%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV045^5 : 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 : n006.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 09:40:09 AM UTC 2026
% Result : Theorem 1.92s 1.65s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 635 ( 181 equ; 0 cnn)
% Maximal formula atoms : 19 ( 11 avg)
% Number of connectives : 956 ( 121 ~; 106 |; 54 &; 618 @)
% ( 4 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 185 ( 0 ^; 177 !; 8 ?; 185 :)
% 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,
g: a > b ).
thf(func_def_3,type,
f: a > b ).
thf(func_def_4,type,
cQ: a > b > b > $o ).
thf(func_def_5,type,
cP: a > a > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: a ).
thf(func_def_12,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f413,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f48,f58,f388,f400,f410]) ).
thf(f410,plain,
spl2_5,
inference(avatar_contradiction_clause,[status(thm)],[f409]) ).
thf(f409,plain,
( $false
| spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f406]) ).
thf(f406,plain,
( ( $true != $true )
| spl2_5 ),
inference(superposition,[status(thm)],[f405,f17]) ).
thf(f17,plain,
( ( cP @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: a,X1: a] :
( ( ( cP @ X0 @ X1 )
!= $true )
| ( ( cQ @ X0 @ ( f @ X0 ) @ ( f @ X1 ) )
= $true ) )
& ( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ ( g @ sK1 ) ) )
& ( ( cP @ sK0 @ sK1 )
= $true )
& ! [X4: a,X5: a] :
( ( ( cQ @ X5 )
= ( cQ @ X4 ) )
| ( $true
!= ( cP @ X5 @ X4 ) ) )
& ! [X6: a,X7: a,X8: a] :
( ( $true
!= ( cP @ X8 @ X7 ) )
| ( $true
!= ( cP @ X7 @ X6 ) )
| ( ( cP @ X8 @ X6 )
= $true ) )
& ! [X9: a] :
( ( ! [X10: b,X11: b] :
( ( ( cQ @ X9 @ X10 @ X11 )
!= $true )
| ( ( cQ @ X9 @ X11 @ X10 )
= $true ) )
& ! [X12: b,X13: b,X14: b] :
( ( $true
!= ( cQ @ X9 @ X13 @ X12 ) )
| ( $true
= ( cQ @ X9 @ X13 @ X14 ) )
| ( $true
!= ( cQ @ X9 @ X12 @ X14 ) ) ) )
| ( $true
!= ( cP @ X9 @ X9 ) ) )
& ! [X15: a,X16: a] :
( ( ( cP @ X16 @ X15 )
= $true )
| ( ( cP @ X15 @ X16 )
!= $true ) )
& ! [X17: a] :
( ( ( cP @ X17 @ X17 )
!= $true )
| ( ( cQ @ X17 @ ( f @ X17 ) @ ( g @ X17 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).
thf(f9,plain,
( ? [X2: a,X3: a] :
( ( ( cQ @ X2 @ ( f @ X2 ) @ ( g @ X3 ) )
!= $true )
& ( ( cP @ X2 @ X3 )
= $true ) )
=> ( ( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ ( g @ sK1 ) ) )
& ( ( cP @ sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: a,X1: a] :
( ( ( cP @ X0 @ X1 )
!= $true )
| ( ( cQ @ X0 @ ( f @ X0 ) @ ( f @ X1 ) )
= $true ) )
& ? [X2: a,X3: a] :
( ( ( cQ @ X2 @ ( f @ X2 ) @ ( g @ X3 ) )
!= $true )
& ( ( cP @ X2 @ X3 )
= $true ) )
& ! [X4: a,X5: a] :
( ( ( cQ @ X5 )
= ( cQ @ X4 ) )
| ( $true
!= ( cP @ X5 @ X4 ) ) )
& ! [X6: a,X7: a,X8: a] :
( ( $true
!= ( cP @ X8 @ X7 ) )
| ( $true
!= ( cP @ X7 @ X6 ) )
| ( ( cP @ X8 @ X6 )
= $true ) )
& ! [X9: a] :
( ( ! [X10: b,X11: b] :
( ( ( cQ @ X9 @ X10 @ X11 )
!= $true )
| ( ( cQ @ X9 @ X11 @ X10 )
= $true ) )
& ! [X12: b,X13: b,X14: b] :
( ( $true
!= ( cQ @ X9 @ X13 @ X12 ) )
| ( $true
= ( cQ @ X9 @ X13 @ X14 ) )
| ( $true
!= ( cQ @ X9 @ X12 @ X14 ) ) ) )
| ( $true
!= ( cP @ X9 @ X9 ) ) )
& ! [X15: a,X16: a] :
( ( ( cP @ X16 @ X15 )
= $true )
| ( ( cP @ X15 @ X16 )
!= $true ) )
& ! [X17: a] :
( ( ( cP @ X17 @ X17 )
!= $true )
| ( ( cQ @ X17 @ ( f @ X17 ) @ ( g @ X17 ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: a,X2: a] :
( ( ( cP @ X1 @ X2 )
!= $true )
| ( $true
= ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) ) )
& ? [X16: a,X17: a] :
( ( ( cQ @ X16 @ ( f @ X16 ) @ ( g @ X17 ) )
!= $true )
& ( ( cP @ X16 @ X17 )
= $true ) )
& ! [X9: a,X8: a] :
( ( ( cQ @ X8 )
= ( cQ @ X9 ) )
| ( $true
!= ( cP @ X8 @ X9 ) ) )
& ! [X7: a,X5: a,X6: a] :
( ( $true
!= ( cP @ X6 @ X5 ) )
| ( $true
!= ( cP @ X5 @ X7 ) )
| ( ( cP @ X6 @ X7 )
= $true ) )
& ! [X10: a] :
( ( ! [X11: b,X12: b] :
( ( $true
!= ( cQ @ X10 @ X11 @ X12 ) )
| ( $true
= ( cQ @ X10 @ X12 @ X11 ) ) )
& ! [X14: b,X15: b,X13: b] :
( ( $true
!= ( cQ @ X10 @ X15 @ X14 ) )
| ( $true
= ( cQ @ X10 @ X15 @ X13 ) )
| ( $true
!= ( cQ @ X10 @ X14 @ X13 ) ) ) )
| ( $true
!= ( cP @ X10 @ X10 ) ) )
& ! [X3: a,X4: a] :
( ( ( cP @ X4 @ X3 )
= $true )
| ( $true
!= ( cP @ X3 @ X4 ) ) )
& ! [X0: a] :
( ( ( cP @ X0 @ X0 )
!= $true )
| ( ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X0 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X16: a,X17: a] :
( ( ( cQ @ X16 @ ( f @ X16 ) @ ( g @ X17 ) )
!= $true )
& ( ( cP @ X16 @ X17 )
= $true ) )
& ! [X9: a,X8: a] :
( ( ( cQ @ X8 )
= ( cQ @ X9 ) )
| ( $true
!= ( cP @ X8 @ X9 ) ) )
& ! [X10: a] :
( ( ! [X13: b,X15: b,X14: b] :
( ( $true
= ( cQ @ X10 @ X15 @ X13 ) )
| ( $true
!= ( cQ @ X10 @ X15 @ X14 ) )
| ( $true
!= ( cQ @ X10 @ X14 @ X13 ) ) )
& ! [X11: b,X12: b] :
( ( $true
!= ( cQ @ X10 @ X11 @ X12 ) )
| ( $true
= ( cQ @ X10 @ X12 @ X11 ) ) ) )
| ( $true
!= ( cP @ X10 @ X10 ) ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( cP @ X6 @ X7 )
= $true )
| ( $true
!= ( cP @ X6 @ X5 ) )
| ( $true
!= ( cP @ X5 @ X7 ) ) )
& ! [X3: a,X4: a] :
( ( ( cP @ X4 @ X3 )
= $true )
| ( $true
!= ( cP @ X3 @ X4 ) ) )
& ! [X1: a,X2: a] :
( ( ( cP @ X1 @ X2 )
!= $true )
| ( $true
= ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) ) )
& ! [X0: a] :
( ( ( cP @ X0 @ X0 )
!= $true )
| ( ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a] :
( ( ( cP @ X0 @ X0 )
= $true )
=> ( ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X0 ) )
= $true ) )
=> ( ! [X2: a,X1: a] :
( ( ( cP @ X1 @ X2 )
= $true )
=> ( $true
= ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) ) )
=> ( ( ! [X5: a,X7: a,X6: a] :
( ( ( $true
= ( cP @ X6 @ X5 ) )
& ( $true
= ( cP @ X5 @ X7 ) ) )
=> ( ( cP @ X6 @ X7 )
= $true ) )
& ! [X3: a,X4: a] :
( ( $true
= ( cP @ X3 @ X4 ) )
=> ( ( cP @ X4 @ X3 )
= $true ) ) )
=> ( ( ! [X9: a,X8: a] :
( ( $true
= ( cP @ X8 @ X9 ) )
=> ( ( cQ @ X8 )
= ( cQ @ X9 ) ) )
& ! [X10: a] :
( ( $true
= ( cP @ X10 @ X10 ) )
=> ( ! [X13: b,X15: b,X14: b] :
( ( ( $true
= ( cQ @ X10 @ X15 @ X14 ) )
& ( $true
= ( cQ @ X10 @ X14 @ X13 ) ) )
=> ( $true
= ( cQ @ X10 @ X15 @ X13 ) ) )
& ! [X11: b,X12: b] :
( ( $true
= ( cQ @ X10 @ X11 @ X12 ) )
=> ( $true
= ( cQ @ X10 @ X12 @ X11 ) ) ) ) ) )
=> ! [X16: a,X17: a] :
( ( ( cP @ X16 @ X17 )
= $true )
=> ( ( cQ @ X16 @ ( f @ X16 ) @ ( g @ X17 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a] :
( ( cP @ X0 @ X0 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X0 ) ) )
=> ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) )
=> ( ( ! [X3: a,X4: a] :
( ( cP @ X3 @ X4 )
=> ( cP @ X4 @ X3 ) )
& ! [X5: a,X6: a,X7: a] :
( ( ( cP @ X5 @ X7 )
& ( cP @ X6 @ X5 ) )
=> ( cP @ X6 @ X7 ) ) )
=> ( ( ! [X8: a,X9: a] :
( ( cP @ X8 @ X9 )
=> ( ( cQ @ X8 )
= ( cQ @ X9 ) ) )
& ! [X10: a] :
( ( cP @ X10 @ X10 )
=> ( ! [X11: b,X12: b] :
( ( cQ @ X10 @ X11 @ X12 )
=> ( cQ @ X10 @ X12 @ X11 ) )
& ! [X13: b,X14: b,X15: b] :
( ( ( cQ @ X10 @ X15 @ X14 )
& ( cQ @ X10 @ X14 @ X13 ) )
=> ( cQ @ X10 @ X15 @ X13 ) ) ) ) )
=> ! [X16: a,X17: a] :
( ( cP @ X16 @ X17 )
=> ( cQ @ X16 @ ( f @ X16 ) @ ( g @ X17 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
( ( cP @ X0 @ X0 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X0 ) ) )
=> ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( f @ X1 ) ) )
=> ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( cP @ X1 @ X0 ) )
& ! [X1: a,X0: a,X2: a] :
( ( ( cP @ X1 @ X2 )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X0 @ X2 ) ) )
=> ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( ( cQ @ X0 )
= ( cQ @ X1 ) ) )
& ! [X0: a] :
( ( cP @ X0 @ X0 )
=> ( ! [X3: b,X1: b] :
( ( cQ @ X0 @ X3 @ X1 )
=> ( cQ @ X0 @ X1 @ X3 ) )
& ! [X2: b,X1: b,X3: b] :
( ( ( cQ @ X0 @ X3 @ X1 )
& ( cQ @ X0 @ X1 @ X2 ) )
=> ( cQ @ X0 @ X3 @ X2 ) ) ) ) )
=> ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a] :
( ( cP @ X0 @ X0 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X0 ) ) )
=> ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( f @ X1 ) ) )
=> ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( cP @ X1 @ X0 ) )
& ! [X1: a,X0: a,X2: a] :
( ( ( cP @ X1 @ X2 )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X0 @ X2 ) ) )
=> ( ( ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( ( cQ @ X0 )
= ( cQ @ X1 ) ) )
& ! [X0: a] :
( ( cP @ X0 @ X0 )
=> ( ! [X3: b,X1: b] :
( ( cQ @ X0 @ X3 @ X1 )
=> ( cQ @ X0 @ X1 @ X3 ) )
& ! [X2: b,X1: b,X3: b] :
( ( ( cQ @ X0 @ X3 @ X1 )
& ( cQ @ X0 @ X1 @ X2 ) )
=> ( cQ @ X0 @ X3 @ X2 ) ) ) ) )
=> ! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
=> ( cQ @ X0 @ ( f @ X0 ) @ ( g @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lrD0QKFhck/DTF2THF_6307.p',cTHM509_pme) ).
thf(f405,plain,
( ! [X0: a] :
( $true
!= ( cP @ X0 @ sK1 ) )
| spl2_5 ),
inference(subsumption_resolution,[status(thm)],[f403,f12]) ).
thf(f12,plain,
! [X16: a,X15: a] :
( ( ( cP @ X16 @ X15 )
= $true )
| ( ( cP @ X15 @ X16 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f403,plain,
( ! [X0: a] :
( ( ( cP @ sK1 @ X0 )
!= $true )
| ( $true
!= ( cP @ X0 @ sK1 ) ) )
| spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f401]) ).
thf(f401,plain,
( ! [X0: a] :
( ( ( cP @ sK1 @ X0 )
!= $true )
| ( $true
!= ( cP @ X0 @ sK1 ) )
| ( $true != $true ) )
| spl2_5 ),
inference(superposition,[status(thm)],[f387,f15]) ).
thf(f15,plain,
! [X8: a,X6: a,X7: a] :
( ( ( cP @ X8 @ X6 )
= $true )
| ( $true
!= ( cP @ X7 @ X6 ) )
| ( $true
!= ( cP @ X8 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f387,plain,
( ( $true
!= ( cP @ sK1 @ sK1 ) )
| spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f385]) ).
thf(f385,definition,
( spl2_5
<=> ( $true
= ( cP @ sK1 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f400,plain,
spl2_4,
inference(avatar_contradiction_clause,[status(thm)],[f399]) ).
thf(f399,plain,
( $false
| spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f398,f17]) ).
thf(f398,plain,
( ( ( cP @ sK0 @ sK1 )
!= $true )
| spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f396]) ).
thf(f396,plain,
( ( $true != $true )
| ( ( cP @ sK0 @ sK1 )
!= $true )
| spl2_4 ),
inference(superposition,[status(thm)],[f383,f12]) ).
thf(f383,plain,
( ( $true
!= ( cP @ sK1 @ sK0 ) )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f381]) ).
thf(f381,definition,
( spl2_4
<=> ( $true
= ( cP @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f388,plain,
( ~ spl2_4
| ~ spl2_5
| ~ spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f379,f46,f385,f381]) ).
thf(f46,definition,
( spl2_3
<=> ! [X0: b] :
( ( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ X0 ) )
| ( $true
!= ( cQ @ sK0 @ X0 @ ( g @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f379,plain,
( ( $true
!= ( cP @ sK1 @ sK0 ) )
| ( $true
!= ( cP @ sK1 @ sK1 ) )
| ~ spl2_3 ),
inference(subsumption_resolution,[status(thm)],[f374,f17]) ).
thf(f374,plain,
( ( $true
!= ( cP @ sK1 @ sK1 ) )
| ( $true
!= ( cP @ sK1 @ sK0 ) )
| ( ( cP @ sK0 @ sK1 )
!= $true )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f364]) ).
thf(f364,plain,
( ( $true != $true )
| ( $true
!= ( cP @ sK1 @ sK1 ) )
| ( ( cP @ sK0 @ sK1 )
!= $true )
| ( $true
!= ( cP @ sK1 @ sK0 ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f72,f181]) ).
thf(f181,plain,
! [X0: a,X1: a] :
( ( $true
= ( cQ @ X1 @ ( f @ X0 ) @ ( g @ X0 ) ) )
| ( ( cP @ X0 @ X0 )
!= $true )
| ( ( cP @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
! [X0: a,X1: a] :
( ( ( cP @ X0 @ X0 )
!= $true )
| ( ( cP @ X0 @ X1 )
!= $true )
| ( $false = $true )
| ( $true
= ( cQ @ X1 @ ( f @ X0 ) @ ( g @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f30,f11]) ).
thf(f11,plain,
! [X17: a] :
( ( ( cQ @ X17 @ ( f @ X17 ) @ ( g @ X17 ) )
= $true )
| ( ( cP @ X17 @ X17 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f30,plain,
! [X6: b,X7: b,X4: a,X5: a] :
( ( ( cQ @ X5 @ X6 @ X7 )
= $false )
| ( ( cQ @ X4 @ X6 @ X7 )
= $true )
| ( $true
!= ( cP @ X5 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X6: b,X7: b,X4: a,X5: a] :
( ( $true
!= ( cP @ X5 @ X4 ) )
| ( ( cQ @ X4 @ X6 @ X7 )
= ( cQ @ X5 @ X6 @ X7 ) ) ),
inference(argument_congruence,[status(thm)],[f20]) ).
thf(f20,plain,
! [X6: b,X4: a,X5: a] :
( ( ( cQ @ X5 @ X6 )
= ( cQ @ X4 @ X6 ) )
| ( $true
!= ( cP @ X5 @ X4 ) ) ),
inference(argument_congruence,[status(thm)],[f16]) ).
thf(f16,plain,
! [X4: a,X5: a] :
( ( ( cQ @ X5 )
= ( cQ @ X4 ) )
| ( $true
!= ( cP @ X5 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f72,plain,
( ! [X0: a] :
( ( $true
!= ( cQ @ sK0 @ ( f @ X0 ) @ ( g @ sK1 ) ) )
| ( ( cP @ sK0 @ X0 )
!= $true ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( cP @ sK0 @ X0 )
!= $true )
| ( $true
!= ( cQ @ sK0 @ ( f @ X0 ) @ ( g @ sK1 ) ) ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f47,f19]) ).
thf(f19,plain,
! [X0: a,X1: a] :
( ( ( cQ @ X0 @ ( f @ X0 ) @ ( f @ X1 ) )
= $true )
| ( ( cP @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f47,plain,
( ! [X0: b] :
( ( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ X0 ) )
| ( $true
!= ( cQ @ sK0 @ X0 @ ( g @ sK1 ) ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f58,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true != $true )
| spl2_2 ),
inference(superposition,[status(thm)],[f53,f17]) ).
thf(f53,plain,
( ! [X0: a] :
( ( cP @ sK0 @ X0 )
!= $true )
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f52,f12]) ).
thf(f52,plain,
( ! [X0: a] :
( ( $true
!= ( cP @ X0 @ sK0 ) )
| ( ( cP @ sK0 @ X0 )
!= $true ) )
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X0: a] :
( ( $true
!= ( cP @ X0 @ sK0 ) )
| ( ( cP @ sK0 @ X0 )
!= $true )
| ( $true != $true ) )
| spl2_2 ),
inference(superposition,[status(thm)],[f41,f15]) ).
thf(f41,plain,
( ( $true
!= ( cP @ sK0 @ sK0 ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_2
<=> ( $true
= ( cP @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f48,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f44,f46,f39]) ).
thf(f44,plain,
! [X0: b] :
( ( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ X0 ) )
| ( $true
!= ( cP @ sK0 @ sK0 ) )
| ( $true
!= ( cQ @ sK0 @ X0 @ ( g @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: b] :
( ( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ X0 ) )
| ( $true
!= ( cP @ sK0 @ sK0 ) )
| ( $true
!= ( cQ @ sK0 @ X0 @ ( g @ sK1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f13]) ).
thf(f13,plain,
! [X9: a,X14: b,X12: b,X13: b] :
( ( $true
= ( cQ @ X9 @ X13 @ X14 ) )
| ( $true
!= ( cP @ X9 @ X9 ) )
| ( $true
!= ( cQ @ X9 @ X13 @ X12 ) )
| ( $true
!= ( cQ @ X9 @ X12 @ X14 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f18,plain,
( $true
!= ( cQ @ sK0 @ ( f @ sK0 ) @ ( g @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV045^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:39:15 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.48 ---- Original DTF file ---
% 0.30/0.48 thf(spec,logic,$$dhol).
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 % File : SEV045^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.48 % Domain : Set Theory (Relations)
% 0.30/0.48 % Problem : TPS problem from PERS-THMS
% 0.30/0.48 % Version : Especial.
% 0.30/0.48 % English :
% 0.30/0.48
% 0.30/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.48 % Source : [Bro09]
% 0.30/0.48 % Names : tps_1134 [Bro09]
% 0.30/0.48
% 0.30/0.48 % Status : Theorem
% 0.30/0.48 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.30/0.48 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.30/0.48 % Number of atoms : 21 ( 1 equ; 0 cnn)
% 0.30/0.48 % Maximal formula atoms : 19 ( 21 avg)
% 0.30/0.48 % Number of connectives : 70 ( 0 ~; 0 |; 5 &; 52 @)
% 0.30/0.48 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.30/0.48 % Maximal formula depth : 17 ( 17 avg)
% 0.30/0.48 % Number of types : 3 ( 2 usr)
% 0.30/0.48 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.30/0.48 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.30/0.48 % Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 0.30/0.48 % SPC : TH0_THM_EQU_NAR
% 0.30/0.48
% 0.30/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 thf(a_type,type,
% 0.30/0.48 a: $tType ).
% 0.30/0.48
% 0.30/0.48 thf(b_type,type,
% 0.30/0.48 b: $tType ).
% 0.30/0.48
% 0.30/0.48 thf(g,type,
% 0.30/0.48 g: a > b ).
% 0.30/0.48
% 0.30/0.48 thf(f,type,
% 0.30/0.48 f: a > b ).
% 0.30/0.48
% 0.30/0.48 thf(cQ,type,
% 0.30/0.48 cQ: a > b > b > $o ).
% 0.30/0.48
% 0.30/0.48 thf(cP,type,
% 0.30/0.48 cP: a > a > $o ).
% 0.30/0.48
% 0.30/0.48 thf(cTHM509_pme,conjecture,
% 0.30/0.48 ( ! [Xx: a] :
% 0.30/0.48 ( ( cP @ Xx @ Xx )
% 0.30/0.48 => ( cQ @ Xx @ ( f @ Xx ) @ ( g @ Xx ) ) )
% 0.30/0.48 => ( ! [Xx: a,Xy: a] :
% 0.30/0.48 ( ( cP @ Xx @ Xy )
% 0.30/0.48 => ( cQ @ Xx @ ( f @ Xx ) @ ( f @ Xy ) ) )
% 0.30/0.48 => ( ( ! [Xx: a,Xy: a] :
% 0.30/0.48 ( ( cP @ Xx @ Xy )
% 0.30/0.48 => ( cP @ Xy @ Xx ) )
% 0.30/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.30/0.48 ( ( ( cP @ Xx @ Xy )
% 0.30/0.48 & ( cP @ Xy @ Xz ) )
% 0.30/0.48 => ( cP @ Xx @ Xz ) ) )
% 0.30/0.48 => ( ( ! [Xx: a] :
% 0.30/0.48 ( ( cP @ Xx @ Xx )
% 0.30/0.48 => ( ! [Xx0: b,Xy: b] :
% 0.30/0.48 ( ( cQ @ Xx @ Xx0 @ Xy )
% 0.30/0.48 => ( cQ @ Xx @ Xy @ Xx0 ) )
% 0.30/0.48 & ! [Xx0: b,Xy: b,Xz: b] :
% 0.30/0.48 ( ( ( cQ @ Xx @ Xx0 @ Xy )
% 0.30/0.48 & ( cQ @ Xx @ Xy @ Xz ) )
% 0.30/0.48 => ( cQ @ Xx @ Xx0 @ Xz ) ) ) )
% 0.30/0.48 & ! [Xx: a,Xy: a] :
% 0.30/0.48 ( ( cP @ Xx @ Xy )
% 0.30/0.48 => ( ( cQ @ Xx )
% 0.30/0.48 = ( cQ @ Xy ) ) ) )
% 0.30/0.48 => ! [Xx: a,Xy: a] :
% 0.30/0.48 ( ( cP @ Xx @ Xy )
% 0.30/0.48 => ( cQ @ Xx @ ( f @ Xx ) @ ( g @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 1.83/1.53 ---- Embedded in THF ---
% 1.83/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.83/1.53 %%% Generated on Tue Feb 24 12:39:16 EST 2026
% 1.83/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 1.83/1.53 %%% Logic specification used:
% 1.83/1.53 %%% thf(spec, logic, $$dhol).
% 1.83/1.53
% 1.83/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lrD0QKFhck/DTF2DTF6307.p
% See solution above
% 1.83/1.53 ------------------------
% 1.83/1.54 ---- Cleaned THF ---
% 1.83/1.54 thf(a_type,type,
% 1.83/1.54 a: $tType ).
% 1.83/1.54
% 1.83/1.54 thf(b_type,type,
% 1.83/1.54 b: $tType ).
% 1.83/1.54
% 1.83/1.54 thf(g,type,
% 1.83/1.54 g: a > b ).
% 1.83/1.54
% 1.83/1.54 thf(f,type,
% 1.83/1.54 f: a > b ).
% 1.83/1.54
% 1.83/1.54 thf(cQ,type,
% 1.83/1.54 cQ: a > b > b > $o ).
% 1.83/1.54
% 1.83/1.54 thf(cP,type,
% 1.83/1.54 cP: a > a > $o ).
% 1.83/1.54
% 1.83/1.54 thf(cTHM509_pme,conjecture,
% 1.83/1.54 ( ! [Xx: a] :
% 1.83/1.54 ( ( cP @ Xx @ Xx )
% 1.83/1.54 => ( cQ @ Xx @ ( f @ Xx ) @ ( g @ Xx ) ) )
% 1.83/1.54 => ( ! [Xx: a,Xy: a] :
% 1.83/1.54 ( ( cP @ Xx @ Xy )
% 1.83/1.54 => ( cQ @ Xx @ ( f @ Xx ) @ ( f @ Xy ) ) )
% 1.83/1.54 => ( ( ! [Xx: a,Xy: a] :
% 1.83/1.54 ( ( cP @ Xx @ Xy )
% 1.83/1.54 => ( cP @ Xy @ Xx ) )
% 1.83/1.54 & ! [Xx: a,Xy: a,Xz: a] :
% 1.83/1.54 ( ( ( cP @ Xx @ Xy )
% 1.83/1.54 & ( cP @ Xy @ Xz ) )
% 1.83/1.54 => ( cP @ Xx @ Xz ) ) )
% 1.83/1.54 => ( ( ! [Xx: a] :
% 1.83/1.54 ( ( cP @ Xx @ Xx )
% 1.83/1.54 => ( ! [Xx0: b,Xy: b] :
% 1.83/1.54 ( ( cQ @ Xx @ Xx0 @ Xy )
% 1.83/1.54 => ( cQ @ Xx @ Xy @ Xx0 ) )
% 1.83/1.54 & ! [Xx0: b,Xy: b,Xz: b] :
% 1.83/1.54 ( ( ( cQ @ Xx @ Xx0 @ Xy )
% 1.83/1.54 & ( cQ @ Xx @ Xy @ Xz ) )
% 1.83/1.54 => ( cQ @ Xx @ Xx0 @ Xz ) ) ) )
% 1.83/1.54 & ! [Xx: a,Xy: a] :
% 1.83/1.54 ( ( cP @ Xx @ Xy )
% 1.83/1.54 => ( ( cQ @ Xx )
% 1.83/1.54 = ( cQ @ Xy ) ) ) )
% 1.83/1.54 => ! [Xx: a,Xy: a] :
% 1.83/1.54 ( ( cP @ Xx @ Xy )
% 1.83/1.54 => ( cQ @ Xx @ ( f @ Xx ) @ ( g @ Xy ) ) ) ) ) ) ) ).
% 1.83/1.54 ------------------------
% 1.83/1.56 % (6433)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_6307 for (2999ds/2Mi)
% 1.83/1.56 % (6434)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_6307 for (2999ds/275Mi)
% 1.83/1.56 % (6435)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/18Mi)
% 1.83/1.56 % (6430)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_6307 for (2999ds/4Mi)
% 1.83/1.56 % (6431)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_6307 for (2999ds/27Mi)
% 1.83/1.56 % (6432)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/2Mi)
% 1.83/1.56 % (6429)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/183Mi)
% 1.83/1.56 % (6432)Instruction limit reached!
% 1.83/1.56 % (6432)------------------------------
% 1.83/1.56 % (6432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.56 % (6432)Termination reason: Unknown
% 1.83/1.56 % (6433)Instruction limit reached!
% 1.83/1.56 % (6433)------------------------------
% 1.83/1.56 % (6433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.56 % (6432)Termination phase: Saturation
% 1.83/1.56
% 1.83/1.56 % (6432)Memory used [KB]: 1023
% 1.83/1.56 % (6432)Time elapsed: 0.003 s
% 1.83/1.56 % (6432)Instructions burned: 3 (million)
% 1.83/1.56 % (6432)------------------------------
% 1.83/1.56 % (6432)------------------------------
% 1.83/1.56 % (6433)Termination reason: Unknown
% 1.83/1.56 % (6433)Termination phase: Property scanning
% 1.83/1.57
% 1.83/1.57 % (6433)Memory used [KB]: 1023
% 1.83/1.57 % (6433)Time elapsed: 0.003 s
% 1.83/1.57 % (6433)Instructions burned: 3 (million)
% 1.83/1.57 % (6433)------------------------------
% 1.83/1.57 % (6433)------------------------------
% 1.83/1.57 % (6430)Instruction limit reached!
% 1.83/1.57 % (6430)------------------------------
% 1.83/1.57 % (6430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.57 % (6430)Termination reason: Unknown
% 1.83/1.57 % (6430)Termination phase: Saturation
% 1.83/1.57
% 1.83/1.57 % (6430)Memory used [KB]: 5500
% 1.83/1.57 % (6430)Time elapsed: 0.004 s
% 1.83/1.57 % (6430)Instructions burned: 4 (million)
% 1.83/1.57 % (6430)------------------------------
% 1.83/1.57 % (6430)------------------------------
% 1.83/1.57 % (6435)Instruction limit reached!
% 1.83/1.57 % (6435)------------------------------
% 1.83/1.57 % (6435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.57 % (6435)Termination reason: Unknown
% 1.83/1.57 % (6435)Termination phase: Saturation
% 1.83/1.57
% 1.83/1.57 % (6435)Memory used [KB]: 5628
% 1.83/1.57 % (6435)Time elapsed: 0.013 s
% 1.83/1.57 % (6435)Instructions burned: 19 (million)
% 1.83/1.57 % (6435)------------------------------
% 1.83/1.57 % (6435)------------------------------
% 1.83/1.58 % (6431)Instruction limit reached!
% 1.83/1.58 % (6431)------------------------------
% 1.83/1.58 % (6431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.58 % (6431)Termination reason: Unknown
% 1.83/1.58 % (6431)Termination phase: Saturation
% 1.83/1.58
% 1.83/1.58 % (6431)Memory used [KB]: 5628
% 1.83/1.58 % (6431)Time elapsed: 0.017 s
% 1.83/1.58 % (6431)Instructions burned: 27 (million)
% 1.83/1.58 % (6431)------------------------------
% 1.83/1.58 % (6431)------------------------------
% 1.83/1.58 % (6438)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/15Mi)
% 1.83/1.58 % (6436)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/3Mi)
% 1.83/1.58 % (6437)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/37Mi)
% 1.83/1.58 % (6436)Instruction limit reached!
% 1.83/1.58 % (6436)------------------------------
% 1.83/1.58 % (6436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.58 % (6436)Termination reason: Unknown
% 1.83/1.58 % (6436)Termination phase: Saturation
% 1.83/1.58
% 1.83/1.58 % (6436)Memory used [KB]: 5500
% 1.83/1.58 % (6436)Time elapsed: 0.003 s
% 1.83/1.58 % (6436)Instructions burned: 3 (million)
% 1.83/1.58 % (6436)------------------------------
% 1.83/1.58 % (6436)------------------------------
% 1.83/1.59 % (6438)Instruction limit reached!
% 1.83/1.59 % (6438)------------------------------
% 1.83/1.59 % (6438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.59 % (6438)Termination reason: Unknown
% 1.83/1.59 % (6438)Termination phase: Saturation
% 1.83/1.59
% 1.83/1.59 % (6438)Memory used [KB]: 5628
% 1.83/1.59 % (6438)Time elapsed: 0.010 s
% 1.83/1.59 % (6438)Instructions burned: 15 (million)
% 1.83/1.59 % (6438)------------------------------
% 1.83/1.59 % (6438)------------------------------
% 1.83/1.59 % (6439)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/3Mi)
% 1.83/1.59 % (6439)Instruction limit reached!
% 1.83/1.59 % (6439)------------------------------
% 1.83/1.59 % (6439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.59 % (6439)Termination reason: Unknown
% 1.83/1.59 % (6439)Termination phase: shuffling
% 1.83/1.59
% 1.83/1.59 % (6439)Memory used [KB]: 1023
% 1.83/1.59 % (6439)Time elapsed: 0.003 s
% 1.83/1.59 % (6439)Instructions burned: 3 (million)
% 1.83/1.59 % (6439)------------------------------
% 1.83/1.59 % (6439)------------------------------
% 1.92/1.60 % (6440)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/1041Mi)
% 1.92/1.60 % (6441)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/7Mi)
% 1.92/1.60 % (6437)Instruction limit reached!
% 1.92/1.60 % (6437)------------------------------
% 1.92/1.60 % (6437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.60 % (6437)Termination reason: Unknown
% 1.92/1.60 % (6437)Termination phase: Saturation
% 1.92/1.60
% 1.92/1.60 % (6437)Memory used [KB]: 5628
% 1.92/1.60 % (6437)Time elapsed: 0.021 s
% 1.92/1.60 % (6437)Instructions burned: 37 (million)
% 1.92/1.60 % (6437)------------------------------
% 1.92/1.60 % (6437)------------------------------
% 1.92/1.61 % (6441)Instruction limit reached!
% 1.92/1.61 % (6441)------------------------------
% 1.92/1.61 % (6441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.61 % (6441)Termination reason: Unknown
% 1.92/1.61 % (6441)Termination phase: Saturation
% 1.92/1.61
% 1.92/1.61 % (6441)Memory used [KB]: 1023
% 1.92/1.61 % (6441)Time elapsed: 0.007 s
% 1.92/1.61 % (6441)Instructions burned: 8 (million)
% 1.92/1.61 % (6441)------------------------------
% 1.92/1.61 % (6441)------------------------------
% 1.92/1.61 % (6442)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/16Mi)
% 1.92/1.61 % (6443)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/3Mi)
% 1.92/1.61 % (6443)Instruction limit reached!
% 1.92/1.61 % (6443)------------------------------
% 1.92/1.61 % (6443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.61 % (6443)Termination reason: Unknown
% 1.92/1.61 % (6443)Termination phase: Property scanning
% 1.92/1.61
% 1.92/1.61 % (6443)Memory used [KB]: 1023
% 1.92/1.61 % (6443)Time elapsed: 0.004 s
% 1.92/1.61 % (6443)Instructions burned: 4 (million)
% 1.92/1.61 % (6443)------------------------------
% 1.92/1.61 % (6443)------------------------------
% 1.92/1.62 % (6442)Instruction limit reached!
% 1.92/1.62 % (6442)------------------------------
% 1.92/1.62 % (6442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (6442)Termination reason: Unknown
% 1.92/1.62 % (6442)Termination phase: Saturation
% 1.92/1.62
% 1.92/1.62 % (6442)Memory used [KB]: 5628
% 1.92/1.62 % (6442)Time elapsed: 0.011 s
% 1.92/1.62 % (6442)Instructions burned: 16 (million)
% 1.92/1.62 % (6442)------------------------------
% 1.92/1.62 % (6442)------------------------------
% 1.92/1.62 % (6444)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/3Mi)
% 1.92/1.62 % (6444)Instruction limit reached!
% 1.92/1.62 % (6444)------------------------------
% 1.92/1.62 % (6444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (6444)Termination reason: Unknown
% 1.92/1.62 % (6444)Termination phase: Property scanning
% 1.92/1.62
% 1.92/1.62 % (6444)Memory used [KB]: 1023
% 1.92/1.62 % (6444)Time elapsed: 0.004 s
% 1.92/1.62 % (6444)Instructions burned: 4 (million)
% 1.92/1.62 % (6444)------------------------------
% 1.92/1.62 % (6444)------------------------------
% 1.92/1.62 % (6445)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/7Mi)
% 1.92/1.62 % (6445)Refutation not found, incomplete strategy
% 1.92/1.62 % (6445)------------------------------
% 1.92/1.62 % (6445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (6445)Termination reason: Refutation not found, incomplete strategy
% 1.92/1.62
% 1.92/1.62
% 1.92/1.63 % (6445)Memory used [KB]: 5500
% 1.92/1.63 % (6445)Time elapsed: 0.004 s
% 1.92/1.63 % (6445)Instructions burned: 4 (million)
% 1.92/1.63 % (6445)------------------------------
% 1.92/1.63 % (6445)------------------------------
% 1.92/1.63 % (6446)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/3Mi)
% 1.92/1.63 % (6446)Instruction limit reached!
% 1.92/1.63 % (6446)------------------------------
% 1.92/1.63 % (6446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.63 % (6446)Termination reason: Unknown
% 1.92/1.63 % (6446)Termination phase: Property scanning
% 1.92/1.63
% 1.92/1.63 % (6446)Memory used [KB]: 1023
% 1.92/1.63 % (6446)Time elapsed: 0.003 s
% 1.92/1.63 % (6446)Instructions burned: 3 (million)
% 1.92/1.63 % (6446)------------------------------
% 1.92/1.63 % (6446)------------------------------
% 1.92/1.63 % (6447)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/4Mi)
% 1.92/1.64 % (6447)Instruction limit reached!
% 1.92/1.64 % (6447)------------------------------
% 1.92/1.64 % (6447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.64 % (6447)Termination reason: Unknown
% 1.92/1.64 % (6448)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/18Mi)
% 1.92/1.64 % (6447)Termination phase: Saturation
% 1.92/1.64
% 1.92/1.64 % (6447)Memory used [KB]: 5500
% 1.92/1.64 % (6447)Time elapsed: 0.005 s
% 1.92/1.64 % (6447)Instructions burned: 5 (million)
% 1.92/1.64 % (6447)------------------------------
% 1.92/1.64 % (6447)------------------------------
% 1.92/1.64 % (6449)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6307 for (2999ds/710Mi)
% 1.92/1.64 % (6429)First to succeed.
% 1.92/1.65 % (6448)Instruction limit reached!
% 1.92/1.65 % (6448)------------------------------
% 1.92/1.65 % (6448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.65 % (6448)Termination reason: Unknown
% 1.92/1.65 % (6448)Termination phase: Saturation
% 1.92/1.65
% 1.92/1.65 % (6448)Memory used [KB]: 5628
% 1.92/1.65 % (6448)Time elapsed: 0.012 s
% 1.92/1.65 % (6448)Instructions burned: 19 (million)
% 1.92/1.65 % (6448)------------------------------
% 1.92/1.65 % (6448)------------------------------
% 1.92/1.65 % (6429)Refutation found. Thanks to Tanya!
% 1.92/1.65 % SZS status Theorem for DTF2THF_6307
% 1.92/1.65 % SZS output start Proof for DTF2THF_6307
% 1.92/1.65 thf(type_def_5, type, a: $tType).
% 1.92/1.65 thf(type_def_6, type, b: $tType).
% 1.92/1.65 thf(func_def_0, type, a: $tType).
% 1.92/1.65 thf(func_def_1, type, b: $tType).
% 1.92/1.65 thf(func_def_2, type, g: a > b).
% 1.92/1.65 thf(func_def_3, type, f: a > b).
% 1.92/1.65 thf(func_def_4, type, cQ: a > b > b > $o).
% 1.92/1.65 thf(func_def_5, type, cP: a > a > $o).
% 1.92/1.65 thf(func_def_9, type, sK0: a).
% 1.92/1.65 thf(func_def_10, type, sK1: a).
% 1.92/1.65 thf(func_def_12, type, ph3: !>[X0: $tType]:(X0)).
% 1.92/1.65 thf(f413,plain,(
% 1.92/1.65 $false),
% 1.92/1.65 inference(avatar_sat_refutation,[status(thm)],[f48,f58,f388,f400,f410])).
% 1.92/1.65 thf(f410,plain,(
% 1.92/1.65 spl2_5),
% 1.92/1.65 inference(avatar_contradiction_clause,[status(thm)],[f409])).
% 1.92/1.65 thf(f409,plain,(
% 1.92/1.65 $false | spl2_5),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f406])).
% 1.92/1.65 thf(f406,plain,(
% 1.92/1.65 ($true != $true) | spl2_5),
% 1.92/1.65 inference(superposition,[status(thm)],[f405,f17])).
% 1.92/1.65 thf(f17,plain,(
% 1.92/1.65 ((cP @ sK0 @ sK1) = $true)),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f10,plain,(
% 1.92/1.65 ! [X0 : a,X1 : a] : (((cP @ X0 @ X1) != $true) | ((cQ @ X0 @ (f @ X0) @ (f @ X1)) = $true)) & (($true != (cQ @ sK0 @ (f @ sK0) @ (g @ sK1))) & ((cP @ sK0 @ sK1) = $true)) & ! [X4 : a,X5 : a] : (((cQ @ X5) = (cQ @ X4)) | ($true != (cP @ X5 @ X4))) & ! [X6 : a,X7 : a,X8 : a] : (($true != (cP @ X8 @ X7)) | ($true != (cP @ X7 @ X6)) | ((cP @ X8 @ X6) = $true)) & ! [X9 : a] : ((! [X10 : b,X11 : b] : (((cQ @ X9 @ X10 @ X11) != $true) | ((cQ @ X9 @ X11 @ X10) = $true)) & ! [X12 : b,X13 : b,X14 : b] : (($true != (cQ @ X9 @ X13 @ X12)) | ($true = (cQ @ X9 @ X13 @ X14)) | ($true != (cQ @ X9 @ X12 @ X14)))) | ($true != (cP @ X9 @ X9))) & ! [X15 : a,X16 : a] : (((cP @ X16 @ X15) = $true) | ((cP @ X15 @ X16) != $true)) & ! [X17 : a] : (((cP @ X17 @ X17) != $true) | ((cQ @ X17 @ (f @ X17) @ (g @ X17)) = $true))),
% 1.92/1.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9])).
% 1.92/1.65 thf(f9,plain,(
% 1.92/1.65 ? [X2 : a,X3 : a] : (((cQ @ X2 @ (f @ X2) @ (g @ X3)) != $true) & ((cP @ X2 @ X3) = $true)) => (($true != (cQ @ sK0 @ (f @ sK0) @ (g @ sK1))) & ((cP @ sK0 @ sK1) = $true))),
% 1.92/1.65 introduced(definition,[],[choice_axiom])).
% 1.92/1.65 thf(f8,plain,(
% 1.92/1.65 ! [X0 : a,X1 : a] : (((cP @ X0 @ X1) != $true) | ((cQ @ X0 @ (f @ X0) @ (f @ X1)) = $true)) & ? [X2 : a,X3 : a] : (((cQ @ X2 @ (f @ X2) @ (g @ X3)) != $true) & ((cP @ X2 @ X3) = $true)) & ! [X4 : a,X5 : a] : (((cQ @ X5) = (cQ @ X4)) | ($true != (cP @ X5 @ X4))) & ! [X6 : a,X7 : a,X8 : a] : (($true != (cP @ X8 @ X7)) | ($true != (cP @ X7 @ X6)) | ((cP @ X8 @ X6) = $true)) & ! [X9 : a] : ((! [X10 : b,X11 : b] : (((cQ @ X9 @ X10 @ X11) != $true) | ((cQ @ X9 @ X11 @ X10) = $true)) & ! [X12 : b,X13 : b,X14 : b] : (($true != (cQ @ X9 @ X13 @ X12)) | ($true = (cQ @ X9 @ X13 @ X14)) | ($true != (cQ @ X9 @ X12 @ X14)))) | ($true != (cP @ X9 @ X9))) & ! [X15 : a,X16 : a] : (((cP @ X16 @ X15) = $true) | ((cP @ X15 @ X16) != $true)) & ! [X17 : a] : (((cP @ X17 @ X17) != $true) | ((cQ @ X17 @ (f @ X17) @ (g @ X17)) = $true))),
% 1.92/1.65 inference(rectify,[status(thm)],[f7])).
% 1.92/1.65 thf(f7,plain,(
% 1.92/1.65 ! [X1 : a,X2 : a] : (((cP @ X1 @ X2) != $true) | ($true = (cQ @ X1 @ (f @ X1) @ (f @ X2)))) & ? [X16 : a,X17 : a] : (((cQ @ X16 @ (f @ X16) @ (g @ X17)) != $true) & ((cP @ X16 @ X17) = $true)) & ! [X9 : a,X8 : a] : (((cQ @ X8) = (cQ @ X9)) | ($true != (cP @ X8 @ X9))) & ! [X7 : a,X5 : a,X6 : a] : (($true != (cP @ X6 @ X5)) | ($true != (cP @ X5 @ X7)) | ((cP @ X6 @ X7) = $true)) & ! [X10 : a] : ((! [X11 : b,X12 : b] : (($true != (cQ @ X10 @ X11 @ X12)) | ($true = (cQ @ X10 @ X12 @ X11))) & ! [X14 : b,X15 : b,X13 : b] : (($true != (cQ @ X10 @ X15 @ X14)) | ($true = (cQ @ X10 @ X15 @ X13)) | ($true != (cQ @ X10 @ X14 @ X13)))) | ($true != (cP @ X10 @ X10))) & ! [X3 : a,X4 : a] : (((cP @ X4 @ X3) = $true) | ($true != (cP @ X3 @ X4))) & ! [X0 : a] : (((cP @ X0 @ X0) != $true) | ((cQ @ X0 @ (f @ X0) @ (g @ X0)) = $true))),
% 1.92/1.65 inference(flattening,[status(thm)],[f6])).
% 1.92/1.65 thf(f6,plain,(
% 1.92/1.65 (((? [X16 : a,X17 : a] : (((cQ @ X16 @ (f @ X16) @ (g @ X17)) != $true) & ((cP @ X16 @ X17) = $true)) & (! [X9 : a,X8 : a] : (((cQ @ X8) = (cQ @ X9)) | ($true != (cP @ X8 @ X9))) & ! [X10 : a] : ((! [X13 : b,X15 : b,X14 : b] : (($true = (cQ @ X10 @ X15 @ X13)) | (($true != (cQ @ X10 @ X15 @ X14)) | ($true != (cQ @ X10 @ X14 @ X13)))) & ! [X11 : b,X12 : b] : (($true != (cQ @ X10 @ X11 @ X12)) | ($true = (cQ @ X10 @ X12 @ X11)))) | ($true != (cP @ X10 @ X10))))) & (! [X5 : a,X7 : a,X6 : a] : (((cP @ X6 @ X7) = $true) | (($true != (cP @ X6 @ X5)) | ($true != (cP @ X5 @ X7)))) & ! [X3 : a,X4 : a] : (((cP @ X4 @ X3) = $true) | ($true != (cP @ X3 @ X4))))) & ! [X1 : a,X2 : a] : (((cP @ X1 @ X2) != $true) | ($true = (cQ @ X1 @ (f @ X1) @ (f @ X2))))) & ! [X0 : a] : (((cP @ X0 @ X0) != $true) | ((cQ @ X0 @ (f @ X0) @ (g @ X0)) = $true))),
% 1.92/1.65 inference(ennf_transformation,[status(thm)],[f5])).
% 1.92/1.65 thf(f5,plain,(
% 1.92/1.65 ~(! [X0 : a] : (((cP @ X0 @ X0) = $true) => ((cQ @ X0 @ (f @ X0) @ (g @ X0)) = $true)) => (! [X2 : a,X1 : a] : (((cP @ X1 @ X2) = $true) => ($true = (cQ @ X1 @ (f @ X1) @ (f @ X2)))) => ((! [X5 : a,X7 : a,X6 : a] : ((($true = (cP @ X6 @ X5)) & ($true = (cP @ X5 @ X7))) => ((cP @ X6 @ X7) = $true)) & ! [X3 : a,X4 : a] : (($true = (cP @ X3 @ X4)) => ((cP @ X4 @ X3) = $true))) => ((! [X9 : a,X8 : a] : (($true = (cP @ X8 @ X9)) => ((cQ @ X8) = (cQ @ X9))) & ! [X10 : a] : (($true = (cP @ X10 @ X10)) => (! [X13 : b,X15 : b,X14 : b] : ((($true = (cQ @ X10 @ X15 @ X14)) & ($true = (cQ @ X10 @ X14 @ X13))) => ($true = (cQ @ X10 @ X15 @ X13))) & ! [X11 : b,X12 : b] : (($true = (cQ @ X10 @ X11 @ X12)) => ($true = (cQ @ X10 @ X12 @ X11)))))) => ! [X16 : a,X17 : a] : (((cP @ X16 @ X17) = $true) => ((cQ @ X16 @ (f @ X16) @ (g @ X17)) = $true))))))),
% 1.92/1.65 inference(fool_elimination,[status(thm)],[f4])).
% 1.92/1.65 thf(f4,plain,(
% 1.92/1.65 ~(! [X0 : a] : ((cP @ X0 @ X0) => (cQ @ X0 @ (f @ X0) @ (g @ X0))) => (! [X1 : a,X2 : a] : ((cP @ X1 @ X2) => (cQ @ X1 @ (f @ X1) @ (f @ X2))) => ((! [X3 : a,X4 : a] : ((cP @ X3 @ X4) => (cP @ X4 @ X3)) & ! [X5 : a,X6 : a,X7 : a] : (((cP @ X5 @ X7) & (cP @ X6 @ X5)) => (cP @ X6 @ X7))) => ((! [X8 : a,X9 : a] : ((cP @ X8 @ X9) => ((cQ @ X8) = (cQ @ X9))) & ! [X10 : a] : ((cP @ X10 @ X10) => (! [X11 : b,X12 : b] : ((cQ @ X10 @ X11 @ X12) => (cQ @ X10 @ X12 @ X11)) & ! [X13 : b,X14 : b,X15 : b] : (((cQ @ X10 @ X15 @ X14) & (cQ @ X10 @ X14 @ X13)) => (cQ @ X10 @ X15 @ X13))))) => ! [X16 : a,X17 : a] : ((cP @ X16 @ X17) => (cQ @ X16 @ (f @ X16) @ (g @ X17)))))))),
% 1.92/1.65 inference(rectify,[status(thm)],[f2])).
% 1.92/1.65 thf(f2,negated_conjecture,(
% 1.92/1.65 ~(! [X0 : a] : ((cP @ X0 @ X0) => (cQ @ X0 @ (f @ X0) @ (g @ X0))) => (! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => (cQ @ X0 @ (f @ X0) @ (f @ X1))) => ((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => (cP @ X1 @ X0)) & ! [X1 : a,X0 : a,X2 : a] : (((cP @ X1 @ X2) & (cP @ X0 @ X1)) => (cP @ X0 @ X2))) => ((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => ((cQ @ X0) = (cQ @ X1))) & ! [X0 : a] : ((cP @ X0 @ X0) => (! [X3 : b,X1 : b] : ((cQ @ X0 @ X3 @ X1) => (cQ @ X0 @ X1 @ X3)) & ! [X2 : b,X1 : b,X3 : b] : (((cQ @ X0 @ X3 @ X1) & (cQ @ X0 @ X1 @ X2)) => (cQ @ X0 @ X3 @ X2))))) => ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => (cQ @ X0 @ (f @ X0) @ (g @ X1)))))))),
% 1.92/1.65 inference(negated_conjecture,[status(cth)],[f1])).
% 1.92/1.65 thf(f1,conjecture,(
% 1.92/1.65 ! [X0 : a] : ((cP @ X0 @ X0) => (cQ @ X0 @ (f @ X0) @ (g @ X0))) => (! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => (cQ @ X0 @ (f @ X0) @ (f @ X1))) => ((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => (cP @ X1 @ X0)) & ! [X1 : a,X0 : a,X2 : a] : (((cP @ X1 @ X2) & (cP @ X0 @ X1)) => (cP @ X0 @ X2))) => ((! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => ((cQ @ X0) = (cQ @ X1))) & ! [X0 : a] : ((cP @ X0 @ X0) => (! [X3 : b,X1 : b] : ((cQ @ X0 @ X3 @ X1) => (cQ @ X0 @ X1 @ X3)) & ! [X2 : b,X1 : b,X3 : b] : (((cQ @ X0 @ X3 @ X1) & (cQ @ X0 @ X1 @ X2)) => (cQ @ X0 @ X3 @ X2))))) => ! [X0 : a,X1 : a] : ((cP @ X0 @ X1) => (cQ @ X0 @ (f @ X0) @ (g @ X1))))))),
% 1.92/1.65 file('/export/starexec/sandbox/tmp/tmp.lrD0QKFhck/DTF2THF_6307.p',cTHM509_pme)).
% 1.92/1.65 thf(f405,plain,(
% 1.92/1.65 ( ! [X0 : a] : (($true != (cP @ X0 @ sK1))) ) | spl2_5),
% 1.92/1.65 inference(subsumption_resolution,[status(thm)],[f403,f12])).
% 1.92/1.65 thf(f12,plain,(
% 1.92/1.65 ( ! [X16 : a,X15 : a] : (((cP @ X16 @ X15) = $true) | ((cP @ X15 @ X16) != $true)) )),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f403,plain,(
% 1.92/1.65 ( ! [X0 : a] : (((cP @ sK1 @ X0) != $true) | ($true != (cP @ X0 @ sK1))) ) | spl2_5),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f401])).
% 1.92/1.65 thf(f401,plain,(
% 1.92/1.65 ( ! [X0 : a] : (((cP @ sK1 @ X0) != $true) | ($true != (cP @ X0 @ sK1)) | ($true != $true)) ) | spl2_5),
% 1.92/1.65 inference(superposition,[status(thm)],[f387,f15])).
% 1.92/1.65 thf(f15,plain,(
% 1.92/1.65 ( ! [X8 : a,X6 : a,X7 : a] : (((cP @ X8 @ X6) = $true) | ($true != (cP @ X7 @ X6)) | ($true != (cP @ X8 @ X7))) )),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f387,plain,(
% 1.92/1.65 ($true != (cP @ sK1 @ sK1)) | spl2_5),
% 1.92/1.65 inference(avatar_component_clause,[status(thm)],[f385])).
% 1.92/1.65 thf(f385,definition,(
% 1.92/1.65 spl2_5 <=> ($true = (cP @ sK1 @ sK1))),
% 1.92/1.65 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.92/1.65 thf(f400,plain,(
% 1.92/1.65 spl2_4),
% 1.92/1.65 inference(avatar_contradiction_clause,[status(thm)],[f399])).
% 1.92/1.65 thf(f399,plain,(
% 1.92/1.65 $false | spl2_4),
% 1.92/1.65 inference(subsumption_resolution,[status(thm)],[f398,f17])).
% 1.92/1.65 thf(f398,plain,(
% 1.92/1.65 ((cP @ sK0 @ sK1) != $true) | spl2_4),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f396])).
% 1.92/1.65 thf(f396,plain,(
% 1.92/1.65 ($true != $true) | ((cP @ sK0 @ sK1) != $true) | spl2_4),
% 1.92/1.65 inference(superposition,[status(thm)],[f383,f12])).
% 1.92/1.65 thf(f383,plain,(
% 1.92/1.65 ($true != (cP @ sK1 @ sK0)) | spl2_4),
% 1.92/1.65 inference(avatar_component_clause,[status(thm)],[f381])).
% 1.92/1.65 thf(f381,definition,(
% 1.92/1.65 spl2_4 <=> ($true = (cP @ sK1 @ sK0))),
% 1.92/1.65 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.92/1.65 thf(f388,plain,(
% 1.92/1.65 ~spl2_4 | ~spl2_5 | ~spl2_3),
% 1.92/1.65 inference(avatar_split_clause,[status(thm)],[f379,f46,f385,f381])).
% 1.92/1.65 thf(f46,definition,(
% 1.92/1.65 spl2_3 <=> ! [X0 : b] : (($true != (cQ @ sK0 @ (f @ sK0) @ X0)) | ($true != (cQ @ sK0 @ X0 @ (g @ sK1))))),
% 1.92/1.65 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.92/1.65 thf(f379,plain,(
% 1.92/1.65 ($true != (cP @ sK1 @ sK0)) | ($true != (cP @ sK1 @ sK1)) | ~spl2_3),
% 1.92/1.65 inference(subsumption_resolution,[status(thm)],[f374,f17])).
% 1.92/1.65 thf(f374,plain,(
% 1.92/1.65 ($true != (cP @ sK1 @ sK1)) | ($true != (cP @ sK1 @ sK0)) | ((cP @ sK0 @ sK1) != $true) | ~spl2_3),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f364])).
% 1.92/1.65 thf(f364,plain,(
% 1.92/1.65 ($true != $true) | ($true != (cP @ sK1 @ sK1)) | ((cP @ sK0 @ sK1) != $true) | ($true != (cP @ sK1 @ sK0)) | ~spl2_3),
% 1.92/1.65 inference(superposition,[status(thm)],[f72,f181])).
% 1.92/1.65 thf(f181,plain,(
% 1.92/1.65 ( ! [X0 : a,X1 : a] : (($true = (cQ @ X1 @ (f @ X0) @ (g @ X0))) | ((cP @ X0 @ X0) != $true) | ((cP @ X0 @ X1) != $true)) )),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.92/1.65 thf(f152,plain,(
% 1.92/1.65 ( ! [X0 : a,X1 : a] : (((cP @ X0 @ X0) != $true) | ((cP @ X0 @ X1) != $true) | ($false = $true) | ($true = (cQ @ X1 @ (f @ X0) @ (g @ X0)))) )),
% 1.92/1.65 inference(superposition,[status(thm)],[f30,f11])).
% 1.92/1.65 thf(f11,plain,(
% 1.92/1.65 ( ! [X17 : a] : (((cQ @ X17 @ (f @ X17) @ (g @ X17)) = $true) | ((cP @ X17 @ X17) != $true)) )),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f30,plain,(
% 1.92/1.65 ( ! [X6 : b,X7 : b,X4 : a,X5 : a] : (((cQ @ X5 @ X6 @ X7) = $false) | ((cQ @ X4 @ X6 @ X7) = $true) | ($true != (cP @ X5 @ X4))) )),
% 1.92/1.65 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.92/1.65 thf(f25,plain,(
% 1.92/1.65 ( ! [X6 : b,X7 : b,X4 : a,X5 : a] : (($true != (cP @ X5 @ X4)) | ((cQ @ X4 @ X6 @ X7) = (cQ @ X5 @ X6 @ X7))) )),
% 1.92/1.65 inference(argument_congruence,[status(thm)],[f20])).
% 1.92/1.65 thf(f20,plain,(
% 1.92/1.65 ( ! [X6 : b,X4 : a,X5 : a] : (((cQ @ X5 @ X6) = (cQ @ X4 @ X6)) | ($true != (cP @ X5 @ X4))) )),
% 1.92/1.65 inference(argument_congruence,[status(thm)],[f16])).
% 1.92/1.65 thf(f16,plain,(
% 1.92/1.65 ( ! [X4 : a,X5 : a] : (((cQ @ X5) = (cQ @ X4)) | ($true != (cP @ X5 @ X4))) )),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f72,plain,(
% 1.92/1.65 ( ! [X0 : a] : (($true != (cQ @ sK0 @ (f @ X0) @ (g @ sK1))) | ((cP @ sK0 @ X0) != $true)) ) | ~spl2_3),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.92/1.65 thf(f67,plain,(
% 1.92/1.65 ( ! [X0 : a] : (($true != $true) | ((cP @ sK0 @ X0) != $true) | ($true != (cQ @ sK0 @ (f @ X0) @ (g @ sK1)))) ) | ~spl2_3),
% 1.92/1.65 inference(superposition,[status(thm)],[f47,f19])).
% 1.92/1.65 thf(f19,plain,(
% 1.92/1.65 ( ! [X0 : a,X1 : a] : (((cQ @ X0 @ (f @ X0) @ (f @ X1)) = $true) | ((cP @ X0 @ X1) != $true)) )),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f47,plain,(
% 1.92/1.65 ( ! [X0 : b] : (($true != (cQ @ sK0 @ (f @ sK0) @ X0)) | ($true != (cQ @ sK0 @ X0 @ (g @ sK1)))) ) | ~spl2_3),
% 1.92/1.65 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.92/1.65 thf(f58,plain,(
% 1.92/1.65 spl2_2),
% 1.92/1.65 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.92/1.65 thf(f57,plain,(
% 1.92/1.65 $false | spl2_2),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.92/1.65 thf(f54,plain,(
% 1.92/1.65 ($true != $true) | spl2_2),
% 1.92/1.65 inference(superposition,[status(thm)],[f53,f17])).
% 1.92/1.65 thf(f53,plain,(
% 1.92/1.65 ( ! [X0 : a] : (((cP @ sK0 @ X0) != $true)) ) | spl2_2),
% 1.92/1.65 inference(subsumption_resolution,[status(thm)],[f52,f12])).
% 1.92/1.65 thf(f52,plain,(
% 1.92/1.65 ( ! [X0 : a] : (($true != (cP @ X0 @ sK0)) | ((cP @ sK0 @ X0) != $true)) ) | spl2_2),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.92/1.65 thf(f49,plain,(
% 1.92/1.65 ( ! [X0 : a] : (($true != (cP @ X0 @ sK0)) | ((cP @ sK0 @ X0) != $true) | ($true != $true)) ) | spl2_2),
% 1.92/1.65 inference(superposition,[status(thm)],[f41,f15])).
% 1.92/1.65 thf(f41,plain,(
% 1.92/1.65 ($true != (cP @ sK0 @ sK0)) | spl2_2),
% 1.92/1.65 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.92/1.65 thf(f39,definition,(
% 1.92/1.65 spl2_2 <=> ($true = (cP @ sK0 @ sK0))),
% 1.92/1.65 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.92/1.65 thf(f48,plain,(
% 1.92/1.65 ~spl2_2 | spl2_3),
% 1.92/1.65 inference(avatar_split_clause,[status(thm)],[f44,f46,f39])).
% 1.92/1.65 thf(f44,plain,(
% 1.92/1.65 ( ! [X0 : b] : (($true != (cQ @ sK0 @ (f @ sK0) @ X0)) | ($true != (cP @ sK0 @ sK0)) | ($true != (cQ @ sK0 @ X0 @ (g @ sK1)))) )),
% 1.92/1.65 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.92/1.65 thf(f43,plain,(
% 1.92/1.65 ( ! [X0 : b] : (($true != (cQ @ sK0 @ (f @ sK0) @ X0)) | ($true != (cP @ sK0 @ sK0)) | ($true != (cQ @ sK0 @ X0 @ (g @ sK1))) | ($true != $true)) )),
% 1.92/1.65 inference(superposition,[status(thm)],[f18,f13])).
% 1.92/1.65 thf(f13,plain,(
% 1.92/1.65 ( ! [X9 : a,X14 : b,X12 : b,X13 : b] : (($true = (cQ @ X9 @ X13 @ X14)) | ($true != (cP @ X9 @ X9)) | ($true != (cQ @ X9 @ X13 @ X12)) | ($true != (cQ @ X9 @ X12 @ X14))) )),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 thf(f18,plain,(
% 1.92/1.65 ($true != (cQ @ sK0 @ (f @ sK0) @ (g @ sK1)))),
% 1.92/1.65 inference(cnf_transformation,[status(thm)],[f10])).
% 1.92/1.65 % SZS output end Proof for DTF2THF_6307
% 1.92/1.65 % (6429)------------------------------
% 1.92/1.65 % (6429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.65 % (6429)Termination reason: Refutation
% 1.92/1.65
% 1.92/1.65 % (6429)Memory used [KB]: 6012
% 1.92/1.65 % (6429)Time elapsed: 0.083 s
% 1.92/1.65 % (6429)Instructions burned: 166 (million)
% 1.92/1.65 % (6429)------------------------------
% 1.92/1.65 % (6429)------------------------------
% 1.92/1.65 % (6428)Success in time 0.092 s
%------------------------------------------------------------------------------