $o ) > sK0 ).
thf(func_def_63,type,
sK52: ( sK0 > $o ) > sK0 ).
thf(func_def_64,type,
sK53: ( sK0 > $o ) > sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNION_ACI_2') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
= ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f9,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
!= ( 'const/sets/UNION' @ X0 @ X1 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
( ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9]) ).
thf(f11,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f12,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( X1 = X2 )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
= ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( X1 = X2 )
= $false )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
= ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f19,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( X1 != X2 )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
= ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( X1 != X2 )
| ( $true
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
= ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( X1 != X2 )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( X1 != X2 )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $false )
| ( X1 != X2 ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f36,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f11]) ).
thf(f37,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f11]) ).
thf(f45,plain,
( ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f46,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ) ),
inference(xor_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ) ),
inference(xor_proxy_clausification,[],[f45]) ).
thf(f49,definition,
( spl6_1
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f50,plain,
( ( $false
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) )
| spl6_1 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f51,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f53,definition,
( spl6_2
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f55,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f47,f53,f49]) ).
thf(f58,definition,
( spl6_3
<=> ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f60,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK1 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) @ sK5 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f62,definition,
( spl6_4
<=> ( $true
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f64,plain,
( ( $true
= ( 'const/sets/UNION' @ sK0 @ sK2 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) @ sK5 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f46,f62,f58]) ).
thf(f84,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $false
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f36,f33]) ).
thf(f85,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $false
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f96,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $false
= ( X2 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( X2 != X3 ) ),
inference(constrained_superposition,[],[f36,f23]) ).
thf(f99,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $false
= ( X2 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( X2 != X3 ) ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f112,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(constrained_superposition,[],[f37,f34]) ).
thf(f115,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f124,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f37,f35]) ).
thf(f127,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f133,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f85,f60]) ).
thf(f136,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f139,definition,
( spl6_5
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f140,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| spl6_5 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f141,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f143,definition,
( spl6_6
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f145,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f268,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $true
= ( X2 @ X1 ) )
| ( $false
= ( X3 @ X1 ) )
| ( X2 != X3 ) ),
inference(constrained_superposition,[],[f37,f99]) ).
thf(f284,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( X2 @ X1 ) )
| ( $false
= ( X3 @ X1 ) )
| ( X2 != X3 ) ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f515,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f55,f115]) ).
thf(f520,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f515]) ).
thf(f527,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f55,f127]) ).
thf(f532,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f861,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK5 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f36,f532]) ).
thf(f875,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f861]) ).
thf(f3860,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f35,f520]) ).
thf(f3861,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f34,f520]) ).
thf(f3862,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f3861]) ).
thf(f3863,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f3860]) ).
thf(f3905,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ sK5 ) )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f36,f3862]) ).
thf(f3910,plain,
( ( $false
= ( sK3 @ sK5 ) )
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f3905]) ).
thf(f5325,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_5 ),
inference(constrained_superposition,[],[f3863,f141]) ).
thf(f5355,plain,
( $false
| ~ spl6_2
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f5325]) ).
thf(f5356,plain,
( ~ spl6_2
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f5355]) ).
thf(f5395,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f127,f51]) ).
thf(f5396,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f115,f51]) ).
thf(f5397,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f5396]) ).
thf(f5398,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f5395]) ).
thf(f5492,definition,
( spl6_10
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f5493,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| spl6_10 ),
inference(avatar_component_clause,[],[f5492]) ).
thf(f5494,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f5492]) ).
thf(f5496,definition,
( spl6_11
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f5498,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f5496]) ).
thf(f5553,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK5 ) )
| ~ spl6_10 ),
inference(constrained_superposition,[],[f37,f5494]) ).
thf(f5558,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f5553]) ).
thf(f5622,plain,
( ! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $true = $false )
| ( $true
= ( X2 @ X1 ) )
| ( ( ^ [Y0: X0] :
( sK2
@ ( ^ [Y1: X0] : sK5
@ Y0 ) ) )
!= X2 ) )
| ~ spl6_10 ),
inference(constrained_superposition,[],[f284,f5558]) ).
thf(f5632,plain,
( ! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $true
= ( X2 @ X1 ) )
| ( ( ^ [Y0: X0] :
( sK2
@ ( ^ [Y1: X0] : sK5
@ Y0 ) ) )
!= X2 ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f5622]) ).
thf(f5633,plain,
( ! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( ( ^ [Y0: X0] : ( sK2 @ sK5 ) )
!= X2 )
| ( $true
= ( X2 @ X1 ) ) )
| ~ spl6_10 ),
inference(beta-eta_normalization,[],[f5632]) ).
thf(f5721,plain,
( ! [X0: $tType,X1: X0] :
( $true
= ( ^ [Y0: X0] : ( sK2 @ sK5 )
@ X1 ) )
| ~ spl6_10 ),
inference(equality_resolution,[],[f5633]) ).
thf(f5758,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f35,f5397]) ).
thf(f5759,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f34,f5397]) ).
thf(f5760,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f5759]) ).
thf(f5761,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f5758]) ).
thf(f6147,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_10 ),
inference(constrained_superposition,[],[f5761,f5494]) ).
thf(f6174,plain,
( $false
| ~ spl6_1
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f6147]) ).
thf(f6175,plain,
( ~ spl6_1
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f6174]) ).
thf(f6205,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_11 ),
inference(constrained_superposition,[],[f5498,f33]) ).
thf(f6231,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f6205]) ).
thf(f6247,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| spl6_5
| ~ spl6_11 ),
inference(forward_subsumption_resolution,[],[f6231,f140]) ).
thf(f6251,plain,
( ( $true = $false )
| ~ spl6_1
| spl6_5
| ~ spl6_11 ),
inference(forward_demodulation,[],[f6247,f5760]) ).
thf(f6252,plain,
( $false
| ~ spl6_1
| spl6_5
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f6251]) ).
thf(f6253,plain,
( ~ spl6_1
| spl6_5
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f6252]) ).
thf(f6629,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ~ spl6_3
| spl6_5 ),
inference(forward_subsumption_resolution,[],[f136,f140]) ).
thf(f6703,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_3
| spl6_5 ),
inference(forward_demodulation,[],[f6629,f5397]) ).
thf(f6704,plain,
( $false
| ~ spl6_1
| ~ spl6_3
| spl6_5 ),
inference(trivial_inequality_removal,[],[f6703]) ).
thf(f6705,plain,
( ~ spl6_1
| ~ spl6_3
| spl6_5 ),
inference(avatar_contradiction_clause,[],[f6704]) ).
thf(f6740,plain,
( ( $false != $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| spl6_1 ),
inference(constrained_superposition,[],[f50,f85]) ).
thf(f6741,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| spl6_1 ),
inference(trivial_inequality_removal,[],[f6740]) ).
thf(f6757,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK2 @ sK3 ) ) )
| spl6_1
| spl6_5 ),
inference(forward_subsumption_resolution,[],[f6741,f140]) ).
thf(f6758,plain,
( spl6_6
| spl6_1
| spl6_5 ),
inference(avatar_split_clause,[],[f6757,f139,f49,f143]) ).
thf(f6959,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_6 ),
inference(constrained_superposition,[],[f33,f145]) ).
thf(f6960,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f6959]) ).
thf(f6990,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK3 ) )
| ~ spl6_6
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f6960,f5493]) ).
thf(f7144,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK5 ) )
| ~ spl6_6
| spl6_10 ),
inference(constrained_superposition,[],[f6990,f37]) ).
thf(f7172,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl6_6
| spl6_10 ),
inference(trivial_inequality_removal,[],[f7144]) ).
thf(f7187,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_6
| spl6_10 ),
inference(forward_demodulation,[],[f7172,f3910]) ).
thf(f7188,plain,
( $false
| ~ spl6_2
| ~ spl6_6
| spl6_10 ),
inference(trivial_inequality_removal,[],[f7187]) ).
thf(f7189,plain,
( ~ spl6_2
| ~ spl6_6
| spl6_10 ),
inference(avatar_contradiction_clause,[],[f7188]) ).
thf(f7266,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl6_10 ),
inference(beta-eta_normalization,[],[f5721]) ).
thf(f7320,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_10 ),
inference(forward_demodulation,[],[f7266,f875]) ).
thf(f7321,plain,
( $false
| ~ spl6_2
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f7320]) ).
thf(f7322,plain,
( ~ spl6_2
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f7321]) ).
thf(f8734,plain,
( ( $true = $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f64,f85]) ).
thf(f8753,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/UNION' @ sK0 @ sK1 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK2 ) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f8734]) ).
thf(f8765,plain,
( spl6_10
| spl6_11
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f8753,f62,f5496,f5492]) ).
thf(f8964,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_5 ),
inference(constrained_superposition,[],[f5398,f141]) ).
thf(f8991,plain,
( $false
| ~ spl6_1
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f8964]) ).
thf(f8992,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f8991]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s12,plain,
( ~ spl6_2
| ~ spl6_5 ),
inference(sat_conversion,[],[f5356]) ).
cnf(s18,plain,
( ~ spl6_1
| ~ spl6_10 ),
inference(sat_conversion,[],[f6175]) ).
cnf(s20,plain,
( ~ spl6_1
| spl6_5
| ~ spl6_11 ),
inference(sat_conversion,[],[f6253]) ).
cnf(s26,plain,
( ~ spl6_1
| ~ spl6_3
| spl6_5 ),
inference(sat_conversion,[],[f6705]) ).
cnf(s39,plain,
( spl6_1
| spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f6758]) ).
cnf(s43,plain,
( ~ spl6_2
| ~ spl6_6
| spl6_10 ),
inference(sat_conversion,[],[f7189]) ).
cnf(s48,plain,
( ~ spl6_2
| ~ spl6_10 ),
inference(sat_conversion,[],[f7322]) ).
cnf(s134,plain,
( ~ spl6_4
| spl6_10
| spl6_11 ),
inference(sat_conversion,[],[f8765]) ).
cnf(s142,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(sat_conversion,[],[f8992]) ).
cnf(s145,plain,
spl6_1,
inference(rat,[],[s39,s12,s43,s48,s1]) ).
cnf(s146,plain,
~ spl6_5,
inference(rat,[],[s142,s145]) ).
cnf(s148,plain,
~ spl6_3,
inference(rat,[],[s26,s146,s145]) ).
cnf(s150,plain,
~ spl6_10,
inference(rat,[],[s18,s145]) ).
cnf(s151,plain,
~ spl6_11,
inference(rat,[],[s20,s145,s146]) ).
cnf(s152,plain,
spl6_4,
inference(rat,[],[s2,s148]) ).
cnf(s153,plain,
$false,
inference(rat,[],[s134,s151,s150,s152]) ).
thf(f9008,plain,
$false,
inference(avatar_sat_refutation,[],[s153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV458^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 15:49:01 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.99/0.68 % (4170960)Will run a generic schedule for satisfiability detection.
% 2.99/0.68 % (4170965)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2454287991_2999 on theBenchmark for (2999ds/0Mi)
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4170966)% WARNING: option uhcvi not known.
% 2.99/0.68 % (4170966)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=847510943:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.99/0.68 % (4170966)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.99/0.68 % (4170966)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.99/0.68 % (4170968)dis+10_1_sil=32000:sp=arity:random_seed=2689862784:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.99/0.68 % (4170967)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=86807548:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.99/0.68 % (4170969)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4077294923:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.99/0.68 % (4170970)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2341342385:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.99/0.68 % (4170971)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1457519733:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.99/0.68 % (4170969)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.99/0.68 % (4170973)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3986089393:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4170981)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=732926086:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.99/0.68 % (4170968)Instruction limit reached!
% 2.99/0.68 % (4170968)------------------------------
% 2.99/0.68 % (4170968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170968)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170968)Termination reason: Instruction limit
% 2.99/0.68 % (4170968)Termination phase: Saturation
% 2.99/0.68 % (4170968)Time elapsed: 0.057 s
% 2.99/0.68 % (4170968)Peak memory usage: 12 MB
% 2.99/0.68 % (4170968)Instructions burned: 104 (million)
% 2.99/0.68 % (4170969)Instruction limit reached!
% 2.99/0.68 % (4170969)------------------------------
% 2.99/0.68 % (4170969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170969)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170969)Termination reason: Instruction limit
% 2.99/0.68 % (4170969)Termination phase: Saturation
% 2.99/0.68 % (4170969)Time elapsed: 0.064 s
% 2.99/0.68 % (4170969)Peak memory usage: 12 MB
% 2.99/0.68 % (4170969)Instructions burned: 117 (million)
% 2.99/0.68 % (4170970)Instruction limit reached!
% 2.99/0.68 % (4170970)------------------------------
% 2.99/0.68 % (4170970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170970)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170970)Termination reason: Instruction limit
% 2.99/0.68 % (4170970)Termination phase: Saturation
% 2.99/0.68 % (4170970)Time elapsed: 0.070 s
% 2.99/0.68 % (4170970)Peak memory usage: 13 MB
% 2.99/0.68 % (4170970)Instructions burned: 131 (million)
% 2.99/0.68 % (4170983)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=3748336545:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.99/0.68 % (4170983)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.99/0.68 % (4170983)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.99/0.68 % (4170984)ott-21_1_sil=16000:fs=off:random_seed=1274980457:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.99/0.68 % (4170971)Instruction limit reached!
% 2.99/0.68 % (4170971)------------------------------
% 2.99/0.68 % (4170971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170971)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170971)Termination reason: Instruction limit
% 2.99/0.68 % (4170971)Termination phase: Saturation
% 2.99/0.68 % (4170971)Time elapsed: 0.086 s
% 2.99/0.68 % (4170971)Peak memory usage: 13 MB
% 2.99/0.68 % (4170971)Instructions burned: 160 (million)
% 2.99/0.68 % (4170985)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=315712726:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.99/0.68 % (4170981)Instruction limit reached!
% 2.99/0.68 % (4170981)------------------------------
% 2.99/0.68 % (4170981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170981)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170981)Termination reason: Instruction limit
% 2.99/0.68 % (4170981)Termination phase: Saturation
% 2.99/0.68 % (4170981)Time elapsed: 0.069 s
% 2.99/0.68 % (4170981)Peak memory usage: 12 MB
% 2.99/0.68 % (4170981)Instructions burned: 132 (million)
% 2.99/0.68 % (4170988)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2898826819:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4170990)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4245965490:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.99/0.68 % (4170992)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4183915437:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4170995)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=629430699:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.99/0.68 % (4170995)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.99/0.68 % (4170984)Instruction limit reached!
% 2.99/0.68 % (4170984)------------------------------
% 2.99/0.68 % (4170984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170984)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170984)Termination reason: Instruction limit
% 2.99/0.68 % (4170984)Termination phase: Saturation
% 2.99/0.68 % (4170984)Time elapsed: 0.087 s
% 2.99/0.68 % (4170984)Peak memory usage: 13 MB
% 2.99/0.68 % (4170984)Instructions burned: 181 (million)
% 2.99/0.68 % (4170997)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1156115396:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.99/0.68 % (4170997)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.99/0.68 % (4170985)Instruction limit reached!
% 2.99/0.68 % (4170985)------------------------------
% 2.99/0.68 % (4170985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170985)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170985)Termination reason: Instruction limit
% 2.99/0.68 % (4170985)Termination phase: Saturation
% 2.99/0.68 % (4170985)Time elapsed: 0.259 s
% 2.99/0.68 % (4170985)Peak memory usage: 14 MB
% 2.99/0.68 % (4170985)Instructions burned: 477 (million)
% 2.99/0.68 % (4170999)fmb+10_1_sil=64000:random_seed=402084181:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.99/0.68 % (4170999)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4171001)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4270003312:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4170983)Instruction limit reached!
% 2.99/0.68 % (4170983)------------------------------
% 2.99/0.68 % (4170983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.68 % (4170983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.68 % (4170983)CaDiCaL version: 2.1.3
% 2.99/0.68 % (4170983)Termination reason: Instruction limit
% 2.99/0.68 % (4170983)Termination phase: Saturation
% 2.99/0.68 % (4170983)Time elapsed: 0.330 s
% 2.99/0.68 % (4170983)Peak memory usage: 15 MB
% 2.99/0.68 % (4170983)Instructions burned: 686 (million)
% 2.99/0.68 % (4171003)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1598169985:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 2.99/0.68 % Exception at run slice level
% 2.99/0.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.99/0.68 % (4171004)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2185108286:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 2.99/0.68 % (4171004)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.99/0.68 % (4171006)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1765106215:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 2.99/0.68 % (4171006)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.99/0.68 % (4171006)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.99/0.68 % (4170966) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4170960-4170966"...
% 2.99/0.68 % (4170966)...printing done.
% 2.99/0.68 % (4170966)Refutation found. Thanks to Tanya!
% 2.99/0.68 % SZS status Theorem for theBenchmark
% 2.99/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.99/0.69 % (4170966)------------------------------
% 2.99/0.69 % (4170966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.99/0.69 % (4170966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/0.69 % (4170966)CaDiCaL version: 2.1.3
% 2.99/0.69 % (4170966)Termination reason: Refutation
% 2.99/0.69 % (4170966)Time elapsed: 0.443 s
% 2.99/0.69 % (4170966)Peak memory usage: 15 MB
% 2.99/0.69 % (4170966)Instructions burned: 1810 (million)
% 2.99/0.69 % (4170960)Success in time 0.473 s
% 2.99/0.69 % Vampire exiting
%------------------------------------------------------------------------------