%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:38:12 AM UTC 2026
% Result : Theorem 0.10s 0.17s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 119 ( 26 unt; 0 typ; 6 def)
% Number of atoms : 738 ( 263 equ; 34 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 754 ( 192 ~; 178 |; 47 &; 287 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 29 ( 24 usr; 12 con; 0-4 aty)
% ( 0 !!; 44 ??; 0 @@+; 0 @@-)
% Number of variables : 171 ( 0 sgn 59 !; 7 ?; 171 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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,
vNOT: $o > $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,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def) ).
thf(f2,axiom,
( cONE
= ( cSUCC @ cZERO ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cONE_def) ).
thf(f3,axiom,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X3 != X2 )
& ( X1 @ X3 ) ) )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def) ).
thf(f4,conjecture,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( ^ [X2: $i,X1: $i] : ( X2 = X1 )
@ X1 )
= X0 ) )
= cONE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX6101_pme) ).
thf(f5,negated_conjecture,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( ^ [X2: $i,X1: $i] : ( X2 = X1 )
@ X1 )
= X0 ) )
!= cONE ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( ^ [X2: $i,X3: $i] : ( X2 = X3 )
@ X1 )
= X0 ) )
!= cONE ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( cSUCC
= ( ^ [X0: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X0
@ ^ [X3: $i] :
( ( X3 != X2 )
& ( X1 @ X3 ) ) )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ( ^ [X0: $i > $o] :
~ ? [X1: $i] : ( X0 @ X1 ) )
= cZERO ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f13,plain,
( cONE
= ( cSUCC @ cZERO ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f14,plain,
( cSUCC
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( cZERO
= ( ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( cONE
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( cONE
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f13,f14,f15]) ).
thf(f20,plain,
( ( ^ [Y0: ( $i > $o ) > $o,Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y2 != Y3 ) ) ) ) )
@ ^ [Y0: $i > $o] :
~ ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 )
= Y0 ) ) ) ),
inference(definition_unfolding,[],[f16,f19]) ).
thf(f21,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( (=) @ Y1 )
= Y0 ) ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) )
@ sK0 )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( (=) @ Y1 )
= Y0 ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f21]) ).
thf(f23,plain,
( ( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( (=) @ Y1 )
= Y0 ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ~ ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 != Y2 ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( (=) @ Y1 )
= Y0 ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK0 ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK0 )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( Y0 != Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ X2 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( X2 != Y0 ) ) ) )
= $false )
| ( $false
= ( ( (=) @ X1 )
= sK0 ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( $false
= ( ( (=) @ X1 )
= sK0 ) )
| ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( X2 != Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( X2 != Y0 ) ) ) ) )
| ( ( sK0 @ X2 )
= $false )
| ( sK0
!= ( (=) @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( X2 != Y0 ) ) )
= $true )
| ( sK0
!= ( (=) @ X1 ) ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( sK0
!= ( (=) @ X1 ) )
| ( ( sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( X2 != Y0 ) )
@ ( sK1 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( ( sK0 @ ( sK1 @ X2 ) )
& ( X2
!= ( sK1 @ X2 ) ) )
= $true )
| ( sK0
!= ( (=) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ( X2
!= ( sK1 @ X2 ) )
= $true )
| ( ( sK0 @ X2 )
= $false )
| ( sK0
!= ( (=) @ X1 ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( sK0
!= ( (=) @ X1 ) )
| ( ( sK0 @ ( sK1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2
= ( sK1 @ X2 ) ) )
| ( sK0
!= ( (=) @ X1 ) )
| ( ( sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
!= X2 )
| ( ( sK0 @ X2 )
= $false )
| ( sK0
!= ( (=) @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK0 ) )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f39,plain,
( ( ( ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK0 )
@ sK2 )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( ( ^ [Y0: $i] :
( ( (=) @ Y0 )
= sK0 )
@ sK2 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( Y0 != Y1 ) ) ) )
@ sK3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( ( ( (=) @ sK2 )
= sK0 )
= $true )
| ( ( ( sK0 @ sK3 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK3 != Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK3 != Y0 ) ) ) )
= $true )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(equality_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK3 != Y0 ) ) ) ) )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK3 != Y0 ) ) ) )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(not_proxy_clausification,[],[f43]) ).
thf(f46,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( sK3 != Y0 ) )
@ X1 ) )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( ( $false
= ( ( sK0 @ X1 )
& ( sK3 != X1 ) ) )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK3 != X1 ) )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X1: $i] :
( ( ( sK3 = X1 )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( ( (=) @ sK2 )
= sK0 ) ),
inference(not_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( ( sK3 = X1 )
| ( ( (=) @ sK2 )
= sK0 )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f49]) ).
thf(f52,definition,
( spl4_1
<=> ! [X1: $i] :
( sK0
!= ( (=) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f53,plain,
( ! [X1: $i] :
( sK0
!= ( (=) @ X1 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,definition,
( spl4_2
<=> ! [X2: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( sK0 @ ( sK1 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f56,plain,
( ! [X2: $i] :
( ( ( sK0 @ ( sK1 @ X2 ) )
= $true )
| ( ( sK0 @ X2 )
= $false ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f57,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f35,f55,f52]) ).
thf(f59,definition,
( spl4_3
<=> ! [X2: $i] :
( ( ( sK1 @ X2 )
!= X2 )
| ( ( sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f60,plain,
( ! [X2: $i] :
( ( ( sK1 @ X2 )
!= X2 )
| ( ( sK0 @ X2 )
= $false ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f61,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f37,f52,f59]) ).
thf(f63,definition,
( spl4_4
<=> ( ( (=) @ sK2 )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f65,plain,
( ( ( (=) @ sK2 )
= sK0 )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f67,definition,
( spl4_5
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f69,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f70,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f44,f67,f63]) ).
thf(f72,definition,
( spl4_6
<=> ! [X1: $i] :
( ( sK3 = X1 )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f73,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f74,plain,
( spl4_4
| spl4_6 ),
inference(avatar_split_clause,[],[f50,f72,f63]) ).
thf(f75,plain,
( ! [X1: $i] :
( ( sK2 = X1 )
= ( sK0 @ X1 ) )
| ~ spl4_4 ),
inference(argument_congruence,[],[f65]) ).
thf(f76,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK2 = X1 )
= $true ) )
| ~ spl4_4 ),
inference(iff_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ! [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
| ( $false
= ( sK2 = X1 ) ) )
| ~ spl4_4 ),
inference(iff_proxy_clausification,[],[f75]) ).
thf(f78,plain,
( ! [X1: $i] :
( ( sK2 != X1 )
| ( ( sK0 @ X1 )
= $true ) )
| ~ spl4_4 ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK2 = X1 ) )
| ~ spl4_4 ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f81,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl4_4 ),
inference(equality_resolution,[],[f78]) ).
thf(f84,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( $false = $true )
| ( sK2
= ( sK1 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f56,f79]) ).
thf(f86,plain,
( ! [X0: $i] :
( ( sK2
= ( sK1 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f89,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK2 != X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f60,f86]) ).
thf(f91,plain,
( ! [X0: $i] :
( ( sK2 != X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(duplicate_literal_removal,[],[f89]) ).
thf(f92,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f91,f79]) ).
thf(f95,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f81,f92]) ).
thf(f101,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f102,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f101]) ).
thf(f103,plain,
( ! [X1: $i] :
( ( sK0 @ ( sK5 @ X1 ) )
!= ( X1
= ( sK5 @ X1 ) ) )
| ~ spl4_1 ),
inference(negative_extensionality,[],[f53]) ).
thf(f104,plain,
( ( sK0 != sK0 )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f53,f65]) ).
thf(f105,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f105]) ).
thf(f107,plain,
( ! [X1: $i] :
( ( ( sK0 @ ( sK5 @ X1 ) )
= $true )
| ( $true
= ( X1
= ( sK5 @ X1 ) ) ) )
| ~ spl4_1 ),
inference(xor_proxy_clausification,[],[f103]) ).
thf(f108,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ ( sK5 @ X1 ) ) )
| ( $false
= ( X1
= ( sK5 @ X1 ) ) ) )
| ~ spl4_1 ),
inference(xor_proxy_clausification,[],[f103]) ).
thf(f109,plain,
( ! [X1: $i] :
( ( ( sK5 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ ( sK5 @ X1 ) ) ) )
| ~ spl4_1 ),
inference(equality_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ! [X1: $i] :
( ( ( sK0 @ ( sK5 @ X1 ) )
= $true )
| ( ( sK5 @ X1 )
= X1 ) )
| ~ spl4_1 ),
inference(equality_proxy_clausification,[],[f107]) ).
thf(f112,plain,
( ! [X0: $i] :
( ( ( sK5 @ X0 )
= X0 )
| ( $false = $true )
| ( sK3
= ( sK5 @ X0 ) ) )
| ~ spl4_1
| ~ spl4_6 ),
inference(constrained_superposition,[],[f110,f73]) ).
thf(f114,plain,
( ! [X0: $i] :
( ( ( sK5 @ X0 )
= X0 )
| ( sK3
= ( sK5 @ X0 ) ) )
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f119,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( sK3
= ( sK5 @ X0 ) ) )
| ~ spl4_1
| ~ spl4_6 ),
inference(equality_factoring,[],[f114]) ).
thf(f122,plain,
( ( sK3 != sK3 )
| ( ( sK5 @ sK3 )
= sK3 )
| ~ spl4_1
| ~ spl4_6 ),
inference(imitation,[],[f119]) ).
thf(f124,plain,
( ( ( sK5 @ sK3 )
= sK3 )
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f125,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( sK3 != sK3 )
| ~ spl4_1
| ~ spl4_6 ),
inference(constrained_superposition,[],[f109,f124]) ).
thf(f126,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f127,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f126,f69]) ).
thf(f128,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f129,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f128]) ).
thf(f150,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK3
= ( sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f56,f73]) ).
thf(f152,plain,
( ! [X0: $i] :
( ( sK3
= ( sK1 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f155,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK0 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f60,f152]) ).
thf(f156,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f155]) ).
thf(f158,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f156,f73]) ).
thf(f162,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(constrained_superposition,[],[f69,f158]) ).
thf(f167,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f168,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f167]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f70]) ).
cnf(s4,plain,
( spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f74]) ).
cnf(s6,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f106]) ).
cnf(s8,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s12,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f168]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(rat,[],[s12,s3,s4,s6]) ).
cnf(s14,plain,
spl4_1,
inference(rat,[],[s13,s1,s2]) ).
cnf(s15,plain,
~ spl4_4,
inference(rat,[],[s7,s14]) ).
cnf(s16,plain,
spl4_6,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
spl4_5,
inference(rat,[],[s3,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s8,s14,s16,s17]) ).
thf(f169,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV293^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 15:31:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.13 Running higher-order theorem proving
% 0.10/0.13 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % (250902)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.17 % (250920)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.17 % (250920)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.10/0.17 % (250914)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1756695016:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.17 % (250918)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4058214149:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.10/0.17 % (250915)lrs+10_16_si=on:nwc=1.5:random_seed=105648238:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.10/0.17 % (250919)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1085172483:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.10/0.17 % (250916)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=959048776:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.10/0.17 % (250920)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1268035999:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.10/0.17 % (250917)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3998256271:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.10/0.17 % (250916)Refutation not found, incomplete strategy
% 0.10/0.17 % (250916)------------------------------
% 0.10/0.17 % (250916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.17 % (250916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.17 % (250916)CaDiCaL version: 2.1.3
% 0.10/0.17 % (250916)Termination reason: Refutation not found, incomplete strategy
% 0.10/0.17 % (250916)Time elapsed: 0.001 s
% 0.10/0.17 % (250916)Peak memory usage: 12 MB
% 0.10/0.17 % (250916)Instructions burned: 1 (million)
% 0.10/0.17 % (250916)------------------------------
% 0.10/0.17 % (250916)------------------------------
% 0.10/0.17 % (250914) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-250902-250914"...
% 0.10/0.17 % (250915) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-250902-250915"...
% 0.10/0.17 % (250920) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-250902-250920"...
% 0.10/0.17 % (250914)...printing done.
% 0.10/0.17 % (250914)Refutation found. Thanks to Tanya!
% 0.10/0.17 % SZS status Theorem for theBenchmark
% 0.10/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.17 % (250914)------------------------------
% 0.10/0.17 % (250914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.17 % (250914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.17 % (250914)CaDiCaL version: 2.1.3
% 0.10/0.17 % (250914)Termination reason: Refutation
% 0.10/0.17 % (250914)Time elapsed: 0.004 s
% 0.10/0.17 % (250914)Peak memory usage: 13 MB
% 0.10/0.17 % (250914)Instructions burned: 11 (million)
% 0.10/0.17 % (250902)Success in time 0.034 s
% 0.10/0.17 % Vampire exiting
%------------------------------------------------------------------------------