%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:39:16 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 130 ( 29 unt; 0 typ; 7 def)
% Number of atoms : 765 ( 261 equ; 34 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 772 ( 199 ~; 185 |; 48 &; 289 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 13 con; 0-4 aty)
% ( 0 !!; 44 ??; 0 @@+; 0 @@-)
% Number of variables : 165 ( 0 sgn 53 !; 7 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cONE: ( $i > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK0: $i > $o ).
thf(func_def_16,type,
sK1: $i > $i ).
thf(func_def_20,type,
sK5: $i > $i ).
thf(f1,axiom,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def) ).
thf(f2,axiom,
( cONE
= ( cSUCC @ cZERO ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cONE_def) ).
thf(f3,axiom,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X3 != X2 ) ) )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def) ).
thf(f4,conjecture,
( cONE
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( X0
= ( ^ [X2: $i,X1: $i] : ( X2 = X1 )
@ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_pme) ).
thf(f5,negated_conjecture,
( cONE
!= ( ^ [X0: $i > $o] :
? [X1: $i] :
( X0
= ( ^ [X2: $i,X1: $i] : ( X2 = X1 )
@ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( cZERO
= ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X1 @ X3 )
& ( X3 != X2 ) ) )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( cONE
!= ( ^ [X0: $i > $o] :
? [X1: $i] :
( X0
= ( ^ [X2: $i,X3: $i] : ( X2 = X3 )
@ X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( cONE
= ( cSUCC @ cZERO ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f15,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( cONE
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f14,f15,f13]) ).
thf(f20,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) )
!= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y2 != Y3 )
& ( Y1 @ Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f16,f19]) ).
thf(f21,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( (=) @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f29,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( (=) @ Y1 ) ) )
@ sK0 )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f21]) ).
thf(f30,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( (=) @ Y1 ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( Y0
= ( (=) @ Y1 ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 != Y2 )
& ( Y0 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( sK0
= ( (=) @ Y0 ) ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( sK0
= ( (=) @ Y0 ) )
@ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( sK0
= ( (=) @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0
= ( (=) @ X1 ) ) )
| ( $false
= ( ( sK0 @ X2 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 != Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $false
= ( ( sK0 @ X2 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 != Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 != Y0 )
& ( sK0 @ Y0 ) ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( X2 != Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( X2 != Y0 )
& ( sK0 @ Y0 ) )
@ ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $true
= ( ( X2
!= ( sK1 @ X2 ) )
& ( sK0 @ ( sK1 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $true
= ( sK0 @ ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $true
= ( X2
!= ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( $false
= ( X2
= ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( ( sK1 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( sK0
= ( (=) @ Y0 ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f46,plain,
( ( $true
= ( ^ [Y0: $i] :
( sK0
= ( (=) @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( ^ [Y0: $i] :
( sK0
= ( (=) @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y1 ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $true
= ( sK0
= ( (=) @ sK2 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 != Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
( ( sK0
= ( (=) @ sK2 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 != Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f50,plain,
( ( sK0
= ( (=) @ sK2 ) )
| ( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 != Y0 )
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( sK0
= ( (=) @ sK2 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f52,plain,
( ( sK0
= ( (=) @ sK2 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK3 != Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f50]) ).
thf(f53,plain,
! [X1: $i] :
( ( sK0
= ( (=) @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK3 != Y0 )
& ( sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( ( sK0
= ( (=) @ sK2 ) )
| ( $false
= ( ( sK3 != X1 )
& ( sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( ( sK0
= ( (=) @ sK2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK3 != X1 ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( ( sK0
= ( (=) @ sK2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK3 = X1 ) ) ),
inference(not_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( sK0
= ( (=) @ sK2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) ),
inference(equality_proxy_clausification,[],[f56]) ).
thf(f59,definition,
( spl4_1
<=> ! [X2: $i] :
( ( ( sK1 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f60,plain,
( ! [X2: $i] :
( ( ( sK1 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,definition,
( spl4_2
<=> ! [X1: $i] :
( sK0
!= ( (=) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f63,plain,
( ! [X1: $i] :
( sK0
!= ( (=) @ X1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f64,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f44,f62,f59]) ).
thf(f66,definition,
( spl4_3
<=> ! [X2: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f67,plain,
( ! [X2: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f68,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f41,f62,f66]) ).
thf(f70,definition,
( spl4_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f72,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f74,definition,
( spl4_5
<=> ( sK0
= ( (=) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f76,plain,
( ( sK0
= ( (=) @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f51,f74,f70]) ).
thf(f79,definition,
( spl4_6
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f80,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f81,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f57,f74,f79]) ).
thf(f82,plain,
( ! [X1: $i] :
( ( sK0 @ ( sK5 @ X1 ) )
!= ( X1
= ( sK5 @ X1 ) ) )
| ~ spl4_2 ),
inference(negative_extensionality,[],[f63]) ).
thf(f83,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ ( sK5 @ X1 ) ) )
| ( $true
= ( X1
= ( sK5 @ X1 ) ) ) )
| ~ spl4_2 ),
inference(xor_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ ( sK5 @ X1 ) ) )
| ( $false
= ( X1
= ( sK5 @ X1 ) ) ) )
| ~ spl4_2 ),
inference(xor_proxy_clausification,[],[f82]) ).
thf(f85,plain,
( ! [X1: $i] :
( ( ( sK5 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ ( sK5 @ X1 ) ) ) )
| ~ spl4_2 ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ ( sK5 @ X1 ) ) )
| ( ( sK5 @ X1 )
= X1 ) )
| ~ spl4_2 ),
inference(equality_proxy_clausification,[],[f83]) ).
thf(f87,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f76,f63]) ).
thf(f88,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f87]) ).
thf(f92,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( sK3
= ( sK5 @ X0 ) )
| ( ( sK5 @ X0 )
= X0 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f80,f86]) ).
thf(f93,plain,
( ! [X0: $i] :
( ( sK3
= ( sK5 @ X0 ) )
| ( ( sK5 @ X0 )
= X0 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f99,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( sK3
= ( sK5 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(equality_factoring,[],[f93]) ).
thf(f102,definition,
( spl4_7
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f103,plain,
( ( $false
!= ( sK0 @ sK3 ) )
| spl4_7 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f104,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f110,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_7 ),
inference(constrained_superposition,[],[f104,f72]) ).
thf(f111,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_7 ),
inference(constrained_superposition,[],[f72,f104]) ).
thf(f112,plain,
( $false
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f113,plain,
( ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f112]) ).
thf(f114,plain,
( $false
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f115,plain,
( ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f114]) ).
thf(f120,plain,
( ( sK3
= ( sK5 @ sK3 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(equality_resolution,[],[f99]) ).
thf(f121,plain,
( ( sK3 != sK3 )
| ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f85,f120]) ).
thf(f122,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f123,plain,
( $false
| ~ spl4_2
| ~ spl4_6
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f122,f103]) ).
thf(f124,plain,
( ~ spl4_2
| ~ spl4_6
| spl4_7 ),
inference(avatar_contradiction_clause,[],[f123]) ).
thf(f145,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( sK3
= ( sK1 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f80,f67]) ).
thf(f146,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK3
= ( sK1 @ X0 ) ) )
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f157,plain,
( ( $true = $false )
| ( sK3
= ( sK1 @ sK3 ) )
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(constrained_superposition,[],[f72,f146]) ).
thf(f158,plain,
( ( sK3
= ( sK1 @ sK3 ) )
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f165,plain,
( ( sK3 != sK3 )
| ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(constrained_superposition,[],[f60,f158]) ).
thf(f166,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f167,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f166,f103]) ).
thf(f168,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6
| spl4_7 ),
inference(avatar_contradiction_clause,[],[f167]) ).
thf(f169,plain,
( ! [X1: $i] :
( ( sK0 @ X1 )
= ( sK2 = X1 ) )
| ~ spl4_5 ),
inference(argument_congruence,[],[f76]) ).
thf(f170,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( $false
= ( sK2 = X1 ) ) )
| ~ spl4_5 ),
inference(iff_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK2 = X1 ) ) )
| ~ spl4_5 ),
inference(iff_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK2 = X1 ) )
| ~ spl4_5 ),
inference(equality_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ! [X1: $i] :
( ( sK2 != X1 )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl4_5 ),
inference(equality_proxy_clausification,[],[f170]) ).
thf(f177,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 ) )
| ( sK2
= ( sK1 @ X0 ) ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f67,f172]) ).
thf(f182,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK2
= ( sK1 @ X0 ) ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f177]) ).
thf(f196,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl4_5 ),
inference(equality_resolution,[],[f173]) ).
thf(f202,plain,
( ( $true = $false )
| ( sK2
= ( sK1 @ sK2 ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f196,f182]) ).
thf(f207,plain,
( ( sK2
= ( sK1 @ sK2 ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f217,plain,
( ( sK2 != sK2 )
| ( $false
= ( sK0 @ sK2 ) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f60,f207]) ).
thf(f218,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f243,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5 ),
inference(constrained_superposition,[],[f218,f196]) ).
thf(f247,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f248,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f247]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f68]) ).
cnf(s3,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f77]) ).
cnf(s4,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f81]) ).
cnf(s5,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f88]) ).
cnf(s7,plain,
( ~ spl4_4
| ~ spl4_7 ),
inference(sat_conversion,[],[f113]) ).
cnf(s8,plain,
( ~ spl4_4
| ~ spl4_7 ),
inference(sat_conversion,[],[f115]) ).
cnf(s10,plain,
( ~ spl4_2
| ~ spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f124]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f168]) ).
cnf(s20,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f248]) ).
cnf(s21,plain,
~ spl4_2,
inference(rat,[],[s7,s10,s3,s4,s5]) ).
cnf(s22,plain,
spl4_3,
inference(rat,[],[s2,s21]) ).
cnf(s23,plain,
spl4_1,
inference(rat,[],[s1,s21]) ).
cnf(s24,plain,
~ spl4_5,
inference(rat,[],[s20,s22,s23]) ).
cnf(s25,plain,
spl4_6,
inference(rat,[],[s4,s24]) ).
cnf(s26,plain,
spl4_4,
inference(rat,[],[s3,s24]) ).
cnf(s27,plain,
~ spl4_7,
inference(rat,[],[s8,s26]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s13,s25,s22,s23,s27,s26]) ).
thf(f250,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % 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 15:32:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.08/0.26 % (3302499)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (3302505)% WARNING: option uhcvi not known.
% 0.08/0.26 % (3302505)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1019866830:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (3302505)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (3302505)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (3302505) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3302499-3302505"...
% 0.08/0.26 % (3302505)...printing done.
% 0.08/0.26 % (3302504)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=268818613_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (3302506)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=885671362:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (3302505)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3302505)------------------------------
% 0.08/0.26 % (3302505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3302505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3302505)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3302505)Termination reason: Refutation
% 0.08/0.26 % (3302505)Time elapsed: 0.006 s
% 0.08/0.26 % (3302505)Peak memory usage: 13 MB
% 0.08/0.26 % (3302505)Instructions burned: 15 (million)
% 0.08/0.26 % (3302499)Success in time 0.03 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------