%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV122^5 : 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 : n011.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 08:37:51 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 90 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 611 ( 133 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1338 ( 56 ~; 104 |; 39 &; 866 @)
% ( 4 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 438 ( 438 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 10 con; 0-4 aty)
% ( 105 !!; 63 ??; 0 @@+; 0 @@-)
% Number of variables : 357 ( 4 sgn 113 !; 7 ?; 357 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vIMP: $o > $o > $o ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
sK1: a ).
thf(func_def_14,type,
sK2: a ).
thf(func_def_15,type,
sK3: a > a > $o ).
thf(func_def_16,type,
sK4: a > a > $o ).
thf(func_def_17,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_18,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_19,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_20,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_21,type,
sK9: ( a > a > $o ) > a > a > $o ).
thf(func_def_22,type,
sK10: ( a > a > $o ) > a > a > $o ).
thf(func_def_23,type,
sK11: ( a > a > $o ) > a > a > $o ).
thf(func_def_25,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,conjecture,
! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM530_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] : ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ( X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ( ( X1 @ X10 )
& ! [X11: a,X12: a] :
( ? [X13: a > a > $o] : ( X13 @ X12 @ X11 )
=> ( X10 @ X12 @ X11 ) ) )
=> ( X10 @ X8 @ X9 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] : ( Y5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK0 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ sK1 @ Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK1 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f15,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK0 @ Y1 ) )
=> ( Y1 @ sK1 @ Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] : ( Y4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) ) ) )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ sK1 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ sK1 @ sK2 ) ) ) )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) )
@ sK3 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] : ( Y3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK0 @ Y0 ) )
=> ( Y0 @ sK1 @ sK2 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ( ( sK0 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
=> ( sK3 @ sK1 @ sK2 ) ) )
| ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
=> ( sK4 @ sK1 @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
=> ( sK4 @ sK1 @ sK2 ) )
= $false )
| ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( ( ( sK0 @ sK3 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
=> ( sK4 @ sK1 @ sK2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
=> ( sK4 @ sK1 @ sK2 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f35,plain,
! [X1: a] :
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
=> ( sK4 @ sK1 @ sK2 ) )
= $false )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f36,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: a] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f39,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f40,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: a,X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X2 @ Y0 ) )
=> ( sK4 @ X2 @ Y0 ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: a,X3: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X2 @ Y0 ) )
=> ( sK4 @ X2 @ Y0 ) )
@ X3 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) )
@ X4 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X2 @ Y0 ) )
=> ( sK4 @ X2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X3 ) )
=> ( sK4 @ X2 @ X3 ) )
= $true )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X1 ) )
=> ( sK3 @ X4 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( sK4 @ X2 @ X3 )
= $true )
| ( $false
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X3 ) ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X1 ) )
=> ( sK3 @ X4 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: a,X3: a,X1: a,X4: a,X5: a > a > $o] :
( ( $false
= ( ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X3 )
@ X5 ) )
| ( ( sK4 @ X2 @ X3 )
= $true )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X1 ) )
=> ( sK3 @ X4 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: a,X3: a,X1: a,X4: a,X5: a > a > $o] :
( ( ( sK4 @ X2 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X3 )
@ X5 ) )
| ( $false
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X1 ) ) )
| ( ( sK3 @ X4 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X4: a,X5: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] : ( Y0 @ X4 @ X1 )
@ X6 )
= $false )
| ( ( sK3 @ X4 @ X1 )
= $true )
| ( ( sK4 @ X2 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X3 )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X4: a,X5: a > a > $o] :
( ( $false
= ( X6 @ X4 @ X1 ) )
| ( $false
= ( X5 @ X2 @ X3 ) )
| ( ( sK4 @ X2 @ X3 )
= $true )
| ( ( sK3 @ X4 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f56,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) ) )
= $true )
| ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f57,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ Y0 @ X1 ) )
=> ( sK3 @ Y0 @ X1 ) )
@ X2 ) )
| ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 ) )
=> ( sK3 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ( $false
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 ) ) )
| ( ( sK3 @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ^ [Y0: a > a > $o] : ( Y0 @ X2 @ X1 )
@ X3 ) )
| ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ( ( sK3 @ X2 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK3 @ X2 @ X1 )
= $true )
| ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ( $false
= ( X3 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ( $false
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f63,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
& ( sK0 @ sK4 ) )
= $true )
| ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f65,plain,
( ( $false
= ( sK3 @ sK1 @ sK2 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f66,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] : ( Y2 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X1: a] :
( ( $false
= ( sK3 @ sK1 @ sK2 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X1 @ Y0 ) )
=> ( sK4 @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK3 @ sK1 @ sK2 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] : ( Y1 @ X1 @ Y0 ) )
=> ( sK4 @ X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: a,X1: a] :
( ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X1 @ X2 ) )
=> ( sK4 @ X1 @ X2 ) )
= $true )
| ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( ( ( sK4 @ X1 @ X2 )
= $true )
| ( $false
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] : ( Y0 @ X1 @ X2 ) ) )
| ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ^ [Y0: a > a > $o] : ( Y0 @ X1 @ X2 )
@ X3 ) )
| ( ( sK4 @ X1 @ X2 )
= $true )
| ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK4 @ X1 @ X2 )
= $true )
| ( $false
= ( sK3 @ sK1 @ sK2 ) )
| ( $false
= ( X3 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f104,definition,
( spl12_2
<=> ! [X2: a,X1: a,X3: a > a > $o] :
( ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK4 @ X1 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f105,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK4 @ X1 @ X2 )
= $true ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f113,definition,
( spl12_4
<=> ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f115,plain,
( ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f118,definition,
( spl12_5
<=> ! [X6: a > a > $o,X4: a,X1: a] :
( ( $false
= ( X6 @ X4 @ X1 ) )
| ( ( sK3 @ X4 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f119,plain,
( ! [X1: a,X6: a > a > $o,X4: a] :
( ( ( sK3 @ X4 @ X1 )
= $true )
| ( $false
= ( X6 @ X4 @ X1 ) ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f120,plain,
( spl12_5
| spl12_2 ),
inference(avatar_split_clause,[],[f49,f104,f118]) ).
thf(f122,plain,
( spl12_4
| spl12_5 ),
inference(avatar_split_clause,[],[f61,f118,f113]) ).
thf(f124,definition,
( spl12_6
<=> ( $false
= ( sK3 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f126,plain,
( ( $false
= ( sK3 @ sK1 @ sK2 ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f127,plain,
( spl12_6
| spl12_2 ),
inference(avatar_split_clause,[],[f72,f104,f124]) ).
thf(f129,plain,
( spl12_6
| spl12_4 ),
inference(avatar_split_clause,[],[f62,f113,f124]) ).
thf(f154,plain,
( ! [X0: a > a > $o] :
( ( $false = $true )
| ( ( X0 @ sK1 @ sK2 )
= $false ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(constrained_superposition,[],[f105,f115]) ).
thf(f158,plain,
( ! [X0: a > a > $o] :
( ( X0 @ sK1 @ sK2 )
= $false )
| ~ spl12_2
| ~ spl12_4 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ sK1
@ sK2 ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(primitive_instantiation,[],[f158]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: a,Y1: a] : ( Y0 != Y1 )
@ sK1
@ sK2 ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(primitive_instantiation,[],[f158]) ).
thf(f180,plain,
( ( $false
= ( sK1 = sK2 ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f181,plain,
( ( sK1 != sK2 )
| ~ spl12_2
| ~ spl12_4 ),
inference(equality_proxy_clausification,[],[f180]) ).
thf(f187,plain,
( ( $false
= ( sK1 != sK2 ) )
| ~ spl12_2
| ~ spl12_4 ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f188,plain,
( ( ( sK1 = sK2 )
= $true )
| ~ spl12_2
| ~ spl12_4 ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( sK1 = sK2 )
| ~ spl12_2
| ~ spl12_4 ),
inference(equality_proxy_clausification,[],[f188]) ).
thf(f193,plain,
( $false
| ~ spl12_2
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f189,f181]) ).
thf(f194,plain,
( ~ spl12_2
| ~ spl12_4 ),
inference(avatar_contradiction_clause,[],[f193]) ).
thf(f200,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK1 @ sK2 )
= $false )
| ( $false = $true ) )
| ~ spl12_5
| ~ spl12_6 ),
inference(constrained_superposition,[],[f119,f126]) ).
thf(f211,plain,
( ! [X0: a > a > $o] :
( ( X0 @ sK1 @ sK2 )
= $false )
| ~ spl12_5
| ~ spl12_6 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f218,plain,
( ( $false
= ( ^ [Y0: a,Y1: a] : $true
@ sK1
@ sK2 ) )
| ~ spl12_5
| ~ spl12_6 ),
inference(primitive_instantiation,[],[f211]) ).
thf(f223,plain,
( ( $false = $true )
| ~ spl12_5
| ~ spl12_6 ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f224,plain,
( $false
| ~ spl12_5
| ~ spl12_6 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f225,plain,
( ~ spl12_5
| ~ spl12_6 ),
inference(avatar_contradiction_clause,[],[f224]) ).
cnf(s4,plain,
( spl12_2
| spl12_5 ),
inference(sat_conversion,[],[f120]) ).
cnf(s6,plain,
( spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f122]) ).
cnf(s7,plain,
( spl12_2
| spl12_6 ),
inference(sat_conversion,[],[f127]) ).
cnf(s9,plain,
( spl12_4
| spl12_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s16,plain,
( ~ spl12_2
| ~ spl12_4 ),
inference(sat_conversion,[],[f194]) ).
cnf(s17,plain,
( ~ spl12_5
| ~ spl12_6 ),
inference(sat_conversion,[],[f225]) ).
cnf(s21,plain,
spl12_4,
inference(rat,[],[s17,s6,s9]) ).
cnf(s22,plain,
~ spl12_2,
inference(rat,[],[s16,s21]) ).
cnf(s23,plain,
spl12_6,
inference(rat,[],[s7,s22]) ).
cnf(s24,plain,
spl12_5,
inference(rat,[],[s4,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s17,s23,s24]) ).
thf(f241,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV122^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:12:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.26 % (205370)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.26 % (205376)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2402955177:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.26 % (205376) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-205370-205376"...
% 0.21/0.26 % (205382)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.26 % (205382)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
% 0.21/0.26 % (205376)...printing done.
% 0.21/0.26 % (205376)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (205376)------------------------------
% 0.21/0.27 % (205376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (205376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (205376)CaDiCaL version: 2.1.3
% 0.21/0.27 % (205376)Termination reason: Refutation
% 0.21/0.27 % (205376)Time elapsed: 0.005 s
% 0.21/0.27 % (205376)Peak memory usage: 13 MB
% 0.21/0.27 % (205376)Instructions burned: 16 (million)
% 0.21/0.27 % (205370)Success in time 0.019 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------