%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ047^5 : 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 : n015.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 08:20:50 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 547 ( 152 equ; 0 cnn)
% Maximal formula atoms : 30 ( 18 avg)
% Number of connectives : 1571 ( 73 ~; 53 |; 101 &;1284 @)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-5 aty)
% Number of variables : 156 ( 0 ^; 152 !; 4 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cN: a ).
thf(func_def_1,type,
cP: a > a > a > a > b > $o ).
thf(func_def_2,type,
cD: b > b ).
thf(func_def_3,type,
cS: a ).
thf(func_def_4,type,
cG: b > b ).
thf(func_def_5,type,
cW: b > b ).
thf(func_def_6,type,
cL: b > b ).
thf(func_def_7,type,
cO: b ).
thf(f1,conjecture,
( ( ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [X15: b] :
( ( cP @ cN @ cN @ cS @ cN @ X15 )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ X15 ) ) )
& ! [X2: b] :
( ( cP @ cS @ cS @ cN @ cS @ X2 )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ X2 ) ) )
& ! [X6: b] :
( ( cP @ cS @ cS @ cN @ cS @ X6 )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ X6 ) ) )
& ! [X5: b] :
( ( cP @ cN @ cN @ cS @ cN @ X5 )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ X5 ) ) )
& ! [X0: b] :
( ( cP @ cS @ cN @ cS @ cN @ X0 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ X0 ) ) )
& ! [X10: b,X8: a,X9: a] :
( ( cP @ cS @ X8 @ cS @ X9 @ X10 )
=> ( cP @ cN @ X8 @ cN @ X9 @ ( cG @ X10 ) ) )
& ! [X13: b,X11: a,X12: a] :
( ( cP @ cN @ X11 @ cN @ X12 @ X13 )
=> ( cP @ cS @ X11 @ cS @ X12 @ ( cG @ X13 ) ) )
& ! [X14: b] :
( ( cP @ cS @ cN @ cS @ cS @ X14 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ X14 ) ) )
& ! [X17: b] :
( ( cP @ cN @ cS @ cN @ cN @ X17 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ X17 ) ) )
& ! [X16: b] :
( ( cP @ cS @ cS @ cN @ cS @ X16 )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ X16 ) ) )
& ! [X7: b] :
( ( cP @ cN @ cN @ cN @ cS @ X7 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ X7 ) ) )
& ! [X3: b] :
( ( cP @ cN @ cS @ cN @ cS @ X3 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ X3 ) ) )
& ! [X1: b] :
( ( cP @ cN @ cN @ cS @ cN @ X1 )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ X1 ) ) )
& ! [X4: b] :
( ( cP @ cS @ cS @ cS @ cN @ X4 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ X4 ) ) ) )
=> ? [X18: b] : ( cP @ cN @ cN @ cN @ cN @ X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM100A) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [X15: b] :
( ( cP @ cN @ cN @ cS @ cN @ X15 )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ X15 ) ) )
& ! [X2: b] :
( ( cP @ cS @ cS @ cN @ cS @ X2 )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ X2 ) ) )
& ! [X6: b] :
( ( cP @ cS @ cS @ cN @ cS @ X6 )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ X6 ) ) )
& ! [X5: b] :
( ( cP @ cN @ cN @ cS @ cN @ X5 )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ X5 ) ) )
& ! [X0: b] :
( ( cP @ cS @ cN @ cS @ cN @ X0 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ X0 ) ) )
& ! [X10: b,X8: a,X9: a] :
( ( cP @ cS @ X8 @ cS @ X9 @ X10 )
=> ( cP @ cN @ X8 @ cN @ X9 @ ( cG @ X10 ) ) )
& ! [X13: b,X11: a,X12: a] :
( ( cP @ cN @ X11 @ cN @ X12 @ X13 )
=> ( cP @ cS @ X11 @ cS @ X12 @ ( cG @ X13 ) ) )
& ! [X14: b] :
( ( cP @ cS @ cN @ cS @ cS @ X14 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ X14 ) ) )
& ! [X17: b] :
( ( cP @ cN @ cS @ cN @ cN @ X17 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ X17 ) ) )
& ! [X16: b] :
( ( cP @ cS @ cS @ cN @ cS @ X16 )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ X16 ) ) )
& ! [X7: b] :
( ( cP @ cN @ cN @ cN @ cS @ X7 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ X7 ) ) )
& ! [X3: b] :
( ( cP @ cN @ cS @ cN @ cS @ X3 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ X3 ) ) )
& ! [X1: b] :
( ( cP @ cN @ cN @ cS @ cN @ X1 )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ X1 ) ) )
& ! [X4: b] :
( ( cP @ cS @ cS @ cS @ cN @ X4 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ X4 ) ) ) )
=> ? [X18: b] : ( cP @ cN @ cN @ cN @ cN @ X18 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [X0: b] :
( ( cP @ cN @ cN @ cS @ cN @ X0 )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ X0 ) ) )
& ! [X1: b] :
( ( cP @ cS @ cS @ cN @ cS @ X1 )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ X1 ) ) )
& ! [X2: b] :
( ( cP @ cS @ cS @ cN @ cS @ X2 )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ X2 ) ) )
& ! [X3: b] :
( ( cP @ cN @ cN @ cS @ cN @ X3 )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ X3 ) ) )
& ! [X4: b] :
( ( cP @ cS @ cN @ cS @ cN @ X4 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ X4 ) ) )
& ! [X5: b,X6: a,X7: a] :
( ( cP @ cS @ X6 @ cS @ X7 @ X5 )
=> ( cP @ cN @ X6 @ cN @ X7 @ ( cG @ X5 ) ) )
& ! [X8: b,X9: a,X10: a] :
( ( cP @ cN @ X9 @ cN @ X10 @ X8 )
=> ( cP @ cS @ X9 @ cS @ X10 @ ( cG @ X8 ) ) )
& ! [X11: b] :
( ( cP @ cS @ cN @ cS @ cS @ X11 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ X11 ) ) )
& ! [X12: b] :
( ( cP @ cN @ cS @ cN @ cN @ X12 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ X12 ) ) )
& ! [X13: b] :
( ( cP @ cS @ cS @ cN @ cS @ X13 )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ X13 ) ) )
& ! [X14: b] :
( ( cP @ cN @ cN @ cN @ cS @ X14 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ X14 ) ) )
& ! [X15: b] :
( ( cP @ cN @ cS @ cN @ cS @ X15 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ X15 ) ) )
& ! [X16: b] :
( ( cP @ cN @ cN @ cS @ cN @ X16 )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ X16 ) ) )
& ! [X17: b] :
( ( cP @ cS @ cS @ cS @ cN @ X17 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ X17 ) ) ) )
=> ? [X18: b] : ( cP @ cN @ cN @ cN @ cN @ X18 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X2: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ X2 )
= $true )
=> ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X2 ) ) ) )
& ! [X10: a,X8: b,X9: a] :
( ( ( cP @ cN @ X9 @ cN @ X10 @ X8 )
= $true )
=> ( $true
= ( cP @ cS @ X9 @ cS @ X10 @ ( cG @ X8 ) ) ) )
& ! [X14: b] :
( ( $true
= ( cP @ cN @ cN @ cN @ cS @ X14 ) )
=> ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X14 ) ) ) )
& ! [X1: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ X1 ) )
=> ( ( cP @ cN @ cS @ cN @ cS @ ( cL @ X1 ) )
= $true ) )
& ! [X0: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ X0 ) )
=> ( $true
= ( cP @ cS @ cN @ cS @ cS @ ( cD @ X0 ) ) ) )
& ! [X17: b] :
( ( ( cP @ cS @ cS @ cS @ cN @ X17 )
= $true )
=> ( ( cP @ cN @ cN @ cS @ cN @ ( cW @ X17 ) )
= $true ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X11: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cS @ X11 ) )
=> ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X11 ) ) ) )
& ! [X13: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ X13 ) )
=> ( ( cP @ cN @ cS @ cN @ cN @ ( cD @ X13 ) )
= $true ) )
& ! [X16: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ X16 ) )
=> ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X16 ) ) ) )
& ! [X3: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ X3 ) )
=> ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X3 ) ) ) )
& ! [X12: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cN @ X12 ) )
=> ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cD @ X12 ) ) ) )
& ! [X15: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cS @ X15 ) )
=> ( ( cP @ cS @ cS @ cN @ cS @ ( cL @ X15 ) )
= $true ) )
& ! [X5: b,X7: a,X6: a] :
( ( ( cP @ cS @ X6 @ cS @ X7 @ X5 )
= $true )
=> ( $true
= ( cP @ cN @ X6 @ cN @ X7 @ ( cG @ X5 ) ) ) )
& ! [X4: b] :
( ( ( cP @ cS @ cN @ cS @ cN @ X4 )
= $true )
=> ( ( cP @ cN @ cN @ cS @ cN @ ( cL @ X4 ) )
= $true ) ) )
=> ? [X18: b] :
( ( cP @ cN @ cN @ cN @ cN @ X18 )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X18: b] :
( ( cP @ cN @ cN @ cN @ cN @ X18 )
!= $true )
& ! [X2: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ X2 )
!= $true )
| ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X2 ) ) ) )
& ! [X9: a,X8: b,X10: a] :
( ( $true
= ( cP @ cS @ X9 @ cS @ X10 @ ( cG @ X8 ) ) )
| ( ( cP @ cN @ X9 @ cN @ X10 @ X8 )
!= $true ) )
& ! [X14: b] :
( ( $true
!= ( cP @ cN @ cN @ cN @ cS @ X14 ) )
| ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X14 ) ) ) )
& ! [X1: b] :
( ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X1 ) )
| ( ( cP @ cN @ cS @ cN @ cS @ ( cL @ X1 ) )
= $true ) )
& ! [X0: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cS @ ( cD @ X0 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X0 ) ) )
& ! [X17: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ ( cW @ X17 ) )
= $true )
| ( ( cP @ cS @ cS @ cS @ cN @ X17 )
!= $true ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X11: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X11 ) ) )
| ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X11 ) ) )
& ! [X13: b] :
( ( ( cP @ cN @ cS @ cN @ cN @ ( cD @ X13 ) )
= $true )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X13 ) ) )
& ! [X16: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X16 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X16 ) ) ) )
& ! [X3: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X3 ) )
| ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X3 ) ) ) )
& ! [X12: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cD @ X12 ) ) )
| ( $true
!= ( cP @ cN @ cS @ cN @ cN @ X12 ) ) )
& ! [X15: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ ( cL @ X15 ) )
= $true )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X15 ) ) )
& ! [X7: a,X5: b,X6: a] :
( ( $true
= ( cP @ cN @ X6 @ cN @ X7 @ ( cG @ X5 ) ) )
| ( ( cP @ cS @ X6 @ cS @ X7 @ X5 )
!= $true ) )
& ! [X4: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ ( cL @ X4 ) )
= $true )
| ( ( cP @ cS @ cN @ cS @ cN @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X1: b] :
( ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X1 ) )
| ( ( cP @ cN @ cS @ cN @ cS @ ( cL @ X1 ) )
= $true ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X15: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ ( cL @ X15 ) )
= $true )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X15 ) ) )
& ! [X18: b] :
( ( cP @ cN @ cN @ cN @ cN @ X18 )
!= $true )
& ! [X13: b] :
( ( ( cP @ cN @ cS @ cN @ cN @ ( cD @ X13 ) )
= $true )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X13 ) ) )
& ! [X4: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ ( cL @ X4 ) )
= $true )
| ( ( cP @ cS @ cN @ cS @ cN @ X4 )
!= $true ) )
& ! [X11: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X11 ) ) )
| ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X11 ) ) )
& ! [X17: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ ( cW @ X17 ) )
= $true )
| ( ( cP @ cS @ cS @ cS @ cN @ X17 )
!= $true ) )
& ! [X3: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X3 ) )
| ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X3 ) ) ) )
& ! [X12: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cD @ X12 ) ) )
| ( $true
!= ( cP @ cN @ cS @ cN @ cN @ X12 ) ) )
& ! [X7: a,X5: b,X6: a] :
( ( $true
= ( cP @ cN @ X6 @ cN @ X7 @ ( cG @ X5 ) ) )
| ( ( cP @ cS @ X6 @ cS @ X7 @ X5 )
!= $true ) )
& ! [X9: a,X8: b,X10: a] :
( ( $true
= ( cP @ cS @ X9 @ cS @ X10 @ ( cG @ X8 ) ) )
| ( ( cP @ cN @ X9 @ cN @ X10 @ X8 )
!= $true ) )
& ! [X14: b] :
( ( $true
!= ( cP @ cN @ cN @ cN @ cS @ X14 ) )
| ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X14 ) ) ) )
& ! [X2: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ X2 )
!= $true )
| ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X2 ) ) ) )
& ! [X16: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X16 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X16 ) ) ) )
& ! [X0: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cS @ ( cD @ X0 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X0 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ X0 )
!= $true )
| ( $true
= ( cP @ cN @ cS @ cN @ cS @ ( cL @ X0 ) ) ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X1: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ ( cL @ X1 ) )
= $true )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X1 ) ) )
& ! [X2: b] :
( $true
!= ( cP @ cN @ cN @ cN @ cN @ X2 ) )
& ! [X3: b] :
( ( ( cP @ cN @ cS @ cN @ cN @ ( cD @ X3 ) )
= $true )
| ( ( cP @ cS @ cS @ cN @ cS @ X3 )
!= $true ) )
& ! [X4: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ ( cL @ X4 ) )
= $true )
| ( ( cP @ cS @ cN @ cS @ cN @ X4 )
!= $true ) )
& ! [X5: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ ( cD @ X5 ) )
= $true )
| ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X5 ) ) )
& ! [X6: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cW @ X6 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cS @ cN @ X6 ) ) )
& ! [X7: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X7 ) )
| ( ( cP @ cS @ cS @ cS @ cN @ ( cW @ X7 ) )
= $true ) )
& ! [X8: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ ( cD @ X8 ) )
= $true )
| ( ( cP @ cN @ cS @ cN @ cN @ X8 )
!= $true ) )
& ! [X9: a,X10: b,X11: a] :
( ( ( cP @ cN @ X11 @ cN @ X9 @ ( cG @ X10 ) )
= $true )
| ( $true
!= ( cP @ cS @ X11 @ cS @ X9 @ X10 ) ) )
& ! [X12: a,X13: b,X14: a] :
( ( $true
= ( cP @ cS @ X12 @ cS @ X14 @ ( cG @ X13 ) ) )
| ( $true
!= ( cP @ cN @ X12 @ cN @ X14 @ X13 ) ) )
& ! [X15: b] :
( ( ( cP @ cN @ cN @ cN @ cS @ X15 )
!= $true )
| ( ( cP @ cS @ cS @ cN @ cS @ ( cW @ X15 ) )
= $true ) )
& ! [X16: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ X16 )
!= $true )
| ( ( cP @ cN @ cN @ cN @ cS @ ( cW @ X16 ) )
= $true ) )
& ! [X17: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X17 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X17 ) ) ) )
& ! [X18: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cS @ ( cD @ X18 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X18 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f9,plain,
! [X17: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X17 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X17 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X16: b] :
( ( ( cP @ cN @ cN @ cN @ cS @ ( cW @ X16 ) )
= $true )
| ( ( cP @ cS @ cS @ cN @ cS @ X16 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X14: a,X12: a,X13: b] :
( ( $true
= ( cP @ cS @ X12 @ cS @ X14 @ ( cG @ X13 ) ) )
| ( $true
!= ( cP @ cN @ X12 @ cN @ X14 @ X13 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X10: b,X11: a,X9: a] :
( ( ( cP @ cN @ X11 @ cN @ X9 @ ( cG @ X10 ) )
= $true )
| ( $true
!= ( cP @ cS @ X11 @ cS @ X9 @ X10 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f17,plain,
! [X5: b] :
( ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X5 ) )
| ( ( cP @ cN @ cN @ cS @ cN @ ( cD @ X5 ) )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f20,plain,
! [X2: b] :
( $true
!= ( cP @ cN @ cN @ cN @ cN @ X2 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f21,plain,
! [X1: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ ( cL @ X1 ) )
= $true )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f22,plain,
( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f25,plain,
! [X0: b] :
( ( ( cP @ cS @ cN @ cS @ cN @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f20,f13]) ).
thf(f26,plain,
! [X0: b] :
( ( cP @ cS @ cN @ cS @ cN @ X0 )
!= $true ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
! [X0: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f26,f9]) ).
thf(f30,plain,
! [X0: b] :
( $true
!= ( cP @ cN @ cN @ cS @ cN @ X0 ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f36,plain,
! [X5: b] :
( $true
!= ( cP @ cS @ cN @ cS @ cS @ X5 ) ),
inference(forward_subsumption_resolution,[],[f17,f30]) ).
thf(f38,plain,
! [X0: b] :
( ( ( cP @ cN @ cN @ cN @ cS @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f36,f12]) ).
thf(f40,plain,
! [X0: b] :
( ( cP @ cN @ cN @ cN @ cS @ X0 )
!= $true ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f41,plain,
! [X0: b] :
( ( ( cP @ cS @ cS @ cN @ cS @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f40,f10]) ).
thf(f43,plain,
! [X0: b] :
( ( cP @ cS @ cS @ cN @ cS @ X0 )
!= $true ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f49,plain,
! [X1: b] :
( $true
!= ( cP @ cN @ cS @ cN @ cS @ X1 ) ),
inference(forward_subsumption_resolution,[],[f21,f43]) ).
thf(f50,plain,
! [X0: b] :
( ( $true
!= ( cP @ cS @ cS @ cS @ cS @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f49,f13]) ).
thf(f51,plain,
! [X0: b] :
( $true
!= ( cP @ cS @ cS @ cS @ cS @ X0 ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f52,plain,
$true != $true,
inference(superposition,[],[f51,f22]) ).
thf(f54,plain,
$false,
inference(trivial_inequality_removal,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ047^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:25:03 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.21/0.29 % (3503300)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3503312)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3518351663:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (3503312) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3503300-3503312"...
% 0.21/0.29 % (3503312)...printing done.
% 0.21/0.29 % (3503312)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3503312)------------------------------
% 0.21/0.29 % (3503312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3503312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3503312)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3503312)Termination reason: Refutation
% 0.21/0.29 % (3503312)Time elapsed: 0.005 s
% 0.21/0.29 % (3503312)Peak memory usage: 12 MB
% 0.21/0.29 % (3503312)Instructions burned: 16 (million)
% 0.21/0.29 % (3503300)Success in time 0.032 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------