%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU895^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:31:53 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 134 ( 16 unt; 0 typ; 9 def)
% Number of atoms : 866 ( 317 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 907 ( 97 ~; 271 |; 78 &; 416 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 24 usr; 16 con; 0-4 aty)
% ( 0 !!; 36 ??; 0 @@+; 0 @@-)
% Number of variables : 109 ( 0 sgn 34 !; 9 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: b > a ).
thf(func_def_1,type,
y: b > $o ).
thf(func_def_2,type,
x: b > $o ).
thf(func_def_4,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
vOR: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[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_13,type,
sK0: a ).
thf(func_def_14,type,
sK1: b ).
thf(func_def_15,type,
sK2: b ).
thf(func_def_16,type,
sK3: b ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( ( y @ X1 )
| ( x @ X1 ) ) ) )
= ( ^ [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( x @ X1 ) )
| ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5202_pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( ( y @ X1 )
| ( x @ X1 ) ) ) )
!= ( ^ [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( x @ X1 ) )
| ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a] :
? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( ( y @ X1 )
| ( x @ X1 ) ) ) )
!= ( ^ [X2: a] :
( ? [X3: b] :
( ( ( f @ X3 )
= X2 )
& ( x @ X3 ) )
| ? [X4: b] :
( ( ( f @ X4 )
= X2 )
& ( y @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
@ sK0 )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f6]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f11,plain,
( ( $false
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f12,plain,
( ( $false
= ( ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) )
= $false )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) )
= $false )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f12]) ).
thf(f15,plain,
! [X1: b] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X2: b,X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( ( x @ X1 )
| ( y @ X1 ) )
& ( ( f @ X1 )
= sK0 ) ) )
| ( $false
= ( ( y @ X2 )
& ( ( f @ X2 )
= sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( ( f @ X1 )
= sK0 ) )
| ( $false
= ( ( y @ X2 )
& ( ( f @ X2 )
= sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X2: b,X1: b] :
( ( ( y @ X1 )
= $false )
| ( $false
= ( ( y @ X2 )
& ( ( f @ X2 )
= sK0 ) ) )
| ( $false
= ( ( f @ X1 )
= sK0 ) ) ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f24,plain,
! [X2: b,X1: b] :
( ( ( y @ X1 )
= $false )
| ( $false
= ( ( f @ X1 )
= sK0 ) )
| ( $false
= ( y @ X2 ) )
| ( $false
= ( ( f @ X2 )
= sK0 ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f25,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( f @ X2 )
= sK0 ) )
| ( ( y @ X1 )
= $false )
| ( ( f @ X1 )
!= sK0 )
| ( $false
= ( y @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: b,X1: b] :
( ( $false
= ( y @ X2 ) )
| ( sK0
!= ( f @ X2 ) )
| ( ( y @ X1 )
= $false )
| ( ( f @ X1 )
!= sK0 ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: b] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f13]) ).
thf(f28,plain,
! [X2: b,X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( ( x @ X1 )
| ( y @ X1 ) )
& ( ( f @ X1 )
= sK0 ) ) )
| ( $false
= ( ( x @ X2 )
& ( ( f @ X2 )
= sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( x @ X2 )
& ( ( f @ X2 )
= sK0 ) ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( ( f @ X1 )
= sK0 ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( f @ X1 )
= sK0 ) )
| ( $false
= ( ( f @ X2 )
= sK0 ) )
| ( $false
= ( x @ X2 ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: b,X1: b] :
( ( $false
= ( x @ X2 ) )
| ( ( f @ X1 )
!= sK0 )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( ( f @ X2 )
= sK0 ) ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f34,plain,
! [X2: b,X1: b] :
( ( $false
= ( x @ X2 ) )
| ( ( x @ X1 )
= $false )
| ( $false
= ( ( f @ X2 )
= sK0 ) )
| ( ( f @ X1 )
!= sK0 ) ),
inference(or_proxy_clausification,[],[f32]) ).
thf(f35,plain,
! [X2: b,X1: b] :
( ( $false
= ( x @ X2 ) )
| ( sK0
!= ( f @ X2 ) )
| ( ( x @ X1 )
= $false )
| ( ( f @ X1 )
!= sK0 ) ),
inference(equality_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( ( ( ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f38,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true )
| ( ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ( ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
= $true )
| ( ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ sK2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( ( ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 )
= $true )
| ( ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ sK2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( ( ( ( x @ sK1 )
| ( y @ sK1 ) )
& ( ( f @ sK1 )
= sK0 ) )
= $true )
| ( ( ( x @ sK2 )
& ( ( f @ sK2 )
= sK0 ) )
= $true )
| ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
( ( ( ( x @ sK2 )
& ( ( f @ sK2 )
= sK0 ) )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true )
| ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( ( ( x @ sK1 )
| ( y @ sK1 ) )
= $true )
| ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true )
| ( ( ( x @ sK2 )
& ( ( f @ sK2 )
= sK0 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f45,plain,
( ( ( ( x @ sK2 )
& ( ( f @ sK2 )
= sK0 ) )
= $true )
| ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true )
| ( ( x @ sK1 )
= $true )
| ( ( y @ sK1 )
= $true ) ),
inference(or_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( ( y @ sK1 )
= $true )
| ( ( x @ sK1 )
= $true )
| ( ( ( f @ sK2 )
= sK0 )
= $true )
| ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( ( x @ sK2 )
= $true )
| ( ( x @ sK1 )
= $true )
| ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true )
| ( ( y @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f48,plain,
( ( ( x @ sK1 )
= $true )
| ( ( ( f @ sK3 )
= sK0 )
= $true )
| ( ( y @ sK1 )
= $true )
| ( ( x @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( ( x @ sK1 )
= $true )
| ( ( y @ sK1 )
= $true )
| ( ( x @ sK2 )
= $true )
| ( ( y @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( ( ( x @ sK1 )
= $true )
| ( ( y @ sK1 )
= $true )
| ( ( x @ sK2 )
= $true )
| ( sK0
= ( f @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f51,plain,
( ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true )
| ( ( y @ sK1 )
= $true )
| ( sK0
= ( f @ sK2 ) )
| ( ( x @ sK1 )
= $true ) ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f52,plain,
( ( sK0
= ( f @ sK2 ) )
| ( ( y @ sK1 )
= $true )
| ( ( ( f @ sK3 )
= sK0 )
= $true )
| ( ( x @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( sK0
= ( f @ sK2 ) )
| ( ( y @ sK1 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( ( x @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f54,plain,
( ( ( y @ sK1 )
= $true )
| ( ( x @ sK1 )
= $true )
| ( sK0
= ( f @ sK2 ) )
| ( sK0
= ( f @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true )
| ( ( ( f @ sK2 )
= sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f56,plain,
( ( ( ( y @ sK3 )
& ( ( f @ sK3 )
= sK0 ) )
= $true )
| ( ( x @ sK2 )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f57,plain,
( ( ( ( f @ sK3 )
= sK0 )
= $true )
| ( ( x @ sK2 )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( ( ( x @ sK2 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f59,plain,
( ( ( x @ sK2 )
= $true )
| ( sK0
= ( f @ sK1 ) )
| ( ( y @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( ( sK0
= ( f @ sK3 ) )
| ( ( ( f @ sK1 )
= sK0 )
= $true )
| ( ( x @ sK2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f61,plain,
( ( ( x @ sK2 )
= $true )
| ( sK0
= ( f @ sK1 ) )
| ( sK0
= ( f @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( ( ( ( f @ sK3 )
= sK0 )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true )
| ( ( ( f @ sK2 )
= sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f55]) ).
thf(f63,plain,
( ( ( y @ sK3 )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true )
| ( ( ( f @ sK2 )
= sK0 )
= $true ) ),
inference(and_proxy_clausification,[],[f55]) ).
thf(f64,plain,
( ( ( ( f @ sK2 )
= sK0 )
= $true )
| ( ( y @ sK3 )
= $true )
| ( sK0
= ( f @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( ( y @ sK3 )
= $true )
| ( sK0
= ( f @ sK1 ) )
| ( sK0
= ( f @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( sK0
= ( f @ sK3 ) )
| ( ( ( f @ sK2 )
= sK0 )
= $true )
| ( ( ( f @ sK1 )
= sK0 )
= $true ) ),
inference(equality_proxy_clausification,[],[f62]) ).
thf(f67,plain,
( ( sK0
= ( f @ sK3 ) )
| ( sK0
= ( f @ sK2 ) )
| ( ( ( f @ sK1 )
= sK0 )
= $true ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( sK0
= ( f @ sK2 ) )
| ( sK0
= ( f @ sK3 ) )
| ( sK0
= ( f @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f70,definition,
( spl4_1
<=> ! [X1: b] :
( ( ( x @ X1 )
= $false )
| ( ( f @ X1 )
!= sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f71,plain,
( ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( x @ X1 )
= $false ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,definition,
( spl4_2
<=> ! [X2: b] :
( ( $false
= ( y @ X2 ) )
| ( sK0
!= ( f @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f74,plain,
( ! [X2: b] :
( ( sK0
!= ( f @ X2 ) )
| ( $false
= ( y @ X2 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,plain,
( spl4_2
| spl4_2 ),
inference(avatar_split_clause,[],[f26,f73,f73]) ).
thf(f77,plain,
( spl4_1
| spl4_1 ),
inference(avatar_split_clause,[],[f35,f70,f70]) ).
thf(f80,definition,
( spl4_3
<=> ( ( y @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f81,plain,
( ( ( y @ sK3 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f83,definition,
( spl4_4
<=> ( ( x @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f84,plain,
( ( ( x @ sK2 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f86,definition,
( spl4_5
<=> ( ( x @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f87,plain,
( ( ( x @ sK1 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f89,definition,
( spl4_6
<=> ( ( y @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f90,plain,
( ( ( y @ sK1 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f91,plain,
( spl4_3
| spl4_4
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f49,f89,f86,f83,f80]) ).
thf(f93,definition,
( spl4_7
<=> ( sK0
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f94,plain,
( ( sK0
= ( f @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f95,plain,
( spl4_6
| spl4_5
| spl4_7
| spl4_4 ),
inference(avatar_split_clause,[],[f50,f83,f93,f86,f89]) ).
thf(f97,definition,
( spl4_8
<=> ( sK0
= ( f @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f98,plain,
( ( sK0
= ( f @ sK2 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f99,plain,
( spl4_6
| spl4_8
| spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f53,f86,f80,f97,f89]) ).
thf(f100,plain,
( spl4_6
| spl4_8
| spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f54,f86,f93,f97,f89]) ).
thf(f102,definition,
( spl4_9
<=> ( sK0
= ( f @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f103,plain,
( ( sK0
= ( f @ sK1 ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f104,plain,
( spl4_3
| spl4_4
| spl4_9 ),
inference(avatar_split_clause,[],[f59,f102,f83,f80]) ).
thf(f105,plain,
( spl4_4
| spl4_9
| spl4_7 ),
inference(avatar_split_clause,[],[f61,f93,f102,f83]) ).
thf(f106,plain,
( spl4_3
| spl4_9
| spl4_8 ),
inference(avatar_split_clause,[],[f65,f97,f102,f80]) ).
thf(f107,plain,
( spl4_7
| spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f68,f102,f97,f93]) ).
thf(f108,plain,
( ( sK0 != sK0 )
| ( $false
= ( x @ sK2 ) )
| ~ spl4_1
| ~ spl4_8 ),
inference(constrained_superposition,[],[f71,f98]) ).
thf(f109,plain,
( ( $false
= ( x @ sK2 ) )
| ~ spl4_1
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(backward_demodulation,[],[f84,f109]) ).
thf(f111,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f112,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f111]) ).
thf(f115,plain,
( ( sK0 != sK0 )
| ( $false
= ( y @ sK1 ) )
| ~ spl4_2
| ~ spl4_9 ),
inference(constrained_superposition,[],[f74,f103]) ).
thf(f116,plain,
( ( sK0 != sK0 )
| ( $false
= ( x @ sK1 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(constrained_superposition,[],[f71,f103]) ).
thf(f117,plain,
( ( $false
= ( y @ sK1 ) )
| ~ spl4_2
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f118,plain,
( ( $false
= ( x @ sK1 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f119,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(backward_demodulation,[],[f90,f117]) ).
thf(f120,plain,
( $false
| ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f121,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f120]) ).
thf(f122,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(forward_demodulation,[],[f87,f118]) ).
thf(f123,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f124,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f123]) ).
thf(f125,plain,
( ( $false
= ( y @ sK3 ) )
| ( sK0 != sK0 )
| ~ spl4_2
| ~ spl4_7 ),
inference(constrained_superposition,[],[f74,f94]) ).
thf(f127,plain,
( ( $false
= ( y @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f129,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_7 ),
inference(backward_demodulation,[],[f81,f127]) ).
thf(f130,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f131,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f130]) ).
cnf(s2,plain,
( spl4_2
| spl4_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s3,plain,
spl4_2,
inference(rat,[],[s2]) ).
cnf(s4,plain,
( spl4_1
| spl4_1 ),
inference(sat_conversion,[],[f77]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s4]) ).
cnf(s7,plain,
( spl4_3
| spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s8,plain,
( spl4_4
| spl4_5
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f95]) ).
cnf(s9,plain,
( spl4_3
| spl4_5
| spl4_6
| spl4_8 ),
inference(sat_conversion,[],[f99]) ).
cnf(s10,plain,
( spl4_5
| spl4_6
| spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f100]) ).
cnf(s11,plain,
( spl4_3
| spl4_4
| spl4_9 ),
inference(sat_conversion,[],[f104]) ).
cnf(s12,plain,
( spl4_4
| spl4_7
| spl4_9 ),
inference(sat_conversion,[],[f105]) ).
cnf(s13,plain,
( spl4_3
| spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s14,plain,
( spl4_7
| spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f107]) ).
cnf(s15,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(sat_conversion,[],[f112]) ).
cnf(s16,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(sat_conversion,[],[f121]) ).
cnf(s17,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(sat_conversion,[],[f124]) ).
cnf(s18,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_7 ),
inference(sat_conversion,[],[f131]) ).
cnf(s19,plain,
( spl4_4
| spl4_3 ),
inference(rat,[],[s7,s16,s17,s11,s5,s3]) ).
cnf(s20,plain,
( spl4_8
| spl4_3 ),
inference(rat,[],[s9,s16,s17,s13,s5,s3]) ).
cnf(s21,plain,
spl4_3,
inference(rat,[],[s20,s15,s19,s5]) ).
cnf(s22,plain,
~ spl4_7,
inference(rat,[],[s18,s3,s21]) ).
cnf(s23,plain,
( spl4_6
| spl4_5 ),
inference(rat,[],[s15,s10,s8,s22,s5]) ).
cnf(s24,plain,
spl4_9,
inference(rat,[],[s15,s12,s14,s5,s22]) ).
cnf(s25,plain,
~ spl4_5,
inference(rat,[],[s17,s5,s24]) ).
cnf(s26,plain,
~ spl4_6,
inference(rat,[],[s16,s3,s24]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s23,s25,s26]) ).
thf(f132,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU895^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n026.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 14:47:13 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.07/0.26 % (692604)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (692615)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.07/0.26 % (692615)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
% 0.07/0.26 % (692611)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3114003209:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.07/0.26 % (692612)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=4282407812: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.07/0.26 % (692610)lrs+10_16_si=on:nwc=1.5:random_seed=1539346689:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.07/0.26 % (692613)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1984728794:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.07/0.26 % (692614)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3576456773:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.07/0.26 % (692615)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=2567772277:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.07/0.26 % (692611)Refutation not found, incomplete strategy
% 0.07/0.26 % (692611)------------------------------
% 0.07/0.26 % (692611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (692611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (692611)CaDiCaL version: 2.1.3
% 0.07/0.26 % (692611)Termination reason: Refutation not found, incomplete strategy
% 0.07/0.26 % (692611)Time elapsed: 0.001 s
% 0.07/0.26 % (692611)Peak memory usage: 12 MB
% 0.07/0.26 % (692611)Instructions burned: 1 (million)
% 0.07/0.26 % (692611)------------------------------
% 0.07/0.26 % (692611)------------------------------
% 0.07/0.26 % (692612) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-692604-692612"...
% 0.07/0.26 % (692610) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-692604-692610"...
% 0.07/0.26 % (692614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-692604-692614"...
% 0.07/0.26 % (692615) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-692604-692615"...
% 0.07/0.26 % (692609)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1858265591:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.07/0.26 % (692612)...printing done.
% 0.07/0.26 % (692610)...printing done.
% 0.07/0.26 % (692609) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-692604-692609"...
% 0.07/0.26 % (692615)...printing done.
% 0.07/0.26 % (692614)...printing done.
% 0.07/0.26 % (692614)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (692614)------------------------------
% 0.07/0.26 % (692614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (692614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (692614)CaDiCaL version: 2.1.3
% 0.07/0.26 % (692614)Termination reason: Refutation
% 0.07/0.26 % (692614)Time elapsed: 0.007 s
% 0.07/0.26 % (692614)Peak memory usage: 13 MB
% 0.07/0.26 % (692614)Instructions burned: 10 (million)
% 0.07/0.26 % (692604)Success in time 0.033 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------