%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV107^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 09:40:18 AM UTC 2026
% Result : Theorem 1.65s 1.32s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 4 unt; 0 typ; 10 def)
% Number of atoms : 1086 ( 295 equ; 0 cnn)
% Maximal formula atoms : 24 ( 12 avg)
% Number of connectives : 1287 ( 213 ~; 190 |; 140 &; 698 @)
% ( 10 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 19 con; 0-2 aty)
% Number of variables : 277 ( 0 ^; 215 !; 62 ?; 277 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
z: a ).
thf(func_def_2,type,
cR: a > a > $o ).
thf(func_def_3,type,
f: a > $i > $o ).
thf(func_def_4,type,
cS: $i > $i > $o ).
thf(func_def_9,type,
sK1: a ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_13,type,
sK5: a > a ).
thf(func_def_14,type,
sK6: a ).
thf(func_def_15,type,
sK7: $i > a ).
thf(func_def_16,type,
sK8: a > $i ).
thf(f143,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f50,f66,f72,f77,f82,f87,f90,f122,f125,f129,f136,f142]) ).
thf(f142,plain,
( ~ spl9_7
| ~ spl9_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f141]) ).
thf(f141,plain,
( $false
| ~ spl9_7
| ~ spl9_9 ),
inference(subsumption_resolution,[status(thm)],[f71,f61]) ).
thf(f61,plain,
( ! [X3: a] :
( ( f @ X3 @ sK2 )
!= $true )
| ~ spl9_7 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl9_7
<=> ! [X3: a] :
( ( f @ X3 @ sK2 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition]) ).
thf(f71,plain,
( ( ( f @ sK3 @ sK2 )
= $true )
| ~ spl9_9 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl9_9
<=> ( ( f @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_9])],[avatar_definition]) ).
thf(f136,plain,
( ~ spl9_3
| ~ spl9_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f135]) ).
thf(f135,plain,
( $false
| ~ spl9_3
| ~ spl9_4 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true != $true )
| ~ spl9_3
| ~ spl9_4 ),
inference(superposition,[status(thm)],[f130,f34]) ).
thf(f34,plain,
! [X3: a] :
( ( cR @ X3 @ X3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: a,X1: $i,X2: $i] :
( ( ( f @ X0 @ X2 )
!= $true )
| ( $true
!= ( f @ X0 @ X1 ) )
| ( $true
= ( cS @ X1 @ X2 ) ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true )
& ( ! [X5: a] :
( ( ( f @ X5 @ sK4 )
!= $true )
& ( ( ( cR @ X5 @ z )
!= $true )
| ( ( f @ ( sK5 @ X5 ) @ sK4 )
= $true ) ) )
| ( sP0 = $true )
| ! [X8: $i] :
( ( $true
!= ( f @ sK6 @ X8 ) )
& ( ( $true
= ( f @ ( sK7 @ X8 ) @ X8 ) )
| ( ( cR @ sK6 @ z )
!= $true ) ) ) )
& ! [X10: a] :
( ( f @ X10 @ ( sK8 @ X10 ) )
= $true )
& ! [X12: a,X13: $i,X14: a] :
( ( ( cR @ X12 @ X14 )
= $true )
| ( ( f @ X14 @ X13 )
!= $true )
| ( ( f @ X12 @ X13 )
!= $true ) )
& ! [X15: a,X16: a,X17: a] :
( ( ( cR @ X17 @ X15 )
!= $true )
| ( ( cR @ X16 @ X17 )
= $true )
| ( ( cR @ X16 @ X15 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f15,f20,f19,f18,f17,f16]) ).
thf(f16,plain,
( ? [X4: $i] :
! [X5: a] :
? [X6: a] :
( ( $true
!= ( f @ X5 @ X4 ) )
& ( ( ( cR @ X5 @ z )
!= $true )
| ( ( f @ X6 @ X4 )
= $true ) ) )
=> ! [X5: a] :
? [X6: a] :
( ( ( f @ X5 @ sK4 )
!= $true )
& ( ( ( cR @ X5 @ z )
!= $true )
| ( ( f @ X6 @ sK4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X5: a] :
( ? [X6: a] :
( ( ( f @ X5 @ sK4 )
!= $true )
& ( ( ( cR @ X5 @ z )
!= $true )
| ( ( f @ X6 @ sK4 )
= $true ) ) )
=> ( ( ( f @ X5 @ sK4 )
!= $true )
& ( ( ( cR @ X5 @ z )
!= $true )
| ( ( f @ ( sK5 @ X5 ) @ sK4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X7: a] :
! [X8: $i] :
? [X9: a] :
( ( $true
!= ( f @ X7 @ X8 ) )
& ( ( $true
= ( f @ X9 @ X8 ) )
| ( ( cR @ X7 @ z )
!= $true ) ) )
=> ! [X8: $i] :
? [X9: a] :
( ( $true
!= ( f @ sK6 @ X8 ) )
& ( ( $true
= ( f @ X9 @ X8 ) )
| ( ( cR @ sK6 @ z )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X8: $i] :
( ? [X9: a] :
( ( $true
!= ( f @ sK6 @ X8 ) )
& ( ( $true
= ( f @ X9 @ X8 ) )
| ( ( cR @ sK6 @ z )
!= $true ) ) )
=> ( ( $true
!= ( f @ sK6 @ X8 ) )
& ( ( $true
= ( f @ ( sK7 @ X8 ) @ X8 ) )
| ( ( cR @ sK6 @ z )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
! [X10: a] :
( ? [X11: $i] :
( ( f @ X10 @ X11 )
= $true )
=> ( ( f @ X10 @ ( sK8 @ X10 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ! [X0: a,X1: $i,X2: $i] :
( ( ( f @ X0 @ X2 )
!= $true )
| ( $true
!= ( f @ X0 @ X1 ) )
| ( $true
= ( cS @ X1 @ X2 ) ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true )
& ( ? [X4: $i] :
! [X5: a] :
? [X6: a] :
( ( $true
!= ( f @ X5 @ X4 ) )
& ( ( ( cR @ X5 @ z )
!= $true )
| ( ( f @ X6 @ X4 )
= $true ) ) )
| ( sP0 = $true )
| ? [X7: a] :
! [X8: $i] :
? [X9: a] :
( ( $true
!= ( f @ X7 @ X8 ) )
& ( ( $true
= ( f @ X9 @ X8 ) )
| ( ( cR @ X7 @ z )
!= $true ) ) ) )
& ! [X10: a] :
? [X11: $i] :
( ( f @ X10 @ X11 )
= $true )
& ! [X12: a,X13: $i,X14: a] :
( ( ( cR @ X12 @ X14 )
= $true )
| ( ( f @ X14 @ X13 )
!= $true )
| ( ( f @ X12 @ X13 )
!= $true ) )
& ! [X15: a,X16: a,X17: a] :
( ( ( cR @ X17 @ X15 )
!= $true )
| ( ( cR @ X16 @ X17 )
= $true )
| ( ( cR @ X16 @ X15 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X6: a,X8: $i,X7: $i] :
( ( ( f @ X6 @ X7 )
!= $true )
| ( ( f @ X6 @ X8 )
!= $true )
| ( ( cS @ X8 @ X7 )
= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true )
& ( ? [X20: $i] :
! [X21: a] :
? [X22: a] :
( ( ( f @ X21 @ X20 )
!= $true )
& ( ( ( cR @ X21 @ z )
!= $true )
| ( ( f @ X22 @ X20 )
= $true ) ) )
| ( sP0 = $true )
| ? [X17: a] :
! [X18: $i] :
? [X19: a] :
( ( ( f @ X17 @ X18 )
!= $true )
& ( ( ( f @ X19 @ X18 )
= $true )
| ( ( cR @ X17 @ z )
!= $true ) ) ) )
& ! [X4: a] :
? [X5: $i] :
( ( f @ X4 @ X5 )
= $true )
& ! [X10: a,X11: $i,X9: a] :
( ( ( cR @ X10 @ X9 )
= $true )
| ( ( f @ X9 @ X11 )
!= $true )
| ( ( f @ X10 @ X11 )
!= $true ) )
& ! [X0: a,X2: a,X1: a] :
( ( ( cR @ X1 @ X0 )
!= $true )
| ( ( cR @ X2 @ X1 )
= $true )
| ( ( cR @ X2 @ X0 )
!= $true ) ) ),
inference(definition_folding,[status(thm)],[f8,f9]) ).
thf(f9,plain,
( ? [X12: a,X13: $i,X14: a] :
( ! [X16: a] :
( ( ( f @ X12 @ X13 )
= $true )
| ( ( ( f @ X16 @ X13 )
!= $true )
& ( ( cR @ X12 @ z )
= $true ) ) )
& ! [X15: a] :
( ( ( f @ X14 @ X13 )
= $true )
| ( ( ( f @ X15 @ X13 )
!= $true )
& ( ( cR @ X14 @ z )
= $true ) ) )
& ( ( cR @ X14 @ X12 )
!= $true ) )
| ( sP0 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ! [X6: a,X8: $i,X7: $i] :
( ( ( f @ X6 @ X7 )
!= $true )
| ( ( f @ X6 @ X8 )
!= $true )
| ( ( cS @ X8 @ X7 )
= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true )
& ( ? [X20: $i] :
! [X21: a] :
? [X22: a] :
( ( ( f @ X21 @ X20 )
!= $true )
& ( ( ( cR @ X21 @ z )
!= $true )
| ( ( f @ X22 @ X20 )
= $true ) ) )
| ? [X12: a,X13: $i,X14: a] :
( ! [X16: a] :
( ( ( f @ X12 @ X13 )
= $true )
| ( ( ( f @ X16 @ X13 )
!= $true )
& ( ( cR @ X12 @ z )
= $true ) ) )
& ! [X15: a] :
( ( ( f @ X14 @ X13 )
= $true )
| ( ( ( f @ X15 @ X13 )
!= $true )
& ( ( cR @ X14 @ z )
= $true ) ) )
& ( ( cR @ X14 @ X12 )
!= $true ) )
| ? [X17: a] :
! [X18: $i] :
? [X19: a] :
( ( ( f @ X17 @ X18 )
!= $true )
& ( ( ( f @ X19 @ X18 )
= $true )
| ( ( cR @ X17 @ z )
!= $true ) ) ) )
& ! [X4: a] :
? [X5: $i] :
( ( f @ X4 @ X5 )
= $true )
& ! [X10: a,X11: $i,X9: a] :
( ( ( cR @ X10 @ X9 )
= $true )
| ( ( f @ X9 @ X11 )
!= $true )
| ( ( f @ X10 @ X11 )
!= $true ) )
& ! [X0: a,X2: a,X1: a] :
( ( ( cR @ X1 @ X0 )
!= $true )
| ( ( cR @ X2 @ X1 )
= $true )
| ( ( cR @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ? [X17: a] :
! [X18: $i] :
? [X19: a] :
( ( ( f @ X17 @ X18 )
!= $true )
& ( ( ( f @ X19 @ X18 )
= $true )
| ( ( cR @ X17 @ z )
!= $true ) ) )
| ? [X13: $i,X14: a,X12: a] :
( ( ( cR @ X14 @ X12 )
!= $true )
& ! [X15: a] :
( ( ( f @ X14 @ X13 )
= $true )
| ( ( ( f @ X15 @ X13 )
!= $true )
& ( ( cR @ X14 @ z )
= $true ) ) )
& ! [X16: a] :
( ( ( f @ X12 @ X13 )
= $true )
| ( ( ( f @ X16 @ X13 )
!= $true )
& ( ( cR @ X12 @ z )
= $true ) ) ) )
| ? [X20: $i] :
! [X21: a] :
? [X22: a] :
( ( ( f @ X21 @ X20 )
!= $true )
& ( ( ( cR @ X21 @ z )
!= $true )
| ( ( f @ X22 @ X20 )
= $true ) ) ) )
& ! [X6: a,X7: $i,X8: $i] :
( ( ( cS @ X8 @ X7 )
= $true )
| ( ( f @ X6 @ X8 )
!= $true )
| ( ( f @ X6 @ X7 )
!= $true ) )
& ! [X10: a,X9: a,X11: $i] :
( ( ( cR @ X10 @ X9 )
= $true )
| ( ( f @ X9 @ X11 )
!= $true )
| ( ( f @ X10 @ X11 )
!= $true ) )
& ! [X4: a] :
? [X5: $i] :
( ( f @ X4 @ X5 )
= $true )
& ! [X2: a,X0: a,X1: a] :
( ( ( cR @ X2 @ X1 )
= $true )
| ( ( cR @ X2 @ X0 )
!= $true )
| ( ( cR @ X1 @ X0 )
!= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X2: a,X0: a,X1: a] :
( ( ( ( cR @ X2 @ X0 )
= $true )
& ( ( cR @ X1 @ X0 )
= $true ) )
=> ( ( cR @ X2 @ X1 )
= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true ) )
=> ( ( ! [X6: a,X7: $i,X8: $i] :
( ( ( ( f @ X6 @ X8 )
= $true )
& ( ( f @ X6 @ X7 )
= $true ) )
=> ( ( cS @ X8 @ X7 )
= $true ) )
& ! [X10: a,X9: a,X11: $i] :
( ( ( ( f @ X9 @ X11 )
= $true )
& ( ( f @ X10 @ X11 )
= $true ) )
=> ( ( cR @ X10 @ X9 )
= $true ) )
& ! [X4: a] :
? [X5: $i] :
( ( f @ X4 @ X5 )
= $true ) )
=> ( ! [X17: a] :
? [X18: $i] :
! [X19: a] :
( ( ( f @ X17 @ X18 )
= $true )
| ( ( ( f @ X19 @ X18 )
!= $true )
& ( ( cR @ X17 @ z )
= $true ) ) )
& ! [X13: $i,X14: a,X12: a] :
( ( ! [X15: a] :
( ( ( f @ X14 @ X13 )
= $true )
| ( ( ( f @ X15 @ X13 )
!= $true )
& ( ( cR @ X14 @ z )
= $true ) ) )
& ! [X16: a] :
( ( ( f @ X12 @ X13 )
= $true )
| ( ( ( f @ X16 @ X13 )
!= $true )
& ( ( cR @ X12 @ z )
= $true ) ) ) )
=> ( ( cR @ X14 @ X12 )
= $true ) )
& ! [X20: $i] :
? [X21: a] :
! [X22: a] :
( ( ( f @ X21 @ X20 )
= $true )
| ( ( ( cR @ X21 @ z )
= $true )
& ( ( f @ X22 @ X20 )
!= $true ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X2: a,X0: a,X1: a] :
( ( ( ( cR @ X2 @ X0 )
= $true )
& ( ( cR @ X1 @ X0 )
= $true ) )
=> ( ( cR @ X2 @ X1 )
= $true ) )
& ! [X3: a] :
( ( cR @ X3 @ X3 )
= $true ) )
=> ( ( ! [X6: a,X7: $i,X8: $i] :
( ( ( ( f @ X6 @ X8 )
= $true )
& ( ( f @ X6 @ X7 )
= $true ) )
=> ( ( cS @ X8 @ X7 )
= $true ) )
& ! [X10: a,X9: a,X11: $i] :
( ( ( ( f @ X9 @ X11 )
= $true )
& ( ( f @ X10 @ X11 )
= $true ) )
=> ( ( cR @ X10 @ X9 )
= $true ) )
& ! [X4: a] :
? [X5: $i] :
( ( f @ X4 @ X5 )
= $true ) )
=> ( ! [X12: a,X13: $i,X14: a] :
( ( ! [X15: a] :
( ( ( ( f @ X15 @ X13 )
!= $true )
& ( ( cR @ X14 @ z )
= $true ) )
| ( ( f @ X14 @ X13 )
= $true ) )
& ! [X16: a] :
( ( ( ( f @ X16 @ X13 )
!= $true )
& ( ( cR @ X12 @ z )
= $true ) )
| ( ( f @ X12 @ X13 )
= $true ) ) )
=> ( ( cR @ X14 @ X12 )
= $true ) )
& ! [X17: a] :
? [X18: $i] :
! [X19: a] :
( ( ( f @ X17 @ X18 )
= $true )
| ( ( ( cR @ X17 @ z )
= $true )
& ( ( f @ X19 @ X18 )
!= $true ) ) )
& ! [X20: $i] :
? [X21: a] :
! [X22: a] :
( ( ( ( f @ X22 @ X20 )
!= $true )
& ( ( cR @ X21 @ z )
= $true ) )
| ( ( f @ X21 @ X20 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a,X2: a] :
( ( ( cR @ X1 @ X0 )
& ( cR @ X2 @ X0 ) )
=> ( cR @ X2 @ X1 ) )
& ! [X3: a] : ( cR @ X3 @ X3 ) )
=> ( ( ! [X4: a] :
? [X5: $i] : ( f @ X4 @ X5 )
& ! [X6: a,X7: $i,X8: $i] :
( ( ( f @ X6 @ X8 )
& ( f @ X6 @ X7 ) )
=> ( cS @ X8 @ X7 ) )
& ! [X9: a,X10: a,X11: $i] :
( ( ( f @ X9 @ X11 )
& ( f @ X10 @ X11 ) )
=> ( cR @ X10 @ X9 ) ) )
=> ( ! [X12: a,X13: $i,X14: a] :
( ( ! [X15: a] :
( ( ~ ( f @ X15 @ X13 )
& ( cR @ X14 @ z ) )
| ( f @ X14 @ X13 ) )
& ! [X16: a] :
( ( ~ ( f @ X16 @ X13 )
& ( cR @ X12 @ z ) )
| ( f @ X12 @ X13 ) ) )
=> ( cR @ X14 @ X12 ) )
& ! [X17: a] :
? [X18: $i] :
! [X19: a] :
( ( f @ X17 @ X18 )
| ( ( cR @ X17 @ z )
& ~ ( f @ X19 @ X18 ) ) )
& ! [X20: $i] :
? [X21: a] :
! [X22: a] :
( ( ~ ( f @ X22 @ X20 )
& ( cR @ X21 @ z ) )
| ( f @ X21 @ X20 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X2: a,X0: a] :
( ( ( cR @ X2 @ X1 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) )
& ! [X3: a] : ( cR @ X3 @ X3 ) )
=> ( ( ! [X3: a] :
? [X4: $i] : ( f @ X3 @ X4 )
& ! [X3: a,X6: $i,X5: $i] :
( ( ( f @ X3 @ X5 )
& ( f @ X3 @ X6 ) )
=> ( cS @ X5 @ X6 ) )
& ! [X8: a,X7: a,X4: $i] :
( ( ( f @ X8 @ X4 )
& ( f @ X7 @ X4 ) )
=> ( cR @ X7 @ X8 ) ) )
=> ( ! [X8: a,X4: $i,X7: a] :
( ( ! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X7 @ z ) )
| ( f @ X7 @ X4 ) )
& ! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X8 @ z ) )
| ( f @ X8 @ X4 ) ) )
=> ( cR @ X7 @ X8 ) )
& ! [X3: a] :
? [X4: $i] :
! [X2: a] :
( ( f @ X3 @ X4 )
| ( ( cR @ X3 @ z )
& ~ ( f @ X2 @ X4 ) ) )
& ! [X4: $i] :
? [X3: a] :
! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X3 @ z ) )
| ( f @ X3 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a,X2: a,X0: a] :
( ( ( cR @ X2 @ X1 )
& ( cR @ X0 @ X1 ) )
=> ( cR @ X0 @ X2 ) )
& ! [X3: a] : ( cR @ X3 @ X3 ) )
=> ( ( ! [X3: a] :
? [X4: $i] : ( f @ X3 @ X4 )
& ! [X3: a,X6: $i,X5: $i] :
( ( ( f @ X3 @ X5 )
& ( f @ X3 @ X6 ) )
=> ( cS @ X5 @ X6 ) )
& ! [X8: a,X7: a,X4: $i] :
( ( ( f @ X8 @ X4 )
& ( f @ X7 @ X4 ) )
=> ( cR @ X7 @ X8 ) ) )
=> ( ! [X8: a,X4: $i,X7: a] :
( ( ! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X7 @ z ) )
| ( f @ X7 @ X4 ) )
& ! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X8 @ z ) )
| ( f @ X8 @ X4 ) ) )
=> ( cR @ X7 @ X8 ) )
& ! [X3: a] :
? [X4: $i] :
! [X2: a] :
( ( f @ X3 @ X4 )
| ( ( cR @ X3 @ z )
& ~ ( f @ X2 @ X4 ) ) )
& ! [X4: $i] :
? [X3: a] :
! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X3 @ z ) )
| ( f @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vlsEED5hqn/DTF2THF_18979.p',cTHM552B_pme) ).
thf(f130,plain,
( ! [X5: a] :
( ( cR @ X5 @ z )
!= $true )
| ~ spl9_3
| ~ spl9_4 ),
inference(subsumption_resolution,[status(thm)],[f49,f45]) ).
thf(f45,plain,
( ! [X5: a] :
( ( f @ X5 @ sK4 )
!= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl9_3
<=> ! [X5: a] :
( ( f @ X5 @ sK4 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition]) ).
thf(f49,plain,
( ! [X5: a] :
( ( ( f @ ( sK5 @ X5 ) @ sK4 )
= $true )
| ( ( cR @ X5 @ z )
!= $true ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl9_4
<=> ! [X5: a] :
( ( ( f @ ( sK5 @ X5 ) @ sK4 )
= $true )
| ( ( cR @ X5 @ z )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition]) ).
thf(f129,plain,
( ~ spl9_10
| spl9_11
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| ~ spl9_10
| spl9_11
| ~ spl9_12 ),
inference(subsumption_resolution,[status(thm)],[f127,f86]) ).
thf(f86,plain,
( ( ( cR @ sK1 @ z )
= $true )
| ~ spl9_12 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl9_12
<=> ( ( cR @ sK1 @ z )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_12])],[avatar_definition]) ).
thf(f127,plain,
( ( ( cR @ sK1 @ z )
!= $true )
| ~ spl9_10
| spl9_11 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $true != $true )
| ( ( cR @ sK1 @ z )
!= $true )
| ~ spl9_10
| spl9_11 ),
inference(superposition,[status(thm)],[f93,f76]) ).
thf(f76,plain,
( ( ( cR @ sK3 @ z )
= $true )
| ~ spl9_10 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl9_10
<=> ( ( cR @ sK3 @ z )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_10])],[avatar_definition]) ).
thf(f93,plain,
( ! [X0: a] :
( ( ( cR @ sK3 @ X0 )
!= $true )
| ( ( cR @ sK1 @ X0 )
!= $true ) )
| spl9_11 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ! [X0: a] :
( ( ( cR @ sK3 @ X0 )
!= $true )
| ( ( cR @ sK1 @ X0 )
!= $true )
| ( $true != $true ) )
| spl9_11 ),
inference(superposition,[status(thm)],[f81,f27]) ).
thf(f27,plain,
! [X16: a,X17: a,X15: a] :
( ( ( cR @ X16 @ X17 )
= $true )
| ( ( cR @ X17 @ X15 )
!= $true )
| ( ( cR @ X16 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f81,plain,
( ( ( cR @ sK3 @ sK1 )
!= $true )
| spl9_11 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f79,definition,
( spl9_11
<=> ( ( cR @ sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition]) ).
thf(f125,plain,
( ~ spl9_7
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f124]) ).
thf(f124,plain,
( $false
| ~ spl9_7
| ~ spl9_8 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $true != $true )
| ~ spl9_7
| ~ spl9_8 ),
inference(superposition,[status(thm)],[f61,f65]) ).
thf(f65,plain,
( ( ( f @ sK1 @ sK2 )
= $true )
| ~ spl9_8 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl9_8
<=> ( ( f @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_8])],[avatar_definition]) ).
thf(f122,plain,
( ~ spl9_8
| ~ spl9_9
| spl9_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f121]) ).
thf(f121,plain,
( $false
| ~ spl9_8
| ~ spl9_9
| spl9_11 ),
inference(subsumption_resolution,[status(thm)],[f119,f65]) ).
thf(f119,plain,
( ( ( f @ sK1 @ sK2 )
!= $true )
| ~ spl9_9
| spl9_11 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( ( f @ sK1 @ sK2 )
!= $true )
| ( $true != $true )
| ~ spl9_9
| spl9_11 ),
inference(superposition,[status(thm)],[f112,f71]) ).
thf(f112,plain,
( ! [X0: $i] :
( ( ( f @ sK3 @ X0 )
!= $true )
| ( ( f @ sK1 @ X0 )
!= $true ) )
| spl9_11 ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
( ! [X0: $i] :
( ( ( f @ sK3 @ X0 )
!= $true )
| ( $true != $true )
| ( ( f @ sK1 @ X0 )
!= $true ) )
| spl9_11 ),
inference(superposition,[status(thm)],[f98,f28]) ).
thf(f28,plain,
! [X14: a,X12: a,X13: $i] :
( ( ( cR @ X12 @ X14 )
= $true )
| ( ( f @ X12 @ X13 )
!= $true )
| ( ( f @ X14 @ X13 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f98,plain,
( ( ( cR @ sK1 @ sK3 )
!= $true )
| spl9_11 ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( cR @ sK1 @ sK3 )
!= $true )
| ( $true != $true )
| spl9_11 ),
inference(superposition,[status(thm)],[f93,f34]) ).
thf(f90,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| ~ spl9_2 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true != $true )
| ~ spl9_2 ),
inference(superposition,[status(thm)],[f42,f29]) ).
thf(f29,plain,
! [X10: a] :
( ( f @ X10 @ ( sK8 @ X10 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f42,plain,
( ! [X8: $i] :
( $true
!= ( f @ sK6 @ X8 ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl9_2
<=> ! [X8: $i] :
( $true
!= ( f @ sK6 @ X8 ) ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f87,plain,
( spl9_12
| ~ spl9_1
| spl9_8 ),
inference(avatar_split_clause,[status(thm)],[f25,f63,f37,f84]) ).
thf(f37,definition,
( spl9_1
<=> ( sP0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f25,plain,
( ( sP0 != $true )
| ( ( cR @ sK1 @ z )
= $true )
| ( ( f @ sK1 @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ! [X3: a] :
( ( ( f @ sK1 @ sK2 )
= $true )
| ( ( ( f @ X3 @ sK2 )
!= $true )
& ( ( cR @ sK1 @ z )
= $true ) ) )
& ! [X4: a] :
( ( ( f @ sK3 @ sK2 )
= $true )
| ( ( ( f @ X4 @ sK2 )
!= $true )
& ( ( cR @ sK3 @ z )
= $true ) ) )
& ( ( cR @ sK3 @ sK1 )
!= $true ) )
| ( sP0 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: a,X1: $i,X2: a] :
( ! [X3: a] :
( ( $true
= ( f @ X0 @ X1 ) )
| ( ( ( f @ X3 @ X1 )
!= $true )
& ( ( cR @ X0 @ z )
= $true ) ) )
& ! [X4: a] :
( ( ( f @ X2 @ X1 )
= $true )
| ( ( ( f @ X4 @ X1 )
!= $true )
& ( $true
= ( cR @ X2 @ z ) ) ) )
& ( ( cR @ X2 @ X0 )
!= $true ) )
=> ( ! [X3: a] :
( ( ( f @ sK1 @ sK2 )
= $true )
| ( ( ( f @ X3 @ sK2 )
!= $true )
& ( ( cR @ sK1 @ z )
= $true ) ) )
& ! [X4: a] :
( ( ( f @ sK3 @ sK2 )
= $true )
| ( ( ( f @ X4 @ sK2 )
!= $true )
& ( ( cR @ sK3 @ z )
= $true ) ) )
& ( ( cR @ sK3 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: a,X1: $i,X2: a] :
( ! [X3: a] :
( ( $true
= ( f @ X0 @ X1 ) )
| ( ( ( f @ X3 @ X1 )
!= $true )
& ( ( cR @ X0 @ z )
= $true ) ) )
& ! [X4: a] :
( ( ( f @ X2 @ X1 )
= $true )
| ( ( ( f @ X4 @ X1 )
!= $true )
& ( $true
= ( cR @ X2 @ z ) ) ) )
& ( ( cR @ X2 @ X0 )
!= $true ) )
| ( sP0 != $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X12: a,X13: $i,X14: a] :
( ! [X16: a] :
( ( ( f @ X12 @ X13 )
= $true )
| ( ( ( f @ X16 @ X13 )
!= $true )
& ( ( cR @ X12 @ z )
= $true ) ) )
& ! [X15: a] :
( ( ( f @ X14 @ X13 )
= $true )
| ( ( ( f @ X15 @ X13 )
!= $true )
& ( ( cR @ X14 @ z )
= $true ) ) )
& ( ( cR @ X14 @ X12 )
!= $true ) )
| ( sP0 != $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f82,plain,
( ~ spl9_11
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f22,f37,f79]) ).
thf(f22,plain,
( ( sP0 != $true )
| ( ( cR @ sK3 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f77,plain,
( spl9_9
| ~ spl9_1
| spl9_10 ),
inference(avatar_split_clause,[status(thm)],[f23,f74,f37,f69]) ).
thf(f23,plain,
( ( ( cR @ sK3 @ z )
= $true )
| ( ( f @ sK3 @ sK2 )
= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f72,plain,
( spl9_7
| spl9_9
| ~ spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f24,f37,f69,f60]) ).
thf(f24,plain,
! [X4: a] :
( ( ( f @ X4 @ sK2 )
!= $true )
| ( sP0 != $true )
| ( ( f @ sK3 @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f66,plain,
( spl9_7
| ~ spl9_1
| spl9_8 ),
inference(avatar_split_clause,[status(thm)],[f26,f63,f37,f60]) ).
thf(f26,plain,
! [X3: a] :
( ( ( f @ sK1 @ sK2 )
= $true )
| ( sP0 != $true )
| ( ( f @ X3 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f50,plain,
( spl9_2
| spl9_1
| spl9_4 ),
inference(avatar_split_clause,[status(thm)],[f31,f48,f37,f41]) ).
thf(f31,plain,
! [X8: $i,X5: a] :
( ( ( f @ ( sK5 @ X5 ) @ sK4 )
= $true )
| ( ( cR @ X5 @ z )
!= $true )
| ( $true
!= ( f @ sK6 @ X8 ) )
| ( sP0 = $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f46,plain,
( spl9_1
| spl9_2
| spl9_3 ),
inference(avatar_split_clause,[status(thm)],[f33,f44,f41,f37]) ).
thf(f33,plain,
! [X8: $i,X5: a] :
( ( $true
!= ( f @ sK6 @ X8 ) )
| ( sP0 = $true )
| ( ( f @ X5 @ sK4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV107^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:40:24 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEV107^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory (Relations)
% 0.18/0.45 % Problem : TPS problem from RELN-THMS
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_1162 [Bro09]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.18/0.45 % Number of atoms : 24 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 24 ( 24 avg)
% 0.18/0.45 % Number of connectives : 75 ( 4 ~; 4 |; 13 &; 48 @)
% 0.18/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 16 ( 16 avg)
% 0.18/0.45 % Number of types : 3 ( 1 usr)
% 0.18/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 23 ( 0 ^; 20 !; 3 ?; 23 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(z,type,
% 0.18/0.45 z: a ).
% 0.18/0.45
% 0.18/0.45 thf(cR,type,
% 0.18/0.45 cR: a > a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(f,type,
% 0.18/0.45 f: a > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cS,type,
% 0.18/0.45 cS: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM552B_pme,conjecture,
% 0.18/0.45 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 0.18/0.45 ( ( ( cR @ Xu @ Xv )
% 0.18/0.45 & ( cR @ Xw @ Xv ) )
% 0.18/0.45 => ( cR @ Xu @ Xw ) )
% 0.18/0.45 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 0.18/0.45 => ( ( ! [Xx: a] :
% 0.18/0.45 ? [Xy: $i] : ( f @ Xx @ Xy )
% 0.18/0.45 & ! [Xx: a,Xy1: $i,Xy2: $i] :
% 0.18/0.45 ( ( ( f @ Xx @ Xy1 )
% 0.18/0.45 & ( f @ Xx @ Xy2 ) )
% 0.18/0.45 => ( cS @ Xy1 @ Xy2 ) )
% 0.18/0.45 & ! [Xx1: a,Xx2: a,Xy: $i] :
% 0.18/0.45 ( ( ( f @ Xx1 @ Xy )
% 0.18/0.45 & ( f @ Xx2 @ Xy ) )
% 0.18/0.45 => ( cR @ Xx1 @ Xx2 ) ) )
% 0.18/0.45 => ( ! [Xx: a] :
% 0.18/0.45 ? [Xy: $i] :
% 0.18/0.45 ! [Xw: a] :
% 0.18/0.45 ( ( f @ Xx @ Xy )
% 0.18/0.45 | ( ~ ( f @ Xw @ Xy )
% 0.18/0.45 & ( cR @ Xx @ z ) ) )
% 0.18/0.45 & ! [Xy: $i,Xx1: a,Xx2: a] :
% 0.18/0.45 ( ( ! [Xw: a] :
% 0.18/0.45 ( ( f @ Xx1 @ Xy )
% 0.18/0.45 | ( ~ ( f @ Xw @ Xy )
% 0.18/0.45 & ( cR @ Xx1 @ z ) ) )
% 0.18/0.45 & ! [Xw: a] :
% 0.18/0.45 ( ( f @ Xx2 @ Xy )
% 0.18/0.45 | ( ~ ( f @ Xw @ Xy )
% 0.18/0.45 & ( cR @ Xx2 @ z ) ) ) )
% 0.18/0.45 => ( cR @ Xx1 @ Xx2 ) )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ? [Xx: a] :
% 0.18/0.45 ! [Xw: a] :
% 0.18/0.45 ( ( f @ Xx @ Xy )
% 0.18/0.45 | ( ~ ( f @ Xw @ Xy )
% 0.18/0.45 & ( cR @ Xx @ z ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 12:40:25 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.vlsEED5hqn/DTF2DTF18979.p
% See solution above
% 1.47/1.29 ------------------------
% 1.47/1.30 ---- Cleaned THF ---
% 1.47/1.30 thf(a_type,type,
% 1.47/1.30 a: $tType ).
% 1.47/1.30
% 1.47/1.30 thf(z,type,
% 1.47/1.30 z: a ).
% 1.47/1.30
% 1.47/1.30 thf(cR,type,
% 1.47/1.30 cR: a > a > $o ).
% 1.47/1.30
% 1.47/1.30 thf(f,type,
% 1.47/1.30 f: a > $i > $o ).
% 1.47/1.30
% 1.47/1.30 thf(cS,type,
% 1.47/1.30 cS: $i > $i > $o ).
% 1.47/1.30
% 1.47/1.30 thf(cTHM552B_pme,conjecture,
% 1.47/1.30 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 1.47/1.30 ( ( ( cR @ Xu @ Xv )
% 1.47/1.30 & ( cR @ Xw @ Xv ) )
% 1.47/1.30 => ( cR @ Xu @ Xw ) )
% 1.47/1.30 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 1.47/1.30 => ( ( ! [Xx: a] :
% 1.47/1.30 ? [Xy: $i] : ( f @ Xx @ Xy )
% 1.47/1.30 & ! [Xx: a,Xy1: $i,Xy2: $i] :
% 1.47/1.30 ( ( ( f @ Xx @ Xy1 )
% 1.47/1.30 & ( f @ Xx @ Xy2 ) )
% 1.47/1.30 => ( cS @ Xy1 @ Xy2 ) )
% 1.47/1.30 & ! [Xx1: a,Xx2: a,Xy: $i] :
% 1.47/1.30 ( ( ( f @ Xx1 @ Xy )
% 1.47/1.30 & ( f @ Xx2 @ Xy ) )
% 1.47/1.30 => ( cR @ Xx1 @ Xx2 ) ) )
% 1.47/1.30 => ( ! [Xx: a] :
% 1.47/1.30 ? [Xy: $i] :
% 1.47/1.30 ! [Xw: a] :
% 1.47/1.30 ( ( f @ Xx @ Xy )
% 1.47/1.30 | ( ~ ( f @ Xw @ Xy )
% 1.47/1.30 & ( cR @ Xx @ z ) ) )
% 1.47/1.30 & ! [Xy: $i,Xx1: a,Xx2: a] :
% 1.47/1.30 ( ( ! [Xw: a] :
% 1.47/1.30 ( ( f @ Xx1 @ Xy )
% 1.47/1.30 | ( ~ ( f @ Xw @ Xy )
% 1.47/1.30 & ( cR @ Xx1 @ z ) ) )
% 1.47/1.30 & ! [Xw: a] :
% 1.47/1.30 ( ( f @ Xx2 @ Xy )
% 1.47/1.30 | ( ~ ( f @ Xw @ Xy )
% 1.47/1.30 & ( cR @ Xx2 @ z ) ) ) )
% 1.47/1.30 => ( cR @ Xx1 @ Xx2 ) )
% 1.47/1.30 & ! [Xy: $i] :
% 1.47/1.30 ? [Xx: a] :
% 1.47/1.30 ! [Xw: a] :
% 1.47/1.30 ( ( f @ Xx @ Xy )
% 1.47/1.30 | ( ~ ( f @ Xw @ Xy )
% 1.47/1.30 & ( cR @ Xx @ z ) ) ) ) ) ) ).
% 1.47/1.30 ------------------------
% 1.65/1.31 % (19149)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18979 for (3000ds/2Mi)
% 1.65/1.31 % (19146)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18979 for (3000ds/183Mi)
% 1.65/1.31 % (19149)Instruction limit reached!
% 1.65/1.31 % (19149)------------------------------
% 1.65/1.31 % (19149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (19149)Termination reason: Unknown
% 1.65/1.31 % (19149)Termination phase: Preprocessing 3
% 1.65/1.31
% 1.65/1.31 % (19149)Memory used [KB]: 1023
% 1.65/1.31 % (19149)Time elapsed: 0.002 s
% 1.65/1.31 % (19149)Instructions burned: 3 (million)
% 1.65/1.31 % (19149)------------------------------
% 1.65/1.31 % (19149)------------------------------
% 1.65/1.31 % (19151)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_18979 for (3000ds/275Mi)
% 1.65/1.31 % (19146)First to succeed.
% 1.65/1.32 % (19147)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_18979 for (3000ds/4Mi)
% 1.65/1.32 % (19150)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_18979 for (3000ds/2Mi)
% 1.65/1.32 % (19148)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_18979 for (3000ds/27Mi)
% 1.65/1.32 % (19152)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18979 for (3000ds/18Mi)
% 1.65/1.32 % (19150)Instruction limit reached!
% 1.65/1.32 % (19150)------------------------------
% 1.65/1.32 % (19150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (19150)Termination reason: Unknown
% 1.65/1.32 % (19150)Termination phase: shuffling
% 1.65/1.32
% 1.65/1.32 % (19150)Memory used [KB]: 1023
% 1.65/1.32 % (19150)Time elapsed: 0.003 s
% 1.65/1.32 % (19150)Instructions burned: 2 (million)
% 1.65/1.32 % (19150)------------------------------
% 1.65/1.32 % (19150)------------------------------
% 1.65/1.32 % (19146)Refutation found. Thanks to Tanya!
% 1.65/1.32 % SZS status Theorem for DTF2THF_18979
% 1.65/1.32 % SZS output start Proof for DTF2THF_18979
% 1.65/1.32 thf(type_def_5, type, a: $tType).
% 1.65/1.32 thf(func_def_0, type, a: $tType).
% 1.65/1.32 thf(func_def_1, type, z: a).
% 1.65/1.32 thf(func_def_2, type, cR: a > a > $o).
% 1.65/1.32 thf(func_def_3, type, f: a > $i > $o).
% 1.65/1.32 thf(func_def_4, type, cS: $i > $i > $o).
% 1.65/1.32 thf(func_def_9, type, sK1: a).
% 1.65/1.32 thf(func_def_11, type, sK3: a).
% 1.65/1.32 thf(func_def_13, type, sK5: a > a).
% 1.65/1.32 thf(func_def_14, type, sK6: a).
% 1.65/1.32 thf(func_def_15, type, sK7: $i > a).
% 1.65/1.32 thf(func_def_16, type, sK8: a > $i).
% 1.65/1.32 thf(f143,plain,(
% 1.65/1.32 $false),
% 1.65/1.32 inference(avatar_sat_refutation,[status(thm)],[f46,f50,f66,f72,f77,f82,f87,f90,f122,f125,f129,f136,f142])).
% 1.65/1.32 thf(f142,plain,(
% 1.65/1.32 ~spl9_7 | ~spl9_9),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f141])).
% 1.65/1.32 thf(f141,plain,(
% 1.65/1.32 $false | (~spl9_7 | ~spl9_9)),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f71,f61])).
% 1.65/1.32 thf(f61,plain,(
% 1.65/1.32 ( ! [X3 : a] : (((f @ X3 @ sK2) != $true)) ) | ~spl9_7),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.65/1.32 thf(f60,definition,(
% 1.65/1.32 spl9_7 <=> ! [X3 : a] : ((f @ X3 @ sK2) != $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition])).
% 1.65/1.32 thf(f71,plain,(
% 1.65/1.32 ((f @ sK3 @ sK2) = $true) | ~spl9_9),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.65/1.32 thf(f69,definition,(
% 1.65/1.32 spl9_9 <=> ((f @ sK3 @ sK2) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_9])],[avatar_definition])).
% 1.65/1.32 thf(f136,plain,(
% 1.65/1.32 ~spl9_3 | ~spl9_4),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f135])).
% 1.65/1.32 thf(f135,plain,(
% 1.65/1.32 $false | (~spl9_3 | ~spl9_4)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.65/1.32 thf(f131,plain,(
% 1.65/1.32 ($true != $true) | (~spl9_3 | ~spl9_4)),
% 1.65/1.32 inference(superposition,[status(thm)],[f130,f34])).
% 1.65/1.32 thf(f34,plain,(
% 1.65/1.32 ( ! [X3 : a] : (((cR @ X3 @ X3) = $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.32 thf(f21,plain,(
% 1.65/1.32 ! [X0 : a,X1 : $i,X2 : $i] : (((f @ X0 @ X2) != $true) | ($true != (f @ X0 @ X1)) | ($true = (cS @ X1 @ X2))) & ! [X3 : a] : ((cR @ X3 @ X3) = $true) & (! [X5 : a] : (((f @ X5 @ sK4) != $true) & (((cR @ X5 @ z) != $true) | ((f @ (sK5 @ X5) @ sK4) = $true))) | (sP0 = $true) | ! [X8 : $i] : (($true != (f @ sK6 @ X8)) & (($true = (f @ (sK7 @ X8) @ X8)) | ((cR @ sK6 @ z) != $true)))) & ! [X10 : a] : ((f @ X10 @ (sK8 @ X10)) = $true) & ! [X12 : a,X13 : $i,X14 : a] : (((cR @ X12 @ X14) = $true) | ((f @ X14 @ X13) != $true) | ((f @ X12 @ X13) != $true)) & ! [X15 : a,X16 : a,X17 : a] : (((cR @ X17 @ X15) != $true) | ((cR @ X16 @ X17) = $true) | ((cR @ X16 @ X15) != $true))),
% 1.65/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f15,f20,f19,f18,f17,f16])).
% 1.65/1.32 thf(f16,plain,(
% 1.65/1.32 ? [X4 : $i] : ! [X5 : a] : ? [X6 : a] : (($true != (f @ X5 @ X4)) & (((cR @ X5 @ z) != $true) | ((f @ X6 @ X4) = $true))) => ! [X5 : a] : ? [X6 : a] : (((f @ X5 @ sK4) != $true) & (((cR @ X5 @ z) != $true) | ((f @ X6 @ sK4) = $true)))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f17,plain,(
% 1.65/1.32 ! [X5 : a] : (? [X6 : a] : (((f @ X5 @ sK4) != $true) & (((cR @ X5 @ z) != $true) | ((f @ X6 @ sK4) = $true))) => (((f @ X5 @ sK4) != $true) & (((cR @ X5 @ z) != $true) | ((f @ (sK5 @ X5) @ sK4) = $true))))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f18,plain,(
% 1.65/1.32 ? [X7 : a] : ! [X8 : $i] : ? [X9 : a] : (($true != (f @ X7 @ X8)) & (($true = (f @ X9 @ X8)) | ((cR @ X7 @ z) != $true))) => ! [X8 : $i] : ? [X9 : a] : (($true != (f @ sK6 @ X8)) & (($true = (f @ X9 @ X8)) | ((cR @ sK6 @ z) != $true)))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f19,plain,(
% 1.65/1.32 ! [X8 : $i] : (? [X9 : a] : (($true != (f @ sK6 @ X8)) & (($true = (f @ X9 @ X8)) | ((cR @ sK6 @ z) != $true))) => (($true != (f @ sK6 @ X8)) & (($true = (f @ (sK7 @ X8) @ X8)) | ((cR @ sK6 @ z) != $true))))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f20,plain,(
% 1.65/1.32 ! [X10 : a] : (? [X11 : $i] : ((f @ X10 @ X11) = $true) => ((f @ X10 @ (sK8 @ X10)) = $true))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f15,plain,(
% 1.65/1.32 ! [X0 : a,X1 : $i,X2 : $i] : (((f @ X0 @ X2) != $true) | ($true != (f @ X0 @ X1)) | ($true = (cS @ X1 @ X2))) & ! [X3 : a] : ((cR @ X3 @ X3) = $true) & (? [X4 : $i] : ! [X5 : a] : ? [X6 : a] : (($true != (f @ X5 @ X4)) & (((cR @ X5 @ z) != $true) | ((f @ X6 @ X4) = $true))) | (sP0 = $true) | ? [X7 : a] : ! [X8 : $i] : ? [X9 : a] : (($true != (f @ X7 @ X8)) & (($true = (f @ X9 @ X8)) | ((cR @ X7 @ z) != $true)))) & ! [X10 : a] : ? [X11 : $i] : ((f @ X10 @ X11) = $true) & ! [X12 : a,X13 : $i,X14 : a] : (((cR @ X12 @ X14) = $true) | ((f @ X14 @ X13) != $true) | ((f @ X12 @ X13) != $true)) & ! [X15 : a,X16 : a,X17 : a] : (((cR @ X17 @ X15) != $true) | ((cR @ X16 @ X17) = $true) | ((cR @ X16 @ X15) != $true))),
% 1.65/1.32 inference(rectify,[status(thm)],[f10])).
% 1.65/1.32 thf(f10,plain,(
% 1.65/1.32 ! [X6 : a,X8 : $i,X7 : $i] : (((f @ X6 @ X7) != $true) | ((f @ X6 @ X8) != $true) | ((cS @ X8 @ X7) = $true)) & ! [X3 : a] : ((cR @ X3 @ X3) = $true) & (? [X20 : $i] : ! [X21 : a] : ? [X22 : a] : (((f @ X21 @ X20) != $true) & (((cR @ X21 @ z) != $true) | ((f @ X22 @ X20) = $true))) | (sP0 = $true) | ? [X17 : a] : ! [X18 : $i] : ? [X19 : a] : (((f @ X17 @ X18) != $true) & (((f @ X19 @ X18) = $true) | ((cR @ X17 @ z) != $true)))) & ! [X4 : a] : ? [X5 : $i] : ((f @ X4 @ X5) = $true) & ! [X10 : a,X11 : $i,X9 : a] : (((cR @ X10 @ X9) = $true) | ((f @ X9 @ X11) != $true) | ((f @ X10 @ X11) != $true)) & ! [X0 : a,X2 : a,X1 : a] : (((cR @ X1 @ X0) != $true) | ((cR @ X2 @ X1) = $true) | ((cR @ X2 @ X0) != $true))),
% 1.65/1.32 inference(definition_folding,[status(thm)],[f8,f9])).
% 1.65/1.32 thf(f9,plain,(
% 1.65/1.32 ? [X12 : a,X13 : $i,X14 : a] : (! [X16 : a] : (((f @ X12 @ X13) = $true) | (((f @ X16 @ X13) != $true) & ((cR @ X12 @ z) = $true))) & ! [X15 : a] : (((f @ X14 @ X13) = $true) | (((f @ X15 @ X13) != $true) & ((cR @ X14 @ z) = $true))) & ((cR @ X14 @ X12) != $true)) | ~(sP0 = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.65/1.32 thf(f8,plain,(
% 1.65/1.32 ! [X6 : a,X8 : $i,X7 : $i] : (((f @ X6 @ X7) != $true) | ((f @ X6 @ X8) != $true) | ((cS @ X8 @ X7) = $true)) & ! [X3 : a] : ((cR @ X3 @ X3) = $true) & (? [X20 : $i] : ! [X21 : a] : ? [X22 : a] : (((f @ X21 @ X20) != $true) & (((cR @ X21 @ z) != $true) | ((f @ X22 @ X20) = $true))) | ? [X12 : a,X13 : $i,X14 : a] : (! [X16 : a] : (((f @ X12 @ X13) = $true) | (((f @ X16 @ X13) != $true) & ((cR @ X12 @ z) = $true))) & ! [X15 : a] : (((f @ X14 @ X13) = $true) | (((f @ X15 @ X13) != $true) & ((cR @ X14 @ z) = $true))) & ((cR @ X14 @ X12) != $true)) | ? [X17 : a] : ! [X18 : $i] : ? [X19 : a] : (((f @ X17 @ X18) != $true) & (((f @ X19 @ X18) = $true) | ((cR @ X17 @ z) != $true)))) & ! [X4 : a] : ? [X5 : $i] : ((f @ X4 @ X5) = $true) & ! [X10 : a,X11 : $i,X9 : a] : (((cR @ X10 @ X9) = $true) | ((f @ X9 @ X11) != $true) | ((f @ X10 @ X11) != $true)) & ! [X0 : a,X2 : a,X1 : a] : (((cR @ X1 @ X0) != $true) | ((cR @ X2 @ X1) = $true) | ((cR @ X2 @ X0) != $true))),
% 1.65/1.32 inference(flattening,[status(thm)],[f7])).
% 1.65/1.32 thf(f7,plain,(
% 1.65/1.32 ((? [X17 : a] : ! [X18 : $i] : ? [X19 : a] : (((f @ X17 @ X18) != $true) & (((f @ X19 @ X18) = $true) | ((cR @ X17 @ z) != $true))) | ? [X13 : $i,X14 : a,X12 : a] : (((cR @ X14 @ X12) != $true) & (! [X15 : a] : (((f @ X14 @ X13) = $true) | (((f @ X15 @ X13) != $true) & ((cR @ X14 @ z) = $true))) & ! [X16 : a] : (((f @ X12 @ X13) = $true) | (((f @ X16 @ X13) != $true) & ((cR @ X12 @ z) = $true))))) | ? [X20 : $i] : ! [X21 : a] : ? [X22 : a] : (((f @ X21 @ X20) != $true) & (((cR @ X21 @ z) != $true) | ((f @ X22 @ X20) = $true)))) & (! [X6 : a,X7 : $i,X8 : $i] : (((cS @ X8 @ X7) = $true) | (((f @ X6 @ X8) != $true) | ((f @ X6 @ X7) != $true))) & ! [X10 : a,X9 : a,X11 : $i] : (((cR @ X10 @ X9) = $true) | (((f @ X9 @ X11) != $true) | ((f @ X10 @ X11) != $true))) & ! [X4 : a] : ? [X5 : $i] : ((f @ X4 @ X5) = $true))) & (! [X2 : a,X0 : a,X1 : a] : (((cR @ X2 @ X1) = $true) | (((cR @ X2 @ X0) != $true) | ((cR @ X1 @ X0) != $true))) & ! [X3 : a] : ((cR @ X3 @ X3) = $true))),
% 1.65/1.32 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.32 thf(f6,plain,(
% 1.65/1.32 ~((! [X2 : a,X0 : a,X1 : a] : ((((cR @ X2 @ X0) = $true) & ((cR @ X1 @ X0) = $true)) => ((cR @ X2 @ X1) = $true)) & ! [X3 : a] : ((cR @ X3 @ X3) = $true)) => ((! [X6 : a,X7 : $i,X8 : $i] : ((((f @ X6 @ X8) = $true) & ((f @ X6 @ X7) = $true)) => ((cS @ X8 @ X7) = $true)) & ! [X10 : a,X9 : a,X11 : $i] : ((((f @ X9 @ X11) = $true) & ((f @ X10 @ X11) = $true)) => ((cR @ X10 @ X9) = $true)) & ! [X4 : a] : ? [X5 : $i] : ((f @ X4 @ X5) = $true)) => (! [X17 : a] : ? [X18 : $i] : ! [X19 : a] : (((f @ X17 @ X18) = $true) | (((f @ X19 @ X18) != $true) & ((cR @ X17 @ z) = $true))) & ! [X13 : $i,X14 : a,X12 : a] : ((! [X15 : a] : (((f @ X14 @ X13) = $true) | (((f @ X15 @ X13) != $true) & ((cR @ X14 @ z) = $true))) & ! [X16 : a] : (((f @ X12 @ X13) = $true) | (((f @ X16 @ X13) != $true) & ((cR @ X12 @ z) = $true)))) => ((cR @ X14 @ X12) = $true)) & ! [X20 : $i] : ? [X21 : a] : ! [X22 : a] : (((f @ X21 @ X20) = $true) | (((cR @ X21 @ z) = $true) & ((f @ X22 @ X20) != $true))))))),
% 1.65/1.32 inference(flattening,[status(thm)],[f5])).
% 1.65/1.32 thf(f5,plain,(
% 1.65/1.32 ~((! [X2 : a,X0 : a,X1 : a] : ((((cR @ X2 @ X0) = $true) & ((cR @ X1 @ X0) = $true)) => ((cR @ X2 @ X1) = $true)) & ! [X3 : a] : ((cR @ X3 @ X3) = $true)) => ((! [X6 : a,X7 : $i,X8 : $i] : ((((f @ X6 @ X8) = $true) & ((f @ X6 @ X7) = $true)) => ((cS @ X8 @ X7) = $true)) & ! [X10 : a,X9 : a,X11 : $i] : ((((f @ X9 @ X11) = $true) & ((f @ X10 @ X11) = $true)) => ((cR @ X10 @ X9) = $true)) & ! [X4 : a] : ? [X5 : $i] : ((f @ X4 @ X5) = $true)) => (! [X12 : a,X13 : $i,X14 : a] : ((! [X15 : a] : ((~((f @ X15 @ X13) = $true) & ((cR @ X14 @ z) = $true)) | ((f @ X14 @ X13) = $true)) & ! [X16 : a] : ((~((f @ X16 @ X13) = $true) & ((cR @ X12 @ z) = $true)) | ((f @ X12 @ X13) = $true))) => ((cR @ X14 @ X12) = $true)) & ! [X17 : a] : ? [X18 : $i] : ! [X19 : a] : (((f @ X17 @ X18) = $true) | (((cR @ X17 @ z) = $true) & ~((f @ X19 @ X18) = $true))) & ! [X20 : $i] : ? [X21 : a] : ! [X22 : a] : ((~((f @ X22 @ X20) = $true) & ((cR @ X21 @ z) = $true)) | ((f @ X21 @ X20) = $true)))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.32 thf(f4,plain,(
% 1.65/1.32 ~((! [X0 : a,X1 : a,X2 : a] : (((cR @ X1 @ X0) & (cR @ X2 @ X0)) => (cR @ X2 @ X1)) & ! [X3 : a] : (cR @ X3 @ X3)) => ((! [X4 : a] : ? [X5 : $i] : (f @ X4 @ X5) & ! [X6 : a,X7 : $i,X8 : $i] : (((f @ X6 @ X8) & (f @ X6 @ X7)) => (cS @ X8 @ X7)) & ! [X9 : a,X10 : a,X11 : $i] : (((f @ X9 @ X11) & (f @ X10 @ X11)) => (cR @ X10 @ X9))) => (! [X12 : a,X13 : $i,X14 : a] : ((! [X15 : a] : ((~(f @ X15 @ X13) & (cR @ X14 @ z)) | (f @ X14 @ X13)) & ! [X16 : a] : ((~(f @ X16 @ X13) & (cR @ X12 @ z)) | (f @ X12 @ X13))) => (cR @ X14 @ X12)) & ! [X17 : a] : ? [X18 : $i] : ! [X19 : a] : ((f @ X17 @ X18) | ((cR @ X17 @ z) & ~(f @ X19 @ X18))) & ! [X20 : $i] : ? [X21 : a] : ! [X22 : a] : ((~(f @ X22 @ X20) & (cR @ X21 @ z)) | (f @ X21 @ X20)))))),
% 1.65/1.32 inference(rectify,[status(thm)],[f2])).
% 1.65/1.32 thf(f2,negated_conjecture,(
% 1.65/1.32 ~((! [X1 : a,X2 : a,X0 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2)) & ! [X3 : a] : (cR @ X3 @ X3)) => ((! [X3 : a] : ? [X4 : $i] : (f @ X3 @ X4) & ! [X3 : a,X6 : $i,X5 : $i] : (((f @ X3 @ X5) & (f @ X3 @ X6)) => (cS @ X5 @ X6)) & ! [X8 : a,X7 : a,X4 : $i] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8))) => (! [X8 : a,X4 : $i,X7 : a] : ((! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X7 @ z)) | (f @ X7 @ X4)) & ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X8 @ z)) | (f @ X8 @ X4))) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : ! [X2 : a] : ((f @ X3 @ X4) | ((cR @ X3 @ z) & ~(f @ X2 @ X4))) & ! [X4 : $i] : ? [X3 : a] : ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X3 @ z)) | (f @ X3 @ X4)))))),
% 1.65/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.32 thf(f1,conjecture,(
% 1.65/1.32 (! [X1 : a,X2 : a,X0 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2)) & ! [X3 : a] : (cR @ X3 @ X3)) => ((! [X3 : a] : ? [X4 : $i] : (f @ X3 @ X4) & ! [X3 : a,X6 : $i,X5 : $i] : (((f @ X3 @ X5) & (f @ X3 @ X6)) => (cS @ X5 @ X6)) & ! [X8 : a,X7 : a,X4 : $i] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8))) => (! [X8 : a,X4 : $i,X7 : a] : ((! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X7 @ z)) | (f @ X7 @ X4)) & ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X8 @ z)) | (f @ X8 @ X4))) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : ! [X2 : a] : ((f @ X3 @ X4) | ((cR @ X3 @ z) & ~(f @ X2 @ X4))) & ! [X4 : $i] : ? [X3 : a] : ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X3 @ z)) | (f @ X3 @ X4))))),
% 1.65/1.32 file('/export/starexec/sandbox2/tmp/tmp.vlsEED5hqn/DTF2THF_18979.p',cTHM552B_pme)).
% 1.65/1.32 thf(f130,plain,(
% 1.65/1.32 ( ! [X5 : a] : (((cR @ X5 @ z) != $true)) ) | (~spl9_3 | ~spl9_4)),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f49,f45])).
% 1.65/1.32 thf(f45,plain,(
% 1.65/1.32 ( ! [X5 : a] : (((f @ X5 @ sK4) != $true)) ) | ~spl9_3),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.65/1.32 thf(f44,definition,(
% 1.65/1.32 spl9_3 <=> ! [X5 : a] : ((f @ X5 @ sK4) != $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 1.65/1.32 thf(f49,plain,(
% 1.65/1.32 ( ! [X5 : a] : (((f @ (sK5 @ X5) @ sK4) = $true) | ((cR @ X5 @ z) != $true)) ) | ~spl9_4),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.65/1.32 thf(f48,definition,(
% 1.65/1.32 spl9_4 <=> ! [X5 : a] : (((f @ (sK5 @ X5) @ sK4) = $true) | ((cR @ X5 @ z) != $true))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition])).
% 1.65/1.32 thf(f129,plain,(
% 1.65/1.32 ~spl9_10 | spl9_11 | ~spl9_12),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.65/1.32 thf(f128,plain,(
% 1.65/1.32 $false | (~spl9_10 | spl9_11 | ~spl9_12)),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f127,f86])).
% 1.65/1.32 thf(f86,plain,(
% 1.65/1.32 ((cR @ sK1 @ z) = $true) | ~spl9_12),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.65/1.32 thf(f84,definition,(
% 1.65/1.32 spl9_12 <=> ((cR @ sK1 @ z) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_12])],[avatar_definition])).
% 1.65/1.32 thf(f127,plain,(
% 1.65/1.32 ((cR @ sK1 @ z) != $true) | (~spl9_10 | spl9_11)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.65/1.32 thf(f126,plain,(
% 1.65/1.32 ($true != $true) | ((cR @ sK1 @ z) != $true) | (~spl9_10 | spl9_11)),
% 1.65/1.32 inference(superposition,[status(thm)],[f93,f76])).
% 1.65/1.32 thf(f76,plain,(
% 1.65/1.32 ((cR @ sK3 @ z) = $true) | ~spl9_10),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.65/1.32 thf(f74,definition,(
% 1.65/1.32 spl9_10 <=> ((cR @ sK3 @ z) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_10])],[avatar_definition])).
% 1.65/1.32 thf(f93,plain,(
% 1.65/1.32 ( ! [X0 : a] : (((cR @ sK3 @ X0) != $true) | ((cR @ sK1 @ X0) != $true)) ) | spl9_11),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.65/1.32 thf(f92,plain,(
% 1.65/1.32 ( ! [X0 : a] : (((cR @ sK3 @ X0) != $true) | ((cR @ sK1 @ X0) != $true) | ($true != $true)) ) | spl9_11),
% 1.65/1.32 inference(superposition,[status(thm)],[f81,f27])).
% 1.65/1.32 thf(f27,plain,(
% 1.65/1.32 ( ! [X16 : a,X17 : a,X15 : a] : (((cR @ X16 @ X17) = $true) | ((cR @ X17 @ X15) != $true) | ((cR @ X16 @ X15) != $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.32 thf(f81,plain,(
% 1.65/1.32 ((cR @ sK3 @ sK1) != $true) | spl9_11),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f79])).
% 1.65/1.32 thf(f79,definition,(
% 1.65/1.32 spl9_11 <=> ((cR @ sK3 @ sK1) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition])).
% 1.65/1.32 thf(f125,plain,(
% 1.65/1.32 ~spl9_7 | ~spl9_8),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f124])).
% 1.65/1.32 thf(f124,plain,(
% 1.65/1.32 $false | (~spl9_7 | ~spl9_8)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.65/1.32 thf(f123,plain,(
% 1.65/1.32 ($true != $true) | (~spl9_7 | ~spl9_8)),
% 1.65/1.32 inference(superposition,[status(thm)],[f61,f65])).
% 1.65/1.32 thf(f65,plain,(
% 1.65/1.32 ((f @ sK1 @ sK2) = $true) | ~spl9_8),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.65/1.32 thf(f63,definition,(
% 1.65/1.32 spl9_8 <=> ((f @ sK1 @ sK2) = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_8])],[avatar_definition])).
% 1.65/1.32 thf(f122,plain,(
% 1.65/1.32 ~spl9_8 | ~spl9_9 | spl9_11),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f121])).
% 1.65/1.32 thf(f121,plain,(
% 1.65/1.32 $false | (~spl9_8 | ~spl9_9 | spl9_11)),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f119,f65])).
% 1.65/1.32 thf(f119,plain,(
% 1.65/1.32 ((f @ sK1 @ sK2) != $true) | (~spl9_9 | spl9_11)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.65/1.32 thf(f117,plain,(
% 1.65/1.32 ((f @ sK1 @ sK2) != $true) | ($true != $true) | (~spl9_9 | spl9_11)),
% 1.65/1.32 inference(superposition,[status(thm)],[f112,f71])).
% 1.65/1.32 thf(f112,plain,(
% 1.65/1.32 ( ! [X0 : $i] : (((f @ sK3 @ X0) != $true) | ((f @ sK1 @ X0) != $true)) ) | spl9_11),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.65/1.32 thf(f109,plain,(
% 1.65/1.32 ( ! [X0 : $i] : (((f @ sK3 @ X0) != $true) | ($true != $true) | ((f @ sK1 @ X0) != $true)) ) | spl9_11),
% 1.65/1.32 inference(superposition,[status(thm)],[f98,f28])).
% 1.65/1.32 thf(f28,plain,(
% 1.65/1.32 ( ! [X14 : a,X12 : a,X13 : $i] : (((cR @ X12 @ X14) = $true) | ((f @ X12 @ X13) != $true) | ((f @ X14 @ X13) != $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.32 thf(f98,plain,(
% 1.65/1.32 ((cR @ sK1 @ sK3) != $true) | spl9_11),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.65/1.32 thf(f95,plain,(
% 1.65/1.32 ((cR @ sK1 @ sK3) != $true) | ($true != $true) | spl9_11),
% 1.65/1.32 inference(superposition,[status(thm)],[f93,f34])).
% 1.65/1.32 thf(f90,plain,(
% 1.65/1.32 ~spl9_2),
% 1.65/1.32 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 1.65/1.32 thf(f89,plain,(
% 1.65/1.32 $false | ~spl9_2),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.65/1.32 thf(f88,plain,(
% 1.65/1.32 ($true != $true) | ~spl9_2),
% 1.65/1.32 inference(superposition,[status(thm)],[f42,f29])).
% 1.65/1.32 thf(f29,plain,(
% 1.65/1.32 ( ! [X10 : a] : (((f @ X10 @ (sK8 @ X10)) = $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.32 thf(f42,plain,(
% 1.65/1.32 ( ! [X8 : $i] : (($true != (f @ sK6 @ X8))) ) | ~spl9_2),
% 1.65/1.32 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.65/1.32 thf(f41,definition,(
% 1.65/1.32 spl9_2 <=> ! [X8 : $i] : ($true != (f @ sK6 @ X8))),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 1.65/1.32 thf(f87,plain,(
% 1.65/1.32 spl9_12 | ~spl9_1 | spl9_8),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f25,f63,f37,f84])).
% 1.65/1.32 thf(f37,definition,(
% 1.65/1.32 spl9_1 <=> (sP0 = $true)),
% 1.65/1.32 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 1.65/1.32 thf(f25,plain,(
% 1.65/1.32 (sP0 != $true) | ((cR @ sK1 @ z) = $true) | ((f @ sK1 @ sK2) = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.32 thf(f14,plain,(
% 1.65/1.32 (! [X3 : a] : (((f @ sK1 @ sK2) = $true) | (((f @ X3 @ sK2) != $true) & ((cR @ sK1 @ z) = $true))) & ! [X4 : a] : (((f @ sK3 @ sK2) = $true) | (((f @ X4 @ sK2) != $true) & ((cR @ sK3 @ z) = $true))) & ((cR @ sK3 @ sK1) != $true)) | (sP0 != $true)),
% 1.65/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f12,f13])).
% 1.65/1.32 thf(f13,plain,(
% 1.65/1.32 ? [X0 : a,X1 : $i,X2 : a] : (! [X3 : a] : (($true = (f @ X0 @ X1)) | (((f @ X3 @ X1) != $true) & ((cR @ X0 @ z) = $true))) & ! [X4 : a] : (((f @ X2 @ X1) = $true) | (((f @ X4 @ X1) != $true) & ($true = (cR @ X2 @ z)))) & ((cR @ X2 @ X0) != $true)) => (! [X3 : a] : (((f @ sK1 @ sK2) = $true) | (((f @ X3 @ sK2) != $true) & ((cR @ sK1 @ z) = $true))) & ! [X4 : a] : (((f @ sK3 @ sK2) = $true) | (((f @ X4 @ sK2) != $true) & ((cR @ sK3 @ z) = $true))) & ((cR @ sK3 @ sK1) != $true))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f12,plain,(
% 1.65/1.32 ? [X0 : a,X1 : $i,X2 : a] : (! [X3 : a] : (($true = (f @ X0 @ X1)) | (((f @ X3 @ X1) != $true) & ((cR @ X0 @ z) = $true))) & ! [X4 : a] : (((f @ X2 @ X1) = $true) | (((f @ X4 @ X1) != $true) & ($true = (cR @ X2 @ z)))) & ((cR @ X2 @ X0) != $true)) | (sP0 != $true)),
% 1.65/1.32 inference(rectify,[status(thm)],[f11])).
% 1.65/1.32 thf(f11,plain,(
% 1.65/1.32 ? [X12 : a,X13 : $i,X14 : a] : (! [X16 : a] : (((f @ X12 @ X13) = $true) | (((f @ X16 @ X13) != $true) & ((cR @ X12 @ z) = $true))) & ! [X15 : a] : (((f @ X14 @ X13) = $true) | (((f @ X15 @ X13) != $true) & ((cR @ X14 @ z) = $true))) & ((cR @ X14 @ X12) != $true)) | (sP0 != $true)),
% 1.65/1.32 inference(nnf_transformation,[status(thm)],[f9])).
% 1.65/1.32 thf(f82,plain,(
% 1.65/1.32 ~spl9_11 | ~spl9_1),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f22,f37,f79])).
% 1.65/1.32 thf(f22,plain,(
% 1.65/1.32 (sP0 != $true) | ((cR @ sK3 @ sK1) != $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.32 thf(f77,plain,(
% 1.65/1.32 spl9_9 | ~spl9_1 | spl9_10),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f23,f74,f37,f69])).
% 1.65/1.32 thf(f23,plain,(
% 1.65/1.32 ((cR @ sK3 @ z) = $true) | ((f @ sK3 @ sK2) = $true) | (sP0 != $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.32 thf(f72,plain,(
% 1.65/1.32 spl9_7 | spl9_9 | ~spl9_1),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f24,f37,f69,f60])).
% 1.65/1.32 thf(f24,plain,(
% 1.65/1.32 ( ! [X4 : a] : (((f @ X4 @ sK2) != $true) | (sP0 != $true) | ((f @ sK3 @ sK2) = $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.32 thf(f66,plain,(
% 1.65/1.32 spl9_7 | ~spl9_1 | spl9_8),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f26,f63,f37,f60])).
% 1.65/1.32 thf(f26,plain,(
% 1.65/1.32 ( ! [X3 : a] : (((f @ sK1 @ sK2) = $true) | (sP0 != $true) | ((f @ X3 @ sK2) != $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.32 thf(f50,plain,(
% 1.65/1.32 spl9_2 | spl9_1 | spl9_4),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f31,f48,f37,f41])).
% 1.65/1.32 thf(f31,plain,(
% 1.65/1.32 ( ! [X8 : $i,X5 : a] : (((f @ (sK5 @ X5) @ sK4) = $true) | ((cR @ X5 @ z) != $true) | ($true != (f @ sK6 @ X8)) | (sP0 = $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.32 thf(f46,plain,(
% 1.65/1.32 spl9_1 | spl9_2 | spl9_3),
% 1.65/1.32 inference(avatar_split_clause,[status(thm)],[f33,f44,f41,f37])).
% 1.65/1.32 thf(f33,plain,(
% 1.65/1.32 ( ! [X8 : $i,X5 : a] : (($true != (f @ sK6 @ X8)) | (sP0 = $true) | ((f @ X5 @ sK4) != $true)) )),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.32 % SZS output end Proof for DTF2THF_18979
% 1.65/1.32 % (19146)------------------------------
% 1.65/1.32 % (19146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (19146)Termination reason: Refutation
% 1.65/1.32
% 1.65/1.32 % (19146)Memory used [KB]: 5628
% 1.65/1.32 % (19146)Time elapsed: 0.009 s
% 1.65/1.32 % (19146)Instructions burned: 13 (million)
% 1.65/1.32 % (19146)------------------------------
% 1.65/1.32 % (19146)------------------------------
% 1.65/1.32 % (19145)Success in time 0.019 s
%------------------------------------------------------------------------------