%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ047^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:28:22 AM UTC 2026
% Result : Theorem 1.63s 1.31s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 559 ( 156 equ; 0 cnn)
% Maximal formula atoms : 30 ( 18 avg)
% Number of connectives : 1587 ( 77 ~; 55 |; 101 &;1294 @)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-5 aty)
% Number of variables : 158 ( 0 ^; 154 !; 4 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
cN: a ).
thf(func_def_3,type,
cP: a > a > a > a > b > $o ).
thf(func_def_4,type,
cD: b > b ).
thf(func_def_5,type,
cS: a ).
thf(func_def_6,type,
cG: b > b ).
thf(func_def_7,type,
cW: b > b ).
thf(func_def_8,type,
cL: b > b ).
thf(func_def_9,type,
cO: b ).
thf(f57,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
$true != $true,
inference(superposition,[status(thm)],[f49,f19]) ).
thf(f19,plain,
( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: b] :
( ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X0 ) )
| ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X0 ) ) ) )
& ! [X1: b] :
( ( $true
!= ( cP @ cN @ cS @ cN @ cN @ X1 ) )
| ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cD @ X1 ) ) ) )
& ! [X2: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X2 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cS @ ( cD @ X2 ) ) ) )
& ! [X3: b] :
( $true
!= ( cP @ cN @ cN @ cN @ cN @ X3 ) )
& ! [X4: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X4 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X4 ) ) ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X5: b] :
( ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X5 ) )
| ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X5 ) ) ) )
& ! [X6: a,X7: b,X8: a] :
( ( $true
= ( cP @ cN @ X8 @ cN @ X6 @ ( cG @ X7 ) ) )
| ( $true
!= ( cP @ cS @ X8 @ cS @ X6 @ X7 ) ) )
& ! [X9: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cN @ ( cD @ X9 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X9 ) ) )
& ! [X10: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cS @ ( cL @ X10 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X10 ) ) )
& ! [X11: a,X12: a,X13: b] :
( ( $true
= ( cP @ cS @ X12 @ cS @ X11 @ ( cG @ X13 ) ) )
| ( $true
!= ( cP @ cN @ X12 @ cN @ X11 @ X13 ) ) )
& ! [X14: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cL @ X14 ) ) )
| ( $true
!= ( cP @ cS @ cN @ cS @ cN @ X14 ) ) )
& ! [X15: b] :
( ( $true
!= ( cP @ cS @ cS @ cS @ cN @ X15 ) )
| ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cW @ X15 ) ) ) )
& ! [X16: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cL @ X16 ) ) )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X16 ) ) )
& ! [X17: b] :
( ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X17 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X17 ) ) )
& ! [X18: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X18 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cN @ cS @ X18 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X16: b] :
( ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X16 ) )
| ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X16 ) ) ) )
& ! [X17: b] :
( ( ( cP @ cN @ cS @ cN @ cN @ X17 )
!= $true )
| ( ( cP @ cS @ cS @ cN @ cS @ ( cD @ X17 ) )
= $true ) )
& ! [X5: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ X5 )
!= $true )
| ( ( cP @ cS @ cN @ cS @ cS @ ( cD @ X5 ) )
= $true ) )
& ! [X18: b] :
( ( cP @ cN @ cN @ cN @ cN @ X18 )
!= $true )
& ! [X6: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X6 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X6 ) ) ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X4: b] :
( ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X4 ) )
| ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X4 ) ) ) )
& ! [X3: a,X2: b,X1: a] :
( ( $true
= ( cP @ cN @ X1 @ cN @ X3 @ ( cG @ X2 ) ) )
| ( $true
!= ( cP @ cS @ X1 @ cS @ X3 @ X2 ) ) )
& ! [X10: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cN @ ( cD @ X10 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X10 ) ) )
& ! [X7: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cS @ ( cL @ X7 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X7 ) ) )
& ! [X15: a,X14: a,X13: b] :
( ( $true
= ( cP @ cS @ X14 @ cS @ X15 @ ( cG @ X13 ) ) )
| ( $true
!= ( cP @ cN @ X14 @ cN @ X15 @ X13 ) ) )
& ! [X11: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cL @ X11 ) ) )
| ( ( cP @ cS @ cN @ cS @ cN @ X11 )
!= $true ) )
& ! [X12: b] :
( ( $true
!= ( cP @ cS @ cS @ cS @ cN @ X12 ) )
| ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cW @ X12 ) ) ) )
& ! [X0: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cL @ X0 ) ) )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X0 ) ) )
& ! [X9: b] :
( ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X9 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X9 ) ) )
& ! [X8: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X8 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cN @ cS @ X8 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X18: b] :
( ( cP @ cN @ cN @ cN @ cN @ X18 )
!= $true )
& ! [X17: b] :
( ( ( cP @ cN @ cS @ cN @ cN @ X17 )
!= $true )
| ( ( cP @ cS @ cS @ cN @ cS @ ( cD @ X17 ) )
= $true ) )
& ! [X5: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ X5 )
!= $true )
| ( ( cP @ cS @ cN @ cS @ cS @ ( cD @ X5 ) )
= $true ) )
& ! [X0: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cL @ X0 ) ) )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X0 ) ) )
& ! [X8: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X8 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cN @ cS @ X8 ) ) )
& ! [X6: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X6 ) )
| ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X6 ) ) ) )
& ! [X4: b] :
( ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X4 ) )
| ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X4 ) ) ) )
& ! [X11: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cL @ X11 ) ) )
| ( ( cP @ cS @ cN @ cS @ cN @ X11 )
!= $true ) )
& ! [X15: a,X14: a,X13: b] :
( ( $true
= ( cP @ cS @ X14 @ cS @ X15 @ ( cG @ X13 ) ) )
| ( $true
!= ( cP @ cN @ X14 @ cN @ X15 @ X13 ) ) )
& ! [X7: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cS @ ( cL @ X7 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X7 ) ) )
& ! [X3: a,X2: b,X1: a] :
( ( $true
= ( cP @ cN @ X1 @ cN @ X3 @ ( cG @ X2 ) ) )
| ( $true
!= ( cP @ cS @ X1 @ cS @ X3 @ X2 ) ) )
& ! [X16: b] :
( ( $true
!= ( cP @ cS @ cN @ cS @ cS @ X16 ) )
| ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X16 ) ) ) )
& ! [X9: b] :
( ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X9 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X9 ) ) )
& ! [X12: b] :
( ( $true
!= ( cP @ cS @ cS @ cS @ cN @ X12 ) )
| ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cW @ X12 ) ) ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X10: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cN @ ( cD @ X10 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X10 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X17: b] :
( ( ( cP @ cN @ cS @ cN @ cN @ X17 )
= $true )
=> ( ( cP @ cS @ cS @ cN @ cS @ ( cD @ X17 ) )
= $true ) )
& ! [X5: b] :
( ( ( cP @ cN @ cN @ cS @ cN @ X5 )
= $true )
=> ( ( cP @ cS @ cN @ cS @ cS @ ( cD @ X5 ) )
= $true ) )
& ! [X0: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cS @ X0 ) )
=> ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cL @ X0 ) ) ) )
& ! [X8: b] :
( ( $true
= ( cP @ cN @ cN @ cN @ cS @ X8 ) )
=> ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cW @ X8 ) ) ) )
& ! [X6: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ X6 ) )
=> ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X6 ) ) ) )
& ! [X4: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ X4 ) )
=> ( $true
= ( cP @ cN @ cN @ cN @ cS @ ( cW @ X4 ) ) ) )
& ! [X11: b] :
( ( ( cP @ cS @ cN @ cS @ cN @ X11 )
= $true )
=> ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cL @ X11 ) ) ) )
& ! [X13: b,X15: a,X14: a] :
( ( $true
= ( cP @ cN @ X14 @ cN @ X15 @ X13 ) )
=> ( $true
= ( cP @ cS @ X14 @ cS @ X15 @ ( cG @ X13 ) ) ) )
& ! [X7: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ X7 ) )
=> ( $true
= ( cP @ cN @ cS @ cN @ cS @ ( cL @ X7 ) ) ) )
& ! [X2: b,X1: a,X3: a] :
( ( $true
= ( cP @ cS @ X1 @ cS @ X3 @ X2 ) )
=> ( $true
= ( cP @ cN @ X1 @ cN @ X3 @ ( cG @ X2 ) ) ) )
& ! [X16: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cS @ X16 ) )
=> ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cD @ X16 ) ) ) )
& ! [X9: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ X9 ) )
=> ( $true
= ( cP @ cS @ cS @ cS @ cN @ ( cW @ X9 ) ) ) )
& ! [X12: b] :
( ( $true
= ( cP @ cS @ cS @ cS @ cN @ X12 ) )
=> ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cW @ X12 ) ) ) )
& ( ( cP @ cS @ cS @ cS @ cS @ cO )
= $true )
& ! [X10: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ X10 ) )
=> ( $true
= ( cP @ cN @ cS @ cN @ cN @ ( cD @ X10 ) ) ) ) )
=> ? [X18: b] :
( ( cP @ cN @ cN @ cN @ cN @ X18 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: b] :
( ( cP @ cN @ cS @ cN @ cS @ X0 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ X0 ) ) )
& ! [X1: a,X2: b,X3: a] :
( ( cP @ cS @ X1 @ cS @ X3 @ X2 )
=> ( cP @ cN @ X1 @ cN @ X3 @ ( cG @ X2 ) ) )
& ! [X4: b] :
( ( cP @ cS @ cS @ cN @ cS @ X4 )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ X4 ) ) )
& ! [X5: b] :
( ( cP @ cN @ cN @ cS @ cN @ X5 )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ X5 ) ) )
& ! [X6: b] :
( ( cP @ cN @ cN @ cS @ cN @ X6 )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ X6 ) ) )
& ! [X7: b] :
( ( cP @ cS @ cS @ cN @ cS @ X7 )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ X7 ) ) )
& ! [X8: b] :
( ( cP @ cN @ cN @ cN @ cS @ X8 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ X8 ) ) )
& ! [X9: b] :
( ( cP @ cN @ cN @ cS @ cN @ X9 )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ X9 ) ) )
& ! [X10: b] :
( ( cP @ cS @ cS @ cN @ cS @ X10 )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ X10 ) ) )
& ! [X11: b] :
( ( cP @ cS @ cN @ cS @ cN @ X11 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ X11 ) ) )
& ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [X12: b] :
( ( cP @ cS @ cS @ cS @ cN @ X12 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ X12 ) ) )
& ! [X13: b,X14: a,X15: a] :
( ( cP @ cN @ X14 @ cN @ X15 @ X13 )
=> ( cP @ cS @ X14 @ cS @ X15 @ ( cG @ X13 ) ) )
& ! [X16: b] :
( ( cP @ cS @ cN @ cS @ cS @ X16 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cD @ X16 ) ) )
& ! [X17: b] :
( ( cP @ cN @ cS @ cN @ cN @ X17 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cD @ X17 ) ) ) )
=> ? [X18: b] : ( cP @ cN @ cN @ cN @ cN @ X18 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: b] :
( ( cP @ cN @ cS @ cN @ cS @ X3 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ X3 ) ) )
& ! [X8: a,X10: b,X9: a] :
( ( cP @ cS @ X8 @ cS @ X9 @ X10 )
=> ( cP @ cN @ X8 @ cN @ X9 @ ( cG @ X10 ) ) )
& ! [X6: b] :
( ( cP @ cS @ cS @ cN @ cS @ X6 )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ X6 ) ) )
& ! [X15: b] :
( ( cP @ cN @ cN @ cS @ cN @ X15 )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ X15 ) ) )
& ! [X1: b] :
( ( cP @ cN @ cN @ cS @ cN @ X1 )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ X1 ) ) )
& ! [X2: b] :
( ( cP @ cS @ cS @ cN @ cS @ X2 )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ X2 ) ) )
& ! [X7: b] :
( ( cP @ cN @ cN @ cN @ cS @ X7 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ X7 ) ) )
& ! [X5: b] :
( ( cP @ cN @ cN @ cS @ cN @ X5 )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ X5 ) ) )
& ! [X16: b] :
( ( cP @ cS @ cS @ cN @ cS @ X16 )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ X16 ) ) )
& ! [X0: b] :
( ( cP @ cS @ cN @ cS @ cN @ X0 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ X0 ) ) )
& ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [X4: b] :
( ( cP @ cS @ cS @ cS @ cN @ X4 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ X4 ) ) )
& ! [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 ) ) ) )
=> ? [X18: b] : ( cP @ cN @ cN @ cN @ cN @ X18 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: b] :
( ( cP @ cN @ cS @ cN @ cS @ X3 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cL @ X3 ) ) )
& ! [X8: a,X10: b,X9: a] :
( ( cP @ cS @ X8 @ cS @ X9 @ X10 )
=> ( cP @ cN @ X8 @ cN @ X9 @ ( cG @ X10 ) ) )
& ! [X6: b] :
( ( cP @ cS @ cS @ cN @ cS @ X6 )
=> ( cP @ cN @ cN @ cN @ cS @ ( cW @ X6 ) ) )
& ! [X15: b] :
( ( cP @ cN @ cN @ cS @ cN @ X15 )
=> ( cP @ cS @ cN @ cS @ cS @ ( cD @ X15 ) ) )
& ! [X1: b] :
( ( cP @ cN @ cN @ cS @ cN @ X1 )
=> ( cP @ cS @ cN @ cS @ cN @ ( cL @ X1 ) ) )
& ! [X2: b] :
( ( cP @ cS @ cS @ cN @ cS @ X2 )
=> ( cP @ cN @ cS @ cN @ cS @ ( cL @ X2 ) ) )
& ! [X7: b] :
( ( cP @ cN @ cN @ cN @ cS @ X7 )
=> ( cP @ cS @ cS @ cN @ cS @ ( cW @ X7 ) ) )
& ! [X5: b] :
( ( cP @ cN @ cN @ cS @ cN @ X5 )
=> ( cP @ cS @ cS @ cS @ cN @ ( cW @ X5 ) ) )
& ! [X16: b] :
( ( cP @ cS @ cS @ cN @ cS @ X16 )
=> ( cP @ cN @ cS @ cN @ cN @ ( cD @ X16 ) ) )
& ! [X0: b] :
( ( cP @ cS @ cN @ cS @ cN @ X0 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cL @ X0 ) ) )
& ( cP @ cS @ cS @ cS @ cS @ cO )
& ! [X4: b] :
( ( cP @ cS @ cS @ cS @ cN @ X4 )
=> ( cP @ cN @ cN @ cS @ cN @ ( cW @ X4 ) ) )
& ! [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 ) ) ) )
=> ? [X18: b] : ( cP @ cN @ cN @ cN @ cN @ X18 ) ),
file('/export/starexec/sandbox/tmp/tmp.rUOTgdkZ6h/DTF2THF_21750.p',cTHM100A) ).
thf(f49,plain,
! [X0: b] :
( $true
!= ( cP @ cS @ cS @ cS @ cS @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: b] :
( ( $true
!= ( cP @ cS @ cS @ cS @ cS @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f45,f17]) ).
thf(f17,plain,
! [X8: a,X6: a,X7: b] :
( ( $true
= ( cP @ cN @ X8 @ cN @ X6 @ ( cG @ X7 ) ) )
| ( $true
!= ( cP @ cS @ X8 @ cS @ X6 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f45,plain,
! [X0: b] :
( $true
!= ( cP @ cN @ cS @ cN @ cS @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: b] :
( ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f41,f11]) ).
thf(f11,plain,
! [X16: b] :
( ( $true
= ( cP @ cS @ cS @ cN @ cS @ ( cL @ X16 ) ) )
| ( $true
!= ( cP @ cN @ cS @ cN @ cS @ X16 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f41,plain,
! [X0: b] :
( $true
!= ( cP @ cS @ cS @ cN @ cS @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: b] :
( ( $true != $true )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X0 ) ) ),
inference(superposition,[status(thm)],[f37,f16]) ).
thf(f16,plain,
! [X9: b] :
( ( $true
= ( cP @ cN @ cS @ cN @ cN @ ( cD @ X9 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cN @ cS @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f37,plain,
! [X0: b] :
( $true
!= ( cP @ cN @ cS @ cN @ cN @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: b] :
( ( $true != $true )
| ( $true
!= ( cP @ cN @ cS @ cN @ cN @ X0 ) ) ),
inference(superposition,[status(thm)],[f34,f14]) ).
thf(f14,plain,
! [X11: a,X12: a,X13: b] :
( ( $true
= ( cP @ cS @ X12 @ cS @ X11 @ ( cG @ X13 ) ) )
| ( $true
!= ( cP @ cN @ X12 @ cN @ X11 @ X13 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f34,plain,
! [X0: b] :
( $true
!= ( cP @ cS @ cS @ cS @ cN @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: b] :
( ( $true != $true )
| ( $true
!= ( cP @ cS @ cS @ cS @ cN @ X0 ) ) ),
inference(superposition,[status(thm)],[f30,f12]) ).
thf(f12,plain,
! [X15: b] :
( ( $true
= ( cP @ cN @ cN @ cS @ cN @ ( cW @ X15 ) ) )
| ( $true
!= ( cP @ cS @ cS @ cS @ cN @ X15 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f30,plain,
! [X0: b] :
( $true
!= ( cP @ cN @ cN @ cS @ cN @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: b] :
( ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f20]) ).
thf(f20,plain,
! [X4: b] :
( ( $true
= ( cP @ cS @ cN @ cS @ cN @ ( cL @ X4 ) ) )
| ( $true
!= ( cP @ cN @ cN @ cS @ cN @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f26,plain,
! [X0: b] :
( ( cP @ cS @ cN @ cS @ cN @ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: b] :
( ( $true != $true )
| ( ( cP @ cS @ cN @ cS @ cN @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f21,f17]) ).
thf(f21,plain,
! [X3: b] :
( $true
!= ( cP @ cN @ cN @ cN @ cN @ X3 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : PUZ047^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 06:31:40 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 ---- Original DTF file ---
% 0.07/0.34 thf(spec,logic,$$dhol).
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 % File : PUZ047^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.34 % Domain : Puzzles
% 0.07/0.34 % Problem : TPS problem THM100A
% 0.07/0.34 % Version : Especial.
% 0.07/0.34 % English : A naive formalization of the problem of moving man wolf goat
% 0.07/0.34 % cabbage from south to north side of river.
% 0.07/0.34
% 0.07/0.34 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.34 % Source : [Bro09]
% 0.07/0.34 % Names : tps_0543 [Bro09]
% 0.07/0.34 % : tps_0544 [Bro09]
% 0.07/0.34 % : tps_0545 [Bro09]
% 0.07/0.34 % : tps_0427 [Bro09]
% 0.07/0.34 % : THM100 [TPS]
% 0.07/0.34 % : THM100A [TPS]
% 0.07/0.34 % : THM100B [TPS]
% 0.07/0.34 % : THM100-TPS2 [TPS]
% 0.07/0.34
% 0.07/0.34 % Status : Theorem
% 0.07/0.34 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.07/0.34 % Syntax : Number of formulae : 11 ( 0 unt; 10 typ; 0 def)
% 0.07/0.34 % Number of atoms : 30 ( 0 equ; 0 cnn)
% 0.07/0.34 % Maximal formula atoms : 30 ( 30 avg)
% 0.07/0.34 % Number of connectives : 193 ( 0 ~; 0 |; 14 &; 164 @)
% 0.07/0.34 % ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% 0.07/0.34 % Maximal formula depth : 23 ( 23 avg)
% 0.07/0.34 % Number of types : 3 ( 2 usr)
% 0.07/0.34 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.07/0.34 % Number of symbols : 8 ( 8 usr; 3 con; 0-5 aty)
% 0.07/0.34 % Number of variables : 19 ( 0 ^; 18 !; 1 ?; 19 :)
% 0.07/0.34 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.34
% 0.07/0.34 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.34 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.34 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.34 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 thf(a_type,type,
% 0.07/0.34 a: $tType ).
% 0.07/0.34
% 0.07/0.34 thf(b_type,type,
% 0.07/0.34 b: $tType ).
% 0.07/0.34
% 0.07/0.34 thf(cN,type,
% 0.07/0.34 cN: a ).
% 0.07/0.34
% 0.07/0.34 thf(cP,type,
% 0.07/0.34 cP: a > a > a > a > b > $o ).
% 0.07/0.34
% 0.07/0.34 thf(cD,type,
% 0.07/0.34 cD: b > b ).
% 0.07/0.34
% 0.07/0.34 thf(cS,type,
% 0.07/0.34 cS: a ).
% 0.07/0.34
% 0.07/0.34 thf(cG,type,
% 0.07/0.34 cG: b > b ).
% 0.07/0.34
% 0.07/0.34 thf(cW,type,
% 0.07/0.34 cW: b > b ).
% 0.07/0.34
% 0.07/0.34 thf(cL,type,
% 0.07/0.34 cL: b > b ).
% 0.07/0.34
% 0.07/0.34 thf(cO,type,
% 0.07/0.34 cO: b ).
% 0.07/0.34
% 0.07/0.34 thf(cTHM100A,conjecture,
% 0.07/0.34 ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
% 0.07/0.34 & ! [T: b] :
% 0.07/0.34 ( ( cP @ cS @ cN @ cS @ cN @ T )
% 0.07/0.34 => ( cP @ cN @ cN @ cS @ cN @ ( cL @ T ) ) )
% 0.07/0.34 & ! [T1: b] :
% 0.07/0.34 ( ( cP @ cN @ cN @ cS @ cN @ T1 )
% 0.07/0.34 => ( cP @ cS @ cN @ cS @ cN @ ( cL @ T1 ) ) )
% 0.07/0.34 & ! [T2: b] :
% 0.07/0.34 ( ( cP @ cS @ cS @ cN @ cS @ T2 )
% 0.07/0.34 => ( cP @ cN @ cS @ cN @ cS @ ( cL @ T2 ) ) )
% 0.07/0.34 & ! [T3: b] :
% 0.07/0.34 ( ( cP @ cN @ cS @ cN @ cS @ T3 )
% 0.07/0.34 => ( cP @ cS @ cS @ cN @ cS @ ( cL @ T3 ) ) )
% 0.07/0.34 & ! [T4: b] :
% 0.07/0.34 ( ( cP @ cS @ cS @ cS @ cN @ T4 )
% 0.07/0.34 => ( cP @ cN @ cN @ cS @ cN @ ( cW @ T4 ) ) )
% 0.07/0.34 & ! [T5: b] :
% 0.07/0.34 ( ( cP @ cN @ cN @ cS @ cN @ T5 )
% 0.07/0.34 => ( cP @ cS @ cS @ cS @ cN @ ( cW @ T5 ) ) )
% 0.07/0.34 & ! [T6: b] :
% 0.07/0.34 ( ( cP @ cS @ cS @ cN @ cS @ T6 )
% 0.07/0.34 => ( cP @ cN @ cN @ cN @ cS @ ( cW @ T6 ) ) )
% 0.07/0.34 & ! [T7: b] :
% 0.07/0.34 ( ( cP @ cN @ cN @ cN @ cS @ T7 )
% 0.07/0.34 => ( cP @ cS @ cS @ cN @ cS @ ( cW @ T7 ) ) )
% 0.07/0.34 & ! [X: a,Y: a,U: b] :
% 0.07/0.34 ( ( cP @ cS @ X @ cS @ Y @ U )
% 0.07/0.34 => ( cP @ cN @ X @ cN @ Y @ ( cG @ U ) ) )
% 0.07/0.34 & ! [X1: a,Y1: a,V: b] :
% 0.07/0.34 ( ( cP @ cN @ X1 @ cN @ Y1 @ V )
% 0.07/0.34 => ( cP @ cS @ X1 @ cS @ Y1 @ ( cG @ V ) ) )
% 0.07/0.34 & ! [T8: b] :
% 0.07/0.34 ( ( cP @ cS @ cN @ cS @ cS @ T8 )
% 0.07/0.34 => ( cP @ cN @ cN @ cS @ cN @ ( cD @ T8 ) ) )
% 0.07/0.34 & ! [T9: b] :
% 0.07/0.34 ( ( cP @ cN @ cN @ cS @ cN @ T9 )
% 0.07/0.34 => ( cP @ cS @ cN @ cS @ cS @ ( cD @ T9 ) ) )
% 0.07/0.34 & ! [U1: b] :
% 0.07/0.34 ( ( cP @ cS @ cS @ cN @ cS @ U1 )
% 0.07/0.34 => ( cP @ cN @ cS @ cN @ cN @ ( cD @ U1 ) ) )
% 0.07/0.34 & ! [V1: b] :
% 0.07/0.34 ( ( cP @ cN @ cS @ cN @ cN @ V1 )
% 0.07/0.34 => ( cP @ cS @ cS @ cN @ cS @ ( cD @ V1 ) ) ) )
% 0.07/0.34 => ? [Z: b] : ( cP @ cN @ cN @ cN @ cN @ Z ) ) ).
% 0.07/0.34
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 06:31:41 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rUOTgdkZ6h/DTF2DTF21750.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(a_type,type,
% 1.48/1.27 a: $tType ).
% 1.48/1.27
% 1.48/1.27 thf(b_type,type,
% 1.48/1.27 b: $tType ).
% 1.48/1.27
% 1.48/1.27 thf(cN,type,
% 1.48/1.27 cN: a ).
% 1.48/1.27
% 1.48/1.27 thf(cP,type,
% 1.48/1.27 cP: a > a > a > a > b > $o ).
% 1.48/1.27
% 1.48/1.27 thf(cD,type,
% 1.48/1.27 cD: b > b ).
% 1.48/1.27
% 1.48/1.27 thf(cS,type,
% 1.48/1.27 cS: a ).
% 1.48/1.27
% 1.48/1.27 thf(cG,type,
% 1.48/1.27 cG: b > b ).
% 1.48/1.27
% 1.48/1.27 thf(cW,type,
% 1.48/1.27 cW: b > b ).
% 1.48/1.27
% 1.48/1.27 thf(cL,type,
% 1.48/1.27 cL: b > b ).
% 1.48/1.27
% 1.48/1.27 thf(cO,type,
% 1.48/1.27 cO: b ).
% 1.48/1.27
% 1.48/1.27 thf(cTHM100A,conjecture,
% 1.48/1.27 ( ( ( cP @ cS @ cS @ cS @ cS @ cO )
% 1.48/1.27 & ! [T: b] :
% 1.48/1.27 ( ( cP @ cS @ cN @ cS @ cN @ T )
% 1.48/1.27 => ( cP @ cN @ cN @ cS @ cN @ ( cL @ T ) ) )
% 1.48/1.27 & ! [T1: b] :
% 1.48/1.27 ( ( cP @ cN @ cN @ cS @ cN @ T1 )
% 1.48/1.27 => ( cP @ cS @ cN @ cS @ cN @ ( cL @ T1 ) ) )
% 1.48/1.27 & ! [T2: b] :
% 1.48/1.27 ( ( cP @ cS @ cS @ cN @ cS @ T2 )
% 1.48/1.27 => ( cP @ cN @ cS @ cN @ cS @ ( cL @ T2 ) ) )
% 1.48/1.27 & ! [T3: b] :
% 1.48/1.27 ( ( cP @ cN @ cS @ cN @ cS @ T3 )
% 1.48/1.27 => ( cP @ cS @ cS @ cN @ cS @ ( cL @ T3 ) ) )
% 1.48/1.27 & ! [T4: b] :
% 1.48/1.27 ( ( cP @ cS @ cS @ cS @ cN @ T4 )
% 1.48/1.27 => ( cP @ cN @ cN @ cS @ cN @ ( cW @ T4 ) ) )
% 1.48/1.27 & ! [T5: b] :
% 1.48/1.27 ( ( cP @ cN @ cN @ cS @ cN @ T5 )
% 1.48/1.27 => ( cP @ cS @ cS @ cS @ cN @ ( cW @ T5 ) ) )
% 1.48/1.27 & ! [T6: b] :
% 1.48/1.27 ( ( cP @ cS @ cS @ cN @ cS @ T6 )
% 1.48/1.27 => ( cP @ cN @ cN @ cN @ cS @ ( cW @ T6 ) ) )
% 1.48/1.27 & ! [T7: b] :
% 1.48/1.27 ( ( cP @ cN @ cN @ cN @ cS @ T7 )
% 1.48/1.27 => ( cP @ cS @ cS @ cN @ cS @ ( cW @ T7 ) ) )
% 1.48/1.27 & ! [X: a,Y: a,U: b] :
% 1.48/1.27 ( ( cP @ cS @ X @ cS @ Y @ U )
% 1.48/1.27 => ( cP @ cN @ X @ cN @ Y @ ( cG @ U ) ) )
% 1.48/1.27 & ! [X1: a,Y1: a,V: b] :
% 1.48/1.27 ( ( cP @ cN @ X1 @ cN @ Y1 @ V )
% 1.48/1.27 => ( cP @ cS @ X1 @ cS @ Y1 @ ( cG @ V ) ) )
% 1.48/1.27 & ! [T8: b] :
% 1.48/1.27 ( ( cP @ cS @ cN @ cS @ cS @ T8 )
% 1.48/1.27 => ( cP @ cN @ cN @ cS @ cN @ ( cD @ T8 ) ) )
% 1.48/1.27 & ! [T9: b] :
% 1.48/1.27 ( ( cP @ cN @ cN @ cS @ cN @ T9 )
% 1.48/1.27 => ( cP @ cS @ cN @ cS @ cS @ ( cD @ T9 ) ) )
% 1.48/1.27 & ! [U1: b] :
% 1.48/1.27 ( ( cP @ cS @ cS @ cN @ cS @ U1 )
% 1.48/1.27 => ( cP @ cN @ cS @ cN @ cN @ ( cD @ U1 ) ) )
% 1.48/1.27 & ! [V1: b] :
% 1.48/1.27 ( ( cP @ cN @ cS @ cN @ cN @ V1 )
% 1.48/1.27 => ( cP @ cS @ cS @ cN @ cS @ ( cD @ V1 ) ) ) )
% 1.48/1.27 => ? [Z: b] : ( cP @ cN @ cN @ cN @ cN @ Z ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.29 % (21851)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/2Mi)
% 1.48/1.29 % (21850)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/27Mi)
% 1.48/1.29 % (21852)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/2Mi)
% 1.48/1.29 % (21854)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/18Mi)
% 1.48/1.29 % (21853)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/275Mi)
% 1.48/1.29 % (21849)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/4Mi)
% 1.48/1.29 % (21848)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21750 for (2999ds/183Mi)
% 1.48/1.30 % (21851)Instruction limit reached!
% 1.48/1.30 % (21851)------------------------------
% 1.48/1.30 % (21851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (21851)Termination reason: Unknown
% 1.48/1.30 % (21851)Termination phase: shuffling
% 1.48/1.30 % (21852)Instruction limit reached!
% 1.48/1.30 % (21852)------------------------------
% 1.48/1.30 % (21852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (21852)Termination reason: Unknown
% 1.48/1.30 % (21852)Termination phase: Property scanning
% 1.48/1.30
% 1.48/1.30 % (21852)Memory used [KB]: 1023
% 1.48/1.30 % (21852)Time elapsed: 0.003 s
% 1.48/1.30 % (21852)Instructions burned: 3 (million)
% 1.48/1.30 % (21852)------------------------------
% 1.48/1.30 % (21852)------------------------------
% 1.48/1.30
% 1.48/1.30 % (21851)Memory used [KB]: 1023
% 1.48/1.30 % (21851)Time elapsed: 0.003 s
% 1.48/1.30 % (21851)Instructions burned: 3 (million)
% 1.48/1.30 % (21851)------------------------------
% 1.48/1.30 % (21851)------------------------------
% 1.63/1.30 % (21849)Instruction limit reached!
% 1.63/1.30 % (21849)------------------------------
% 1.63/1.30 % (21849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (21849)Termination reason: Unknown
% 1.63/1.30 % (21849)Termination phase: Property scanning
% 1.63/1.30
% 1.63/1.30 % (21849)Memory used [KB]: 1023
% 1.63/1.30 % (21849)Time elapsed: 0.004 s
% 1.63/1.30 % (21849)Instructions burned: 5 (million)
% 1.63/1.30 % (21849)------------------------------
% 1.63/1.30 % (21849)------------------------------
% 1.63/1.30 % (21848)First to succeed.
% 1.63/1.30 % (21854)Instruction limit reached!
% 1.63/1.30 % (21854)------------------------------
% 1.63/1.30 % (21854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (21854)Termination reason: Unknown
% 1.63/1.30 % (21854)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (21854)Memory used [KB]: 5628
% 1.63/1.30 % (21854)Time elapsed: 0.011 s
% 1.63/1.30 % (21854)Instructions burned: 18 (million)
% 1.63/1.30 % (21854)------------------------------
% 1.63/1.30 % (21854)------------------------------
% 1.63/1.31 % (21853)Also succeeded, but the first one will report.
% 1.63/1.31 % (21848)Refutation found. Thanks to Tanya!
% 1.63/1.31 % SZS status Theorem for DTF2THF_21750
% 1.63/1.31 % SZS output start Proof for DTF2THF_21750
% 1.63/1.31 thf(type_def_5, type, a: $tType).
% 1.63/1.31 thf(type_def_6, type, b: $tType).
% 1.63/1.31 thf(func_def_0, type, a: $tType).
% 1.63/1.31 thf(func_def_1, type, b: $tType).
% 1.63/1.31 thf(func_def_2, type, cN: a).
% 1.63/1.31 thf(func_def_3, type, cP: a > a > a > a > b > $o).
% 1.63/1.31 thf(func_def_4, type, cD: b > b).
% 1.63/1.31 thf(func_def_5, type, cS: a).
% 1.63/1.31 thf(func_def_6, type, cG: b > b).
% 1.63/1.31 thf(func_def_7, type, cW: b > b).
% 1.63/1.31 thf(func_def_8, type, cL: b > b).
% 1.63/1.31 thf(func_def_9, type, cO: b).
% 1.63/1.31 thf(f57,plain,(
% 1.63/1.31 $false),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.63/1.31 thf(f55,plain,(
% 1.63/1.31 ($true != $true)),
% 1.63/1.31 inference(superposition,[status(thm)],[f49,f19])).
% 1.63/1.31 thf(f19,plain,(
% 1.63/1.31 ((cP @ cS @ cS @ cS @ cS @ cO) = $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f8,plain,(
% 1.63/1.31 ! [X0 : b] : (($true != (cP @ cS @ cN @ cS @ cS @ X0)) | ($true = (cP @ cN @ cN @ cS @ cN @ (cD @ X0)))) & ! [X1 : b] : (($true != (cP @ cN @ cS @ cN @ cN @ X1)) | ($true = (cP @ cS @ cS @ cN @ cS @ (cD @ X1)))) & ! [X2 : b] : (($true != (cP @ cN @ cN @ cS @ cN @ X2)) | ($true = (cP @ cS @ cN @ cS @ cS @ (cD @ X2)))) & ! [X3 : b] : ($true != (cP @ cN @ cN @ cN @ cN @ X3)) & ! [X4 : b] : (($true != (cP @ cN @ cN @ cS @ cN @ X4)) | ($true = (cP @ cS @ cN @ cS @ cN @ (cL @ X4)))) & ((cP @ cS @ cS @ cS @ cS @ cO) = $true) & ! [X5 : b] : (($true != (cP @ cS @ cS @ cN @ cS @ X5)) | ($true = (cP @ cN @ cN @ cN @ cS @ (cW @ X5)))) & ! [X6 : a,X7 : b,X8 : a] : (($true = (cP @ cN @ X8 @ cN @ X6 @ (cG @ X7))) | ($true != (cP @ cS @ X8 @ cS @ X6 @ X7))) & ! [X9 : b] : (($true = (cP @ cN @ cS @ cN @ cN @ (cD @ X9))) | ($true != (cP @ cS @ cS @ cN @ cS @ X9))) & ! [X10 : b] : (($true = (cP @ cN @ cS @ cN @ cS @ (cL @ X10))) | ($true != (cP @ cS @ cS @ cN @ cS @ X10))) & ! [X11 : a,X12 : a,X13 : b] : (($true = (cP @ cS @ X12 @ cS @ X11 @ (cG @ X13))) | ($true != (cP @ cN @ X12 @ cN @ X11 @ X13))) & ! [X14 : b] : (($true = (cP @ cN @ cN @ cS @ cN @ (cL @ X14))) | ($true != (cP @ cS @ cN @ cS @ cN @ X14))) & ! [X15 : b] : (($true != (cP @ cS @ cS @ cS @ cN @ X15)) | ($true = (cP @ cN @ cN @ cS @ cN @ (cW @ X15)))) & ! [X16 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cL @ X16))) | ($true != (cP @ cN @ cS @ cN @ cS @ X16))) & ! [X17 : b] : (($true = (cP @ cS @ cS @ cS @ cN @ (cW @ X17))) | ($true != (cP @ cN @ cN @ cS @ cN @ X17))) & ! [X18 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cW @ X18))) | ($true != (cP @ cN @ cN @ cN @ cS @ X18)))),
% 1.63/1.31 inference(rectify,[status(thm)],[f7])).
% 1.63/1.31 thf(f7,plain,(
% 1.63/1.31 ! [X16 : b] : (($true != (cP @ cS @ cN @ cS @ cS @ X16)) | ($true = (cP @ cN @ cN @ cS @ cN @ (cD @ X16)))) & ! [X17 : b] : (((cP @ cN @ cS @ cN @ cN @ X17) != $true) | ((cP @ cS @ cS @ cN @ cS @ (cD @ X17)) = $true)) & ! [X5 : b] : (((cP @ cN @ cN @ cS @ cN @ X5) != $true) | ((cP @ cS @ cN @ cS @ cS @ (cD @ X5)) = $true)) & ! [X18 : b] : ((cP @ cN @ cN @ cN @ cN @ X18) != $true) & ! [X6 : b] : (($true != (cP @ cN @ cN @ cS @ cN @ X6)) | ($true = (cP @ cS @ cN @ cS @ cN @ (cL @ X6)))) & ((cP @ cS @ cS @ cS @ cS @ cO) = $true) & ! [X4 : b] : (($true != (cP @ cS @ cS @ cN @ cS @ X4)) | ($true = (cP @ cN @ cN @ cN @ cS @ (cW @ X4)))) & ! [X3 : a,X2 : b,X1 : a] : (($true = (cP @ cN @ X1 @ cN @ X3 @ (cG @ X2))) | ($true != (cP @ cS @ X1 @ cS @ X3 @ X2))) & ! [X10 : b] : (($true = (cP @ cN @ cS @ cN @ cN @ (cD @ X10))) | ($true != (cP @ cS @ cS @ cN @ cS @ X10))) & ! [X7 : b] : (($true = (cP @ cN @ cS @ cN @ cS @ (cL @ X7))) | ($true != (cP @ cS @ cS @ cN @ cS @ X7))) & ! [X15 : a,X14 : a,X13 : b] : (($true = (cP @ cS @ X14 @ cS @ X15 @ (cG @ X13))) | ($true != (cP @ cN @ X14 @ cN @ X15 @ X13))) & ! [X11 : b] : (($true = (cP @ cN @ cN @ cS @ cN @ (cL @ X11))) | ((cP @ cS @ cN @ cS @ cN @ X11) != $true)) & ! [X12 : b] : (($true != (cP @ cS @ cS @ cS @ cN @ X12)) | ($true = (cP @ cN @ cN @ cS @ cN @ (cW @ X12)))) & ! [X0 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cL @ X0))) | ($true != (cP @ cN @ cS @ cN @ cS @ X0))) & ! [X9 : b] : (($true = (cP @ cS @ cS @ cS @ cN @ (cW @ X9))) | ($true != (cP @ cN @ cN @ cS @ cN @ X9))) & ! [X8 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cW @ X8))) | ($true != (cP @ cN @ cN @ cN @ cS @ X8)))),
% 1.63/1.31 inference(flattening,[status(thm)],[f6])).
% 1.63/1.31 thf(f6,plain,(
% 1.63/1.31 ! [X18 : b] : ((cP @ cN @ cN @ cN @ cN @ X18) != $true) & (! [X17 : b] : (((cP @ cN @ cS @ cN @ cN @ X17) != $true) | ((cP @ cS @ cS @ cN @ cS @ (cD @ X17)) = $true)) & ! [X5 : b] : (((cP @ cN @ cN @ cS @ cN @ X5) != $true) | ((cP @ cS @ cN @ cS @ cS @ (cD @ X5)) = $true)) & ! [X0 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cL @ X0))) | ($true != (cP @ cN @ cS @ cN @ cS @ X0))) & ! [X8 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cW @ X8))) | ($true != (cP @ cN @ cN @ cN @ cS @ X8))) & ! [X6 : b] : (($true != (cP @ cN @ cN @ cS @ cN @ X6)) | ($true = (cP @ cS @ cN @ cS @ cN @ (cL @ X6)))) & ! [X4 : b] : (($true != (cP @ cS @ cS @ cN @ cS @ X4)) | ($true = (cP @ cN @ cN @ cN @ cS @ (cW @ X4)))) & ! [X11 : b] : (($true = (cP @ cN @ cN @ cS @ cN @ (cL @ X11))) | ((cP @ cS @ cN @ cS @ cN @ X11) != $true)) & ! [X15 : a,X14 : a,X13 : b] : (($true = (cP @ cS @ X14 @ cS @ X15 @ (cG @ X13))) | ($true != (cP @ cN @ X14 @ cN @ X15 @ X13))) & ! [X7 : b] : (($true = (cP @ cN @ cS @ cN @ cS @ (cL @ X7))) | ($true != (cP @ cS @ cS @ cN @ cS @ X7))) & ! [X3 : a,X2 : b,X1 : a] : (($true = (cP @ cN @ X1 @ cN @ X3 @ (cG @ X2))) | ($true != (cP @ cS @ X1 @ cS @ X3 @ X2))) & ! [X16 : b] : (($true != (cP @ cS @ cN @ cS @ cS @ X16)) | ($true = (cP @ cN @ cN @ cS @ cN @ (cD @ X16)))) & ! [X9 : b] : (($true = (cP @ cS @ cS @ cS @ cN @ (cW @ X9))) | ($true != (cP @ cN @ cN @ cS @ cN @ X9))) & ! [X12 : b] : (($true != (cP @ cS @ cS @ cS @ cN @ X12)) | ($true = (cP @ cN @ cN @ cS @ cN @ (cW @ X12)))) & ((cP @ cS @ cS @ cS @ cS @ cO) = $true) & ! [X10 : b] : (($true = (cP @ cN @ cS @ cN @ cN @ (cD @ X10))) | ($true != (cP @ cS @ cS @ cN @ cS @ X10))))),
% 1.63/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.31 thf(f5,plain,(
% 1.63/1.31 ~((! [X17 : b] : (((cP @ cN @ cS @ cN @ cN @ X17) = $true) => ((cP @ cS @ cS @ cN @ cS @ (cD @ X17)) = $true)) & ! [X5 : b] : (((cP @ cN @ cN @ cS @ cN @ X5) = $true) => ((cP @ cS @ cN @ cS @ cS @ (cD @ X5)) = $true)) & ! [X0 : b] : (($true = (cP @ cN @ cS @ cN @ cS @ X0)) => ($true = (cP @ cS @ cS @ cN @ cS @ (cL @ X0)))) & ! [X8 : b] : (($true = (cP @ cN @ cN @ cN @ cS @ X8)) => ($true = (cP @ cS @ cS @ cN @ cS @ (cW @ X8)))) & ! [X6 : b] : (($true = (cP @ cN @ cN @ cS @ cN @ X6)) => ($true = (cP @ cS @ cN @ cS @ cN @ (cL @ X6)))) & ! [X4 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ X4)) => ($true = (cP @ cN @ cN @ cN @ cS @ (cW @ X4)))) & ! [X11 : b] : (((cP @ cS @ cN @ cS @ cN @ X11) = $true) => ($true = (cP @ cN @ cN @ cS @ cN @ (cL @ X11)))) & ! [X13 : b,X15 : a,X14 : a] : (($true = (cP @ cN @ X14 @ cN @ X15 @ X13)) => ($true = (cP @ cS @ X14 @ cS @ X15 @ (cG @ X13)))) & ! [X7 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ X7)) => ($true = (cP @ cN @ cS @ cN @ cS @ (cL @ X7)))) & ! [X2 : b,X1 : a,X3 : a] : (($true = (cP @ cS @ X1 @ cS @ X3 @ X2)) => ($true = (cP @ cN @ X1 @ cN @ X3 @ (cG @ X2)))) & ! [X16 : b] : (($true = (cP @ cS @ cN @ cS @ cS @ X16)) => ($true = (cP @ cN @ cN @ cS @ cN @ (cD @ X16)))) & ! [X9 : b] : (($true = (cP @ cN @ cN @ cS @ cN @ X9)) => ($true = (cP @ cS @ cS @ cS @ cN @ (cW @ X9)))) & ! [X12 : b] : (($true = (cP @ cS @ cS @ cS @ cN @ X12)) => ($true = (cP @ cN @ cN @ cS @ cN @ (cW @ X12)))) & ((cP @ cS @ cS @ cS @ cS @ cO) = $true) & ! [X10 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ X10)) => ($true = (cP @ cN @ cS @ cN @ cN @ (cD @ X10))))) => ? [X18 : b] : ((cP @ cN @ cN @ cN @ cN @ X18) = $true))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.31 thf(f4,plain,(
% 1.63/1.31 ~((! [X0 : b] : ((cP @ cN @ cS @ cN @ cS @ X0) => (cP @ cS @ cS @ cN @ cS @ (cL @ X0))) & ! [X1 : a,X2 : b,X3 : a] : ((cP @ cS @ X1 @ cS @ X3 @ X2) => (cP @ cN @ X1 @ cN @ X3 @ (cG @ X2))) & ! [X4 : b] : ((cP @ cS @ cS @ cN @ cS @ X4) => (cP @ cN @ cN @ cN @ cS @ (cW @ X4))) & ! [X5 : b] : ((cP @ cN @ cN @ cS @ cN @ X5) => (cP @ cS @ cN @ cS @ cS @ (cD @ X5))) & ! [X6 : b] : ((cP @ cN @ cN @ cS @ cN @ X6) => (cP @ cS @ cN @ cS @ cN @ (cL @ X6))) & ! [X7 : b] : ((cP @ cS @ cS @ cN @ cS @ X7) => (cP @ cN @ cS @ cN @ cS @ (cL @ X7))) & ! [X8 : b] : ((cP @ cN @ cN @ cN @ cS @ X8) => (cP @ cS @ cS @ cN @ cS @ (cW @ X8))) & ! [X9 : b] : ((cP @ cN @ cN @ cS @ cN @ X9) => (cP @ cS @ cS @ cS @ cN @ (cW @ X9))) & ! [X10 : b] : ((cP @ cS @ cS @ cN @ cS @ X10) => (cP @ cN @ cS @ cN @ cN @ (cD @ X10))) & ! [X11 : b] : ((cP @ cS @ cN @ cS @ cN @ X11) => (cP @ cN @ cN @ cS @ cN @ (cL @ X11))) & (cP @ cS @ cS @ cS @ cS @ cO) & ! [X12 : b] : ((cP @ cS @ cS @ cS @ cN @ X12) => (cP @ cN @ cN @ cS @ cN @ (cW @ X12))) & ! [X13 : b,X14 : a,X15 : a] : ((cP @ cN @ X14 @ cN @ X15 @ X13) => (cP @ cS @ X14 @ cS @ X15 @ (cG @ X13))) & ! [X16 : b] : ((cP @ cS @ cN @ cS @ cS @ X16) => (cP @ cN @ cN @ cS @ cN @ (cD @ X16))) & ! [X17 : b] : ((cP @ cN @ cS @ cN @ cN @ X17) => (cP @ cS @ cS @ cN @ cS @ (cD @ X17)))) => ? [X18 : b] : (cP @ cN @ cN @ cN @ cN @ X18))),
% 1.63/1.31 inference(rectify,[status(thm)],[f2])).
% 1.63/1.31 thf(f2,negated_conjecture,(
% 1.63/1.31 ~((! [X3 : b] : ((cP @ cN @ cS @ cN @ cS @ X3) => (cP @ cS @ cS @ cN @ cS @ (cL @ X3))) & ! [X8 : a,X10 : b,X9 : a] : ((cP @ cS @ X8 @ cS @ X9 @ X10) => (cP @ cN @ X8 @ cN @ X9 @ (cG @ X10))) & ! [X6 : b] : ((cP @ cS @ cS @ cN @ cS @ X6) => (cP @ cN @ cN @ cN @ cS @ (cW @ X6))) & ! [X15 : b] : ((cP @ cN @ cN @ cS @ cN @ X15) => (cP @ cS @ cN @ cS @ cS @ (cD @ X15))) & ! [X1 : b] : ((cP @ cN @ cN @ cS @ cN @ X1) => (cP @ cS @ cN @ cS @ cN @ (cL @ X1))) & ! [X2 : b] : ((cP @ cS @ cS @ cN @ cS @ X2) => (cP @ cN @ cS @ cN @ cS @ (cL @ X2))) & ! [X7 : b] : ((cP @ cN @ cN @ cN @ cS @ X7) => (cP @ cS @ cS @ cN @ cS @ (cW @ X7))) & ! [X5 : b] : ((cP @ cN @ cN @ cS @ cN @ X5) => (cP @ cS @ cS @ cS @ cN @ (cW @ X5))) & ! [X16 : b] : ((cP @ cS @ cS @ cN @ cS @ X16) => (cP @ cN @ cS @ cN @ cN @ (cD @ X16))) & ! [X0 : b] : ((cP @ cS @ cN @ cS @ cN @ X0) => (cP @ cN @ cN @ cS @ cN @ (cL @ X0))) & (cP @ cS @ cS @ cS @ cS @ cO) & ! [X4 : b] : ((cP @ cS @ cS @ cS @ cN @ X4) => (cP @ cN @ cN @ cS @ cN @ (cW @ X4))) & ! [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)))) => ? [X18 : b] : (cP @ cN @ cN @ cN @ cN @ X18))),
% 1.63/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.31 thf(f1,conjecture,(
% 1.63/1.31 (! [X3 : b] : ((cP @ cN @ cS @ cN @ cS @ X3) => (cP @ cS @ cS @ cN @ cS @ (cL @ X3))) & ! [X8 : a,X10 : b,X9 : a] : ((cP @ cS @ X8 @ cS @ X9 @ X10) => (cP @ cN @ X8 @ cN @ X9 @ (cG @ X10))) & ! [X6 : b] : ((cP @ cS @ cS @ cN @ cS @ X6) => (cP @ cN @ cN @ cN @ cS @ (cW @ X6))) & ! [X15 : b] : ((cP @ cN @ cN @ cS @ cN @ X15) => (cP @ cS @ cN @ cS @ cS @ (cD @ X15))) & ! [X1 : b] : ((cP @ cN @ cN @ cS @ cN @ X1) => (cP @ cS @ cN @ cS @ cN @ (cL @ X1))) & ! [X2 : b] : ((cP @ cS @ cS @ cN @ cS @ X2) => (cP @ cN @ cS @ cN @ cS @ (cL @ X2))) & ! [X7 : b] : ((cP @ cN @ cN @ cN @ cS @ X7) => (cP @ cS @ cS @ cN @ cS @ (cW @ X7))) & ! [X5 : b] : ((cP @ cN @ cN @ cS @ cN @ X5) => (cP @ cS @ cS @ cS @ cN @ (cW @ X5))) & ! [X16 : b] : ((cP @ cS @ cS @ cN @ cS @ X16) => (cP @ cN @ cS @ cN @ cN @ (cD @ X16))) & ! [X0 : b] : ((cP @ cS @ cN @ cS @ cN @ X0) => (cP @ cN @ cN @ cS @ cN @ (cL @ X0))) & (cP @ cS @ cS @ cS @ cS @ cO) & ! [X4 : b] : ((cP @ cS @ cS @ cS @ cN @ X4) => (cP @ cN @ cN @ cS @ cN @ (cW @ X4))) & ! [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)))) => ? [X18 : b] : (cP @ cN @ cN @ cN @ cN @ X18)),
% 1.63/1.31 file('/export/starexec/sandbox/tmp/tmp.rUOTgdkZ6h/DTF2THF_21750.p',cTHM100A)).
% 1.63/1.31 thf(f49,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cS @ cS @ cS @ cS @ X0))) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.63/1.31 thf(f48,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cS @ cS @ cS @ cS @ X0)) | ($true != $true)) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f45,f17])).
% 1.63/1.31 thf(f17,plain,(
% 1.63/1.31 ( ! [X8 : a,X6 : a,X7 : b] : (($true = (cP @ cN @ X8 @ cN @ X6 @ (cG @ X7))) | ($true != (cP @ cS @ X8 @ cS @ X6 @ X7))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f45,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cN @ cS @ cN @ cS @ X0))) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.63/1.31 thf(f44,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cN @ cS @ cN @ cS @ X0)) | ($true != $true)) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f41,f11])).
% 1.63/1.31 thf(f11,plain,(
% 1.63/1.31 ( ! [X16 : b] : (($true = (cP @ cS @ cS @ cN @ cS @ (cL @ X16))) | ($true != (cP @ cN @ cS @ cN @ cS @ X16))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f41,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cS @ cS @ cN @ cS @ X0))) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.63/1.31 thf(f39,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != $true) | ($true != (cP @ cS @ cS @ cN @ cS @ X0))) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f37,f16])).
% 1.63/1.31 thf(f16,plain,(
% 1.63/1.31 ( ! [X9 : b] : (($true = (cP @ cN @ cS @ cN @ cN @ (cD @ X9))) | ($true != (cP @ cS @ cS @ cN @ cS @ X9))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f37,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cN @ cS @ cN @ cN @ X0))) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.63/1.31 thf(f36,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != $true) | ($true != (cP @ cN @ cS @ cN @ cN @ X0))) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f34,f14])).
% 1.63/1.31 thf(f14,plain,(
% 1.63/1.31 ( ! [X11 : a,X12 : a,X13 : b] : (($true = (cP @ cS @ X12 @ cS @ X11 @ (cG @ X13))) | ($true != (cP @ cN @ X12 @ cN @ X11 @ X13))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f34,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cS @ cS @ cS @ cN @ X0))) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.63/1.31 thf(f31,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != $true) | ($true != (cP @ cS @ cS @ cS @ cN @ X0))) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f30,f12])).
% 1.63/1.31 thf(f12,plain,(
% 1.63/1.31 ( ! [X15 : b] : (($true = (cP @ cN @ cN @ cS @ cN @ (cW @ X15))) | ($true != (cP @ cS @ cS @ cS @ cN @ X15))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f30,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cN @ cN @ cS @ cN @ X0))) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.63/1.31 thf(f29,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != (cP @ cN @ cN @ cS @ cN @ X0)) | ($true != $true)) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f26,f20])).
% 1.63/1.31 thf(f20,plain,(
% 1.63/1.31 ( ! [X4 : b] : (($true = (cP @ cS @ cN @ cS @ cN @ (cL @ X4))) | ($true != (cP @ cN @ cN @ cS @ cN @ X4))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f26,plain,(
% 1.63/1.31 ( ! [X0 : b] : (((cP @ cS @ cN @ cS @ cN @ X0) != $true)) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.63/1.31 thf(f25,plain,(
% 1.63/1.31 ( ! [X0 : b] : (($true != $true) | ((cP @ cS @ cN @ cS @ cN @ X0) != $true)) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f21,f17])).
% 1.63/1.31 thf(f21,plain,(
% 1.63/1.31 ( ! [X3 : b] : (($true != (cP @ cN @ cN @ cN @ cN @ X3))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 % SZS output end Proof for DTF2THF_21750
% 1.63/1.31 % (21848)------------------------------
% 1.63/1.31 % (21848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (21848)Termination reason: Refutation
% 1.63/1.31
% 1.63/1.31 % (21848)Memory used [KB]: 5628
% 1.63/1.31 % (21848)Time elapsed: 0.012 s
% 1.63/1.31 % (21848)Instructions burned: 14 (million)
% 1.63/1.31 % (21848)------------------------------
% 1.63/1.31 % (21848)------------------------------
% 1.63/1.31 % (21847)Success in time 0.027 s
%------------------------------------------------------------------------------