%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU550^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:30:02 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 172 ( 13 unt; 0 typ; 8 def)
% Number of atoms : 1240 ( 342 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1232 ( 253 ~; 371 |; 32 &; 445 @)
% ( 14 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 14 con; 0-4 aty)
% ( 37 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 217 ( 0 sgn 114 !; 6 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: $i > $o ).
thf(func_def_12,type,
sK1: $i > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK2: $i > $i ).
thf(func_def_17,type,
sK3: $i > $i ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu_def) ).
thf(f2,conjecture,
! [X1: $i > $o,X0: $i > $o] :
( ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X3 )
<=> ( X0 @ X2 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(f3,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o] :
( ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X3 )
<=> ( X0 @ X2 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
<=> ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) )
<=> ( exu
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $i > $o,X0: $i > $o] :
( ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $i > $o,X0: $i > $o] :
( ! [X3: $i,X2: $i] :
( ( ( X0 @ X2 )
= ( X1 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= ( X1 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ! [X2: $i,X3: $i] :
( ( ( sK1 @ X3 )
= ( sK0 @ X2 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f12,plain,
! [X2: $i,X3: $i] :
( ( ( sK1 @ X3 )
= ( sK0 @ X2 ) )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f16,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(definition_unfolding,[],[f11,f13,f13]) ).
thf(f17,plain,
! [X3: $i] :
( ( sK0 @ X3 )
= ( sK1 @ X3 ) ),
inference(equality_resolution,[],[f12]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
= $false )
| ( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f20,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) ) )
| ( ( ( sK1 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ( sK1 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK2 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK3 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK2 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ( sK1 @ ( sK2 @ X2 ) )
=> ( X2
= ( sK2 @ X2 ) ) )
= $false )
| ( ( ( sK0 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2
= ( sK2 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( ( sK0 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ ( sK2 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( ( sK0 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ( X1
= ( sK3 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( sK1 @ ( sK2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
| ( $true
= ( sK1 @ ( sK2 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ ( sK2 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK3 @ X1 )
!= X1 ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK2 @ X2 )
!= X2 )
| ( ( ( sK0 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( X1
= ( sK3 @ X1 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK2 @ X2 )
!= X2 ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X2 )
!= X2 )
| ( ( sK1 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK0 @ ( sK3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( ( sK2 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK3 @ X1 )
!= X1 ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f39,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK4 )
= $true )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK5 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK4 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $true
= ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK4 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
( ( $true
= ( ( sK0 @ sK4 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $true
= ( ( sK0 @ sK4 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f44,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f46,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X1 ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f47,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ X1 )
=> ( sK4 = X1 ) ) )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK4 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK4 = X1 )
| ( $true
= ( sK1 @ sK5 ) ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f50,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f51,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f52,plain,
! [X1: $i] :
( ( ( sK0 @ sK4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: $i] :
( ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( ( sK1 @ X1 )
=> ( sK5 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( ( $true
= ( sK5 = X1 ) )
| ( ( sK0 @ sK4 )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( ( sK5 = X1 )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X2 )
=> ( sK4 = X2 ) ) )
| ( $true
= ( ( sK1 @ X1 )
=> ( sK5 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK4 = X2 ) )
| ( $true
= ( ( sK1 @ X1 )
=> ( sK5 = X1 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( sK4 = X2 )
| ( $true
= ( ( sK1 @ X1 )
=> ( sK5 = X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK5 = X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( sK4 = X2 ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( sK5 = X1 )
| ( $false
= ( sK1 @ X1 ) )
| ( sK4 = X2 ) ),
inference(equality_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X3: $i] :
( ( ( sK1 @ X3 )
= $false )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f64,plain,
! [X3: $i] :
( ( $true
= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f66,definition,
( spl6_1
<=> ! [X2: $i] :
( ( $true
= ( sK1 @ ( sK2 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f67,plain,
( ! [X2: $i] :
( ( $true
= ( sK1 @ ( sK2 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f69,definition,
( spl6_2
<=> ! [X1: $i] :
( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f70,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f71,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f32,f69,f66]) ).
thf(f73,definition,
( spl6_3
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK3 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f74,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f75,plain,
( spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f33,f66,f73]) ).
thf(f77,definition,
( spl6_4
<=> ! [X2: $i] :
( ( ( sK2 @ X2 )
!= X2 )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f78,plain,
( ! [X2: $i] :
( ( ( sK2 @ X2 )
!= X2 )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f79,plain,
( spl6_4
| spl6_2 ),
inference(avatar_split_clause,[],[f36,f69,f77]) ).
thf(f80,plain,
( spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f37,f73,f77]) ).
thf(f82,definition,
( spl6_5
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f84,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f86,definition,
( spl6_6
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f88,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f89,plain,
( spl6_5
| spl6_6 ),
inference(avatar_split_clause,[],[f45,f86,f82]) ).
thf(f91,definition,
( spl6_7
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f92,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK4 = X1 ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f93,plain,
( spl6_7
| spl6_6 ),
inference(avatar_split_clause,[],[f49,f86,f91]) ).
thf(f95,definition,
( spl6_8
<=> ! [X1: $i] :
( ( sK5 = X1 )
| ( $false
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f96,plain,
( ! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK5 = X1 ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f97,plain,
( spl6_8
| spl6_5 ),
inference(avatar_split_clause,[],[f55,f82,f95]) ).
thf(f98,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f62,f95,f91]) ).
thf(f103,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( ( sK3 @ X0 )
= sK4 )
| ( $true = $false ) )
| ~ spl6_2
| ~ spl6_7 ),
inference(constrained_superposition,[],[f92,f70]) ).
thf(f104,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( ( sK3 @ X0 )
= sK4 ) )
| ~ spl6_2
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f106,plain,
( ( $true = $false )
| ( ( sK3 @ sK4 )
= sK4 )
| ~ spl6_2
| ~ spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f104,f84]) ).
thf(f111,plain,
( ( ( sK3 @ sK4 )
= sK4 )
| ~ spl6_2
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f115,plain,
( ( sK4 != sK4 )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f74,f111]) ).
thf(f116,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f117,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(forward_demodulation,[],[f116,f84]) ).
thf(f118,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f119,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f118]) ).
thf(f121,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true = $false )
| ~ spl6_6 ),
inference(constrained_superposition,[],[f88,f63]) ).
thf(f123,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f137,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( $true = $false )
| ( sK5 = X0 ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f96,f64]) ).
thf(f139,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK5 = X0 ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f142,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK3 @ X0 )
= sK5 )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl6_2
| ~ spl6_8 ),
inference(constrained_superposition,[],[f70,f139]) ).
thf(f144,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( ( sK3 @ X0 )
= sK5 ) )
| ~ spl6_2
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f150,plain,
( ( $true = $false )
| ( sK5
= ( sK3 @ sK5 ) )
| ~ spl6_2
| ~ spl6_6
| ~ spl6_8 ),
inference(constrained_superposition,[],[f123,f144]) ).
thf(f151,plain,
( ( sK5
= ( sK3 @ sK5 ) )
| ~ spl6_2
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f156,plain,
( ( sK5 != sK5 )
| ( ( sK0 @ sK5 )
= $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(constrained_superposition,[],[f74,f151]) ).
thf(f157,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f158,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(forward_demodulation,[],[f157,f123]) ).
thf(f159,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f160,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f159]) ).
thf(f168,plain,
( ( sK5 = sK4 )
| ( $true = $false )
| ~ spl6_5
| ~ spl6_8 ),
inference(constrained_superposition,[],[f139,f84]) ).
thf(f169,plain,
( ( sK5 = sK4 )
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f189,plain,
( ! [X0: $i] :
( ( sK5
= ( sK2 @ X0 ) )
| ( $true = $false )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(constrained_superposition,[],[f67,f96]) ).
thf(f190,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $true = $false )
| ( $true
= ( sK0 @ ( sK2 @ X0 ) ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f67,f63]) ).
thf(f191,plain,
( ! [X0: $i] :
( ( sK5
= ( sK2 @ X0 ) )
| ( $true = $false )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(constrained_superposition,[],[f96,f67]) ).
thf(f193,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f195,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK5
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f196,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK5
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f197,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK4
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_8 ),
inference(forward_demodulation,[],[f195,f169]) ).
thf(f199,plain,
( ! [X0: $i] :
( ( sK4
= ( sK2 @ X0 ) )
| ( $true = $false )
| ( $false
= ( sK0 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_8 ),
inference(constrained_superposition,[],[f197,f64]) ).
thf(f205,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK4
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f199]) ).
thf(f210,plain,
( ( $true = $false )
| ( ( sK2 @ sK4 )
= sK4 )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_8 ),
inference(constrained_superposition,[],[f84,f205]) ).
thf(f211,plain,
( ( ( sK2 @ sK4 )
= sK4 )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f216,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( sK4 != sK4 )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(constrained_superposition,[],[f78,f211]) ).
thf(f217,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f219,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(constrained_superposition,[],[f64,f217]) ).
thf(f221,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f225,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(forward_demodulation,[],[f221,f84]) ).
thf(f226,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f227,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f226]) ).
thf(f238,plain,
( ( ( sK2 @ sK5 )
= sK5 )
| ( $true = $false )
| ~ spl6_1
| ~ spl6_6
| ~ spl6_8 ),
inference(constrained_superposition,[],[f88,f196]) ).
thf(f243,plain,
( ( ( sK2 @ sK5 )
= sK5 )
| ~ spl6_1
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f246,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( sK5 != sK5 )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(constrained_superposition,[],[f78,f243]) ).
thf(f247,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f248,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(forward_demodulation,[],[f247,f88]) ).
thf(f249,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f250,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f249]) ).
thf(f251,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $true = $false )
| ( sK4
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_7 ),
inference(constrained_superposition,[],[f193,f92]) ).
thf(f253,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK4
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f257,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 ) )
| ( sK4
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_7 ),
inference(constrained_superposition,[],[f64,f253]) ).
thf(f259,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK4
= ( sK2 @ X0 ) ) )
| ~ spl6_1
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f263,plain,
( ( $true = $false )
| ( ( sK2 @ sK4 )
= sK4 )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f259,f84]) ).
thf(f268,plain,
( ( ( sK2 @ sK4 )
= sK4 )
| ~ spl6_1
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f263]) ).
thf(f273,plain,
( ( sK4 != sK4 )
| ( ( sK1 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f78,f268]) ).
thf(f274,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f276,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $true = $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(constrained_superposition,[],[f64,f274]) ).
thf(f278,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f282,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(forward_demodulation,[],[f278,f84]) ).
thf(f283,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f284,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f283]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f71]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f75]) ).
cnf(s3,plain,
( spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f79]) ).
cnf(s4,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f80]) ).
cnf(s5,plain,
( spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f89]) ).
cnf(s6,plain,
( spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f93]) ).
cnf(s7,plain,
( spl6_5
| spl6_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s8,plain,
( spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f98]) ).
cnf(s9,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(sat_conversion,[],[f119]) ).
cnf(s11,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(sat_conversion,[],[f160]) ).
cnf(s13,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_8 ),
inference(sat_conversion,[],[f227]) ).
cnf(s14,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(sat_conversion,[],[f250]) ).
cnf(s16,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_7 ),
inference(sat_conversion,[],[f284]) ).
cnf(s17,plain,
( spl6_5
| spl6_1 ),
inference(rat,[],[s11,s5,s7,s2,s1]) ).
cnf(s18,plain,
( ~ spl6_5
| ~ spl6_2
| ~ spl6_3 ),
inference(rat,[],[s11,s6,s8,s9]) ).
cnf(s19,plain,
spl6_1,
inference(rat,[],[s18,s17,s1,s2]) ).
cnf(s20,plain,
( ~ spl6_3
| ~ spl6_2 ),
inference(rat,[],[s11,s5,s7,s18]) ).
cnf(s21,plain,
( spl6_5
| ~ spl6_4 ),
inference(rat,[],[s14,s5,s7,s19]) ).
cnf(s22,plain,
( ~ spl6_5
| ~ spl6_4 ),
inference(rat,[],[s8,s13,s16,s19]) ).
cnf(s23,plain,
~ spl6_4,
inference(rat,[],[s22,s21]) ).
cnf(s24,plain,
spl6_3,
inference(rat,[],[s4,s23]) ).
cnf(s25,plain,
spl6_2,
inference(rat,[],[s3,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s20,s25,s24]) ).
thf(f285,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU550^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:49:37 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.31 % (1317805)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (1317816)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (1317816)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
% 0.23/0.31 % (1317814)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=265805614:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (1317810)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2657488202:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (1317812)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3766709803:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (1317815)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=475306209:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (1317813)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=3954446530: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)
% 0.23/0.31 % (1317816)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=3060689165:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (1317812)Refutation not found, incomplete strategy
% 0.23/0.31 % (1317812)------------------------------
% 0.23/0.31 % (1317812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1317812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1317812)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1317812)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (1317812)Time elapsed: 0.001 s
% 0.23/0.31 % (1317812)Peak memory usage: 12 MB
% 0.23/0.31 % (1317812)Instructions burned: 1 (million)
% 0.23/0.31 % (1317811)lrs+10_16_si=on:nwc=1.5:random_seed=3635369481:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (1317812)------------------------------
% 0.23/0.31 % (1317812)------------------------------
% 0.23/0.31 % (1317810) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1317805-1317810"...
% 0.23/0.31 % (1317810)...printing done.
% 0.23/0.31 % (1317814)Instruction limit reached!
% 0.23/0.31 % (1317814)------------------------------
% 0.23/0.31 % (1317814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1317814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1317814)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1317814)Termination reason: Instruction limit
% 0.23/0.31 % (1317814)Termination phase: Saturation
% 0.23/0.31 % (1317814)Time elapsed: 0.013 s
% 0.23/0.31 % (1317814)Peak memory usage: 11 MB
% 0.23/0.31 % (1317814)Instructions burned: 24 (million)
% 0.23/0.31 % (1317816) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1317805-1317816"...
% 0.23/0.31 % (1317810)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (1317810)------------------------------
% 0.23/0.31 % (1317810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1317810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1317810)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1317810)Termination reason: Refutation
% 0.23/0.31 % (1317810)Time elapsed: 0.011 s
% 0.23/0.31 % (1317810)Peak memory usage: 13 MB
% 0.23/0.32 % (1317810)Instructions burned: 17 (million)
% 0.23/0.32 % (1317805)Success in time 0.058 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------