%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n019.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 08:34:21 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 131 ( 17 unt; 0 typ; 9 def)
% Number of atoms : 812 ( 285 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 896 ( 101 ~; 268 |; 81 &; 404 @)
% ( 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 !!; 33 ??; 0 @@+; 0 @@-)
% Number of variables : 109 ( 0 sgn 35 !; 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 ) )
& ( y @ X1 ) )
| ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( x @ 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 ) )
& ( y @ X1 ) )
| ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( x @ 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 )
& ( y @ X3 ) )
| ? [X4: b] :
( ( ( f @ X4 )
= X2 )
& ( x @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( y @ 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] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( y @ 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] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 )
!= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f6]) ).
thf(f17,plain,
( ( $true
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( x @ Y1 )
| ( y @ Y1 ) )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( x @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
| ( ?? @ b
@ ^ [Y1: b] :
( ( y @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) )
| ( $false
= ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f23,plain,
! [X2: b,X1: b] :
( ( $false
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( ( x @ X1 )
| ( y @ X1 ) )
& ( ( f @ X1 )
= sK0 ) ) )
| ( $false
= ( ( x @ X2 )
& ( ( f @ X2 )
= sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( f @ X1 )
= sK0 ) )
| ( $false
= ( ( x @ X2 )
& ( ( f @ X2 )
= sK0 ) ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( $false
= ( ( x @ X2 )
& ( ( f @ X2 )
= sK0 ) ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( $false
= ( ( f @ X2 )
= sK0 ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( x @ X2 ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( sK0
!= ( f @ X2 ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( x @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f30,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( sK0
!= ( f @ X2 ) )
| ( ( x @ X1 )
= $false )
| ( $false
= ( x @ X2 ) ) ),
inference(or_proxy_clausification,[],[f28]) ).
thf(f31,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,[],[f21]) ).
thf(f32,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( ( x @ X1 )
| ( y @ X1 ) )
& ( ( f @ X1 )
= sK0 ) ) )
| ( $false
= ( ( y @ X2 )
& ( ( f @ X2 )
= sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X2: b,X1: b] :
( ( $false
= ( ( f @ X1 )
= sK0 ) )
| ( $false
= ( ( y @ X2 )
& ( ( f @ X2 )
= sK0 ) ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( $false
= ( ( y @ X2 )
& ( ( f @ X2 )
= sK0 ) ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( $false
= ( ( f @ X2 )
= sK0 ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( y @ X2 ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( sK0
!= ( f @ X2 ) )
| ( $false
= ( ( x @ X1 )
| ( y @ X1 ) ) )
| ( $false
= ( y @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( sK0
!= ( f @ X2 ) )
| ( ( y @ X1 )
= $false )
| ( $false
= ( y @ X2 ) ) ),
inference(or_proxy_clausification,[],[f36]) ).
thf(f39,plain,
( ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) ) ) )
| ( $true
= ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f40,plain,
( ( $true
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 ) )
| ( $true
= ( ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) )
| ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $true
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $true
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ sK2 ) )
| ( $true
= ( ?? @ b
@ ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $true
= ( ^ [Y0: b] :
( ( ( x @ Y0 )
| ( y @ Y0 ) )
& ( ( f @ Y0 )
= sK0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: b] :
( ( y @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: b] :
( ( x @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( ( ( x @ sK1 )
| ( y @ sK1 ) )
& ( ( f @ sK1 )
= sK0 ) ) )
| ( $true
= ( ( y @ sK2 )
& ( ( f @ sK2 )
= sK0 ) ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
( ( $true
= ( ( f @ sK1 )
= sK0 ) )
| ( $true
= ( ( y @ sK2 )
& ( ( f @ sK2 )
= sK0 ) ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( ( x @ sK1 )
| ( y @ sK1 ) ) )
| ( $true
= ( ( y @ sK2 )
& ( ( f @ sK2 )
= sK0 ) ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f47,plain,
( ( $true
= ( y @ sK1 ) )
| ( $true
= ( ( y @ sK2 )
& ( ( f @ sK2 )
= sK0 ) ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $true
= ( y @ sK1 ) )
| ( $true
= ( ( f @ sK2 )
= sK0 ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( $true
= ( y @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( ( $true
= ( y @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( $true
= ( ( f @ sK3 )
= sK0 ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( $true
= ( y @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( $true
= ( x @ sK3 ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f52,plain,
( ( $true
= ( y @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( sK0
= ( f @ sK3 ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f50]) ).
thf(f53,plain,
( ( $true
= ( y @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f54,plain,
( ( $true
= ( y @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( $true
= ( ( f @ sK3 )
= sK0 ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f55,plain,
( ( $true
= ( y @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( $true
= ( x @ sK3 ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f56,plain,
( ( $true
= ( y @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( sK0
= ( f @ sK3 ) )
| ( $true
= ( x @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f57,plain,
( ( sK0
= ( f @ sK1 ) )
| ( $true
= ( ( y @ sK2 )
& ( ( f @ sK2 )
= sK0 ) ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(equality_proxy_clausification,[],[f45]) ).
thf(f58,plain,
( ( sK0
= ( f @ sK1 ) )
| ( $true
= ( ( f @ sK2 )
= sK0 ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f59,plain,
( ( sK0
= ( f @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f60,plain,
( ( sK0
= ( f @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( $true
= ( ( f @ sK3 )
= sK0 ) ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( sK0
= ( f @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( $true
= ( x @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f62,plain,
( ( sK0
= ( f @ sK1 ) )
| ( $true
= ( y @ sK2 ) )
| ( sK0
= ( f @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f60]) ).
thf(f63,plain,
( ( sK0
= ( f @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( $true
= ( ( x @ sK3 )
& ( ( f @ sK3 )
= sK0 ) ) ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f64,plain,
( ( sK0
= ( f @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( $true
= ( ( f @ sK3 )
= sK0 ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( sK0
= ( f @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( $true
= ( x @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( sK0
= ( f @ sK1 ) )
| ( sK0
= ( f @ sK2 ) )
| ( sK0
= ( f @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f64]) ).
thf(f68,definition,
( spl4_1
<=> ! [X2: b] :
( ( sK0
!= ( f @ X2 ) )
| ( $false
= ( x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f69,plain,
( ! [X2: b] :
( ( sK0
!= ( f @ X2 ) )
| ( $false
= ( x @ X2 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f70,plain,
( spl4_1
| spl4_1 ),
inference(avatar_split_clause,[],[f30,f68,f68]) ).
thf(f72,definition,
( spl4_2
<=> ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( y @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f73,plain,
( ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( y @ X1 )
= $false ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f76,plain,
( spl4_2
| spl4_2 ),
inference(avatar_split_clause,[],[f37,f72,f72]) ).
thf(f78,definition,
( spl4_3
<=> ( $true
= ( x @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( x @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f82,definition,
( spl4_4
<=> ( $true
= ( x @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f84,plain,
( ( $true
= ( x @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f86,definition,
( spl4_5
<=> ( $true
= ( y @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f88,plain,
( ( $true
= ( y @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f90,definition,
( spl4_6
<=> ( $true
= ( y @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f92,plain,
( ( $true
= ( y @ sK1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f93,plain,
( spl4_3
| spl4_4
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f51,f90,f86,f82,f78]) ).
thf(f95,definition,
( spl4_7
<=> ( sK0
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f97,plain,
( ( sK0
= ( f @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f98,plain,
( spl4_3
| spl4_7
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f52,f90,f86,f95,f78]) ).
thf(f100,definition,
( spl4_8
<=> ( sK0
= ( f @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f102,plain,
( ( sK0
= ( f @ sK2 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f103,plain,
( spl4_3
| spl4_4
| spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f55,f90,f100,f82,f78]) ).
thf(f104,plain,
( spl4_3
| spl4_7
| spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f56,f90,f100,f95,f78]) ).
thf(f106,definition,
( spl4_9
<=> ( sK0
= ( f @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f108,plain,
( ( sK0
= ( f @ sK1 ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f109,plain,
( spl4_4
| spl4_5
| spl4_9 ),
inference(avatar_split_clause,[],[f61,f106,f86,f82]) ).
thf(f110,plain,
( spl4_7
| spl4_5
| spl4_9 ),
inference(avatar_split_clause,[],[f62,f106,f86,f95]) ).
thf(f111,plain,
( spl4_4
| spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f65,f106,f100,f82]) ).
thf(f112,plain,
( spl4_7
| spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f66,f106,f100,f95]) ).
thf(f114,plain,
( ( sK0 != sK0 )
| ( $false
= ( x @ sK3 ) )
| ~ spl4_1
| ~ spl4_7 ),
inference(constrained_superposition,[],[f69,f97]) ).
thf(f115,plain,
( ( $false
= ( x @ sK3 ) )
| ~ spl4_1
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f118,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(constrained_superposition,[],[f115,f84]) ).
thf(f122,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f123,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f122]) ).
thf(f126,plain,
( ( sK0 != sK0 )
| ( $false
= ( y @ sK1 ) )
| ~ spl4_2
| ~ spl4_9 ),
inference(constrained_superposition,[],[f73,f108]) ).
thf(f127,plain,
( ( sK0 != sK0 )
| ( $false
= ( x @ sK1 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(constrained_superposition,[],[f69,f108]) ).
thf(f128,plain,
( ( $false
= ( x @ sK1 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f129,plain,
( ( $false
= ( y @ sK1 ) )
| ~ spl4_2
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f133,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_9 ),
inference(constrained_superposition,[],[f128,f80]) ).
thf(f137,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f138,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f137]) ).
thf(f141,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(forward_demodulation,[],[f92,f129]) ).
thf(f142,plain,
( $false
| ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f143,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f142]) ).
thf(f145,plain,
( ( sK0 != sK0 )
| ( $false
= ( y @ sK2 ) )
| ~ spl4_2
| ~ spl4_8 ),
inference(constrained_superposition,[],[f73,f102]) ).
thf(f148,plain,
( ( $false
= ( y @ sK2 ) )
| ~ spl4_2
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f154,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_8 ),
inference(constrained_superposition,[],[f148,f88]) ).
thf(f158,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f159,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f158]) ).
cnf(s1,plain,
( spl4_1
| spl4_1 ),
inference(sat_conversion,[],[f70]) ).
cnf(s2,plain,
spl4_1,
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl4_2
| spl4_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( spl4_3
| spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s8,plain,
( spl4_3
| spl4_5
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f98]) ).
cnf(s9,plain,
( spl4_3
| spl4_4
| spl4_6
| spl4_8 ),
inference(sat_conversion,[],[f103]) ).
cnf(s10,plain,
( spl4_3
| spl4_6
| spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f104]) ).
cnf(s11,plain,
( spl4_4
| spl4_5
| spl4_9 ),
inference(sat_conversion,[],[f109]) ).
cnf(s12,plain,
( spl4_5
| spl4_7
| spl4_9 ),
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( spl4_4
| spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f111]) ).
cnf(s14,plain,
( spl4_7
| spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f112]) ).
cnf(s16,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(sat_conversion,[],[f123]) ).
cnf(s18,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_9 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(sat_conversion,[],[f143]) ).
cnf(s21,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_8 ),
inference(sat_conversion,[],[f159]) ).
cnf(s22,plain,
( spl4_5
| spl4_4
| spl4_3 ),
inference(rat,[],[s19,s7,s11,s6]) ).
cnf(s23,plain,
( spl4_4
| spl4_3 ),
inference(rat,[],[s19,s9,s13,s21,s22,s6]) ).
cnf(s24,plain,
( spl4_5
| spl4_3 ),
inference(rat,[],[s19,s8,s12,s16,s23,s6,s2]) ).
cnf(s25,plain,
( spl4_8
| spl4_7
| spl4_3 ),
inference(rat,[],[s19,s14,s10,s6]) ).
cnf(s26,plain,
spl4_3,
inference(rat,[],[s25,s21,s24,s16,s23,s6,s2]) ).
cnf(s27,plain,
~ spl4_9,
inference(rat,[],[s18,s2,s26]) ).
cnf(s28,plain,
spl4_5,
inference(rat,[],[s16,s12,s11,s2,s27]) ).
cnf(s29,plain,
~ spl4_8,
inference(rat,[],[s21,s6,s28]) ).
cnf(s30,plain,
spl4_4,
inference(rat,[],[s13,s27,s29]) ).
cnf(s31,plain,
spl4_7,
inference(rat,[],[s14,s27,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s16,s2,s31,s30]) ).
thf(f161,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.08/0.18 % Computer : n019.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 14:44:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 % (877587)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (877593)% WARNING: option uhcvi not known.
% 0.08/0.26 % (877592)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3366719095_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (877595)dis+10_1_sil=32000:sp=arity:random_seed=2711875949:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (877594)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3265053497:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (877596)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=819218029:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (877593)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2745847134:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (877596)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % Exception at run slice level
% 0.08/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.26 % (877593)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (877593)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (877597)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1017288889:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (877596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-877587-877596"...
% 0.08/0.26 % (877595) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-877587-877595"...
% 0.08/0.26 % (877593) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-877587-877593"...
% 0.08/0.26 % (877598)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=66517048:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.26 % (877597) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-877587-877597"...
% 0.08/0.26 % (877594) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-877587-877594"...
% 0.08/0.26 % (877597)...printing done.
% 0.08/0.26 % (877596)...printing done.
% 0.08/0.26 % (877595)...printing done.
% 0.08/0.26 % (877593)...printing done.
% 0.08/0.26 % (877597)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
% 0.34/0.26 % (877597)------------------------------
% 0.34/0.26 % (877597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.26 % (877597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.26 % (877597)CaDiCaL version: 2.1.3
% 0.34/0.26 % (877597)Termination reason: Refutation
% 0.34/0.26 % (877597)Time elapsed: 0.003 s
% 0.34/0.26 % (877597)Peak memory usage: 13 MB
% 0.34/0.26 % (877597)Instructions burned: 10 (million)
% 0.34/0.26 % (877587)Success in time 0.044 s
% 0.34/0.26 % Vampire exiting
%------------------------------------------------------------------------------