%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV104^5 : 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 : 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 09:40:17 AM UTC 2026
% Result : Theorem 1.70s 1.33s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 3 unt; 0 typ; 5 def)
% Number of atoms : 636 ( 175 equ; 0 cnn)
% Maximal formula atoms : 18 ( 11 avg)
% Number of connectives : 794 ( 117 ~; 105 |; 89 &; 446 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 177 ( 0 ^; 156 !; 21 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
cR: a > a > $o ).
thf(func_def_3,type,
z: a ).
thf(func_def_4,type,
f: a > b > $o ).
thf(func_def_5,type,
cS: b > b > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: b ).
thf(func_def_11,type,
sK2: a ).
thf(func_def_12,type,
sK3: a > b ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f30,f39,f44,f45,f80,f83,f111,f113]) ).
thf(f113,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f29,f25]) ).
thf(f25,plain,
( ! [X7: a] :
( $true
!= ( f @ X7 @ sK1 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl4_1
<=> ! [X7: a] :
( $true
!= ( f @ X7 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
= ( f @ sK0 @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl4_2
<=> ( $true
= ( f @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f111,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(subsumption_resolution,[status(thm)],[f109,f16]) ).
thf(f16,plain,
( $true
!= ( cR @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X1: a,X2: a,X3: b] :
( ( ( f @ X1 @ X3 )
!= $true )
| ( $true
!= ( f @ X2 @ X3 ) )
| ( $true
= ( cR @ X1 @ X2 ) ) )
& ! [X7: a] :
( ( ( $true
= ( cR @ sK0 @ z ) )
& ( $true
!= ( f @ X7 @ sK1 ) ) )
| ( $true
= ( f @ sK0 @ sK1 ) ) )
& ! [X8: a] :
( ( $true
= ( f @ sK2 @ sK1 ) )
| ( ( $true
!= ( f @ X8 @ sK1 ) )
& ( $true
= ( cR @ sK2 @ z ) ) ) )
& ( $true
!= ( cR @ sK0 @ sK2 ) )
& ! [X9: a,X10: a,X11: a] :
( ( $true
!= ( cR @ X9 @ X10 ) )
| ( $true
!= ( cR @ X11 @ X10 ) )
| ( $true
= ( cR @ X11 @ X9 ) ) )
& ! [X12: a] :
( $true
= ( f @ X12 @ ( sK3 @ X12 ) ) )
& ! [X14: b,X15: b,X16: a] :
( ( $true
!= ( f @ X16 @ X15 ) )
| ( $true
!= ( f @ X16 @ X14 ) )
| ( $true
= ( cS @ X14 @ X15 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X4: a,X5: b,X6: a] :
( ! [X7: a] :
( ( ( $true
= ( cR @ X4 @ z ) )
& ( $true
!= ( f @ X7 @ X5 ) ) )
| ( $true
= ( f @ X4 @ X5 ) ) )
& ! [X8: a] :
( ( $true
= ( f @ X6 @ X5 ) )
| ( ( $true
!= ( f @ X8 @ X5 ) )
& ( $true
= ( cR @ X6 @ z ) ) ) )
& ( $true
!= ( cR @ X4 @ X6 ) ) )
=> ( ! [X7: a] :
( ( ( $true
= ( cR @ sK0 @ z ) )
& ( $true
!= ( f @ X7 @ sK1 ) ) )
| ( $true
= ( f @ sK0 @ sK1 ) ) )
& ! [X8: a] :
( ( $true
= ( f @ sK2 @ sK1 ) )
| ( ( $true
!= ( f @ X8 @ sK1 ) )
& ( $true
= ( cR @ sK2 @ z ) ) ) )
& ( $true
!= ( cR @ sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X12: a] :
( ? [X13: b] :
( $true
= ( f @ X12 @ X13 ) )
=> ( $true
= ( f @ X12 @ ( sK3 @ X12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X1: a,X2: a,X3: b] :
( ( ( f @ X1 @ X3 )
!= $true )
| ( $true
!= ( f @ X2 @ X3 ) )
| ( $true
= ( cR @ X1 @ X2 ) ) )
& ? [X4: a,X5: b,X6: a] :
( ! [X7: a] :
( ( ( $true
= ( cR @ X4 @ z ) )
& ( $true
!= ( f @ X7 @ X5 ) ) )
| ( $true
= ( f @ X4 @ X5 ) ) )
& ! [X8: a] :
( ( $true
= ( f @ X6 @ X5 ) )
| ( ( $true
!= ( f @ X8 @ X5 ) )
& ( $true
= ( cR @ X6 @ z ) ) ) )
& ( $true
!= ( cR @ X4 @ X6 ) ) )
& ! [X9: a,X10: a,X11: a] :
( ( $true
!= ( cR @ X9 @ X10 ) )
| ( $true
!= ( cR @ X11 @ X10 ) )
| ( $true
= ( cR @ X11 @ X9 ) ) )
& ! [X12: a] :
? [X13: b] :
( $true
= ( f @ X12 @ X13 ) )
& ! [X14: b,X15: b,X16: a] :
( ( $true
!= ( f @ X16 @ X15 ) )
| ( $true
!= ( f @ X16 @ X14 ) )
| ( $true
= ( cS @ X14 @ X15 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) )
& ! [X5: a,X6: a,X4: b] :
( ( $true
!= ( f @ X5 @ X4 ) )
| ( $true
!= ( f @ X6 @ X4 ) )
| ( $true
= ( cR @ X5 @ X6 ) ) )
& ? [X13: a,X12: b,X14: a] :
( ! [X15: a] :
( ( ( $true
= ( cR @ X13 @ z ) )
& ( $true
!= ( f @ X15 @ X12 ) ) )
| ( $true
= ( f @ X13 @ X12 ) ) )
& ! [X16: a] :
( ( $true
= ( f @ X14 @ X12 ) )
| ( ( $true
!= ( f @ X16 @ X12 ) )
& ( $true
= ( cR @ X14 @ z ) ) ) )
& ( $true
!= ( cR @ X13 @ X14 ) ) )
& ! [X1: a,X3: a,X2: a] :
( ( $true
!= ( cR @ X1 @ X3 ) )
| ( $true
!= ( cR @ X2 @ X3 ) )
| ( ( cR @ X2 @ X1 )
= $true ) )
& ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) )
& ! [X10: b,X11: b,X9: a] :
( ( $true
!= ( f @ X9 @ X11 ) )
| ( $true
!= ( f @ X9 @ X10 ) )
| ( $true
= ( cS @ X10 @ X11 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X12: b,X14: a,X13: a] :
( ( $true
!= ( cR @ X13 @ X14 ) )
& ! [X16: a] :
( ( $true
= ( f @ X14 @ X12 ) )
| ( ( $true
!= ( f @ X16 @ X12 ) )
& ( $true
= ( cR @ X14 @ z ) ) ) )
& ! [X15: a] :
( ( ( $true
= ( cR @ X13 @ z ) )
& ( $true
!= ( f @ X15 @ X12 ) ) )
| ( $true
= ( f @ X13 @ X12 ) ) ) )
& ! [X5: a,X4: b,X6: a] :
( ( $true
= ( cR @ X5 @ X6 ) )
| ( $true
!= ( f @ X5 @ X4 ) )
| ( $true
!= ( f @ X6 @ X4 ) ) )
& ! [X11: b,X10: b,X9: a] :
( ( $true
= ( cS @ X10 @ X11 ) )
| ( $true
!= ( f @ X9 @ X11 ) )
| ( $true
!= ( f @ X9 @ X10 ) ) )
& ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) )
& ! [X1: a,X2: a,X3: a] :
( ( ( cR @ X2 @ X1 )
= $true )
| ( $true
!= ( cR @ X2 @ X3 ) )
| ( $true
!= ( cR @ X1 @ X3 ) ) )
& ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X1: a,X2: a,X3: a] :
( ( ( $true
= ( cR @ X2 @ X3 ) )
& ( $true
= ( cR @ X1 @ X3 ) ) )
=> ( ( cR @ X2 @ X1 )
= $true ) )
& ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) ) )
=> ( ( ! [X5: a,X4: b,X6: a] :
( ( ( $true
= ( f @ X5 @ X4 ) )
& ( $true
= ( f @ X6 @ X4 ) ) )
=> ( $true
= ( cR @ X5 @ X6 ) ) )
& ! [X11: b,X10: b,X9: a] :
( ( ( $true
= ( f @ X9 @ X11 ) )
& ( $true
= ( f @ X9 @ X10 ) ) )
=> ( $true
= ( cS @ X10 @ X11 ) ) )
& ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) ) )
=> ! [X12: b,X14: a,X13: a] :
( ( ! [X16: a] :
( ( $true
= ( f @ X14 @ X12 ) )
| ( ( $true
!= ( f @ X16 @ X12 ) )
& ( $true
= ( cR @ X14 @ z ) ) ) )
& ! [X15: a] :
( ( ( $true
= ( cR @ X13 @ z ) )
& ( $true
!= ( f @ X15 @ X12 ) ) )
| ( $true
= ( f @ X13 @ X12 ) ) ) )
=> ( $true
= ( cR @ X13 @ X14 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X1: a,X2: a,X3: a] :
( ( ( $true
= ( cR @ X2 @ X3 ) )
& ( $true
= ( cR @ X1 @ X3 ) ) )
=> ( ( cR @ X2 @ X1 )
= $true ) )
& ! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) ) )
=> ( ( ! [X5: a,X4: b,X6: a] :
( ( ( $true
= ( f @ X5 @ X4 ) )
& ( $true
= ( f @ X6 @ X4 ) ) )
=> ( $true
= ( cR @ X5 @ X6 ) ) )
& ! [X11: b,X10: b,X9: a] :
( ( ( $true
= ( f @ X9 @ X11 ) )
& ( $true
= ( f @ X9 @ X10 ) ) )
=> ( $true
= ( cS @ X10 @ X11 ) ) )
& ! [X7: a] :
? [X8: b] :
( $true
= ( f @ X7 @ X8 ) ) )
=> ! [X12: b,X13: a,X14: a] :
( ( ! [X15: a] :
( ( ( $true
= ( cR @ X13 @ z ) )
& ( $true
!= ( f @ X15 @ X12 ) ) )
| ( $true
= ( f @ X13 @ X12 ) ) )
& ! [X16: a] :
( ( ( $true
!= ( f @ X16 @ X12 ) )
& ( $true
= ( cR @ X14 @ z ) ) )
| ( $true
= ( f @ X14 @ X12 ) ) ) )
=> ( $true
= ( cR @ X13 @ X14 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a] : ( cR @ X0 @ X0 )
& ! [X1: a,X2: a,X3: a] :
( ( ( cR @ X2 @ X3 )
& ( cR @ X1 @ X3 ) )
=> ( cR @ X2 @ X1 ) ) )
=> ( ( ! [X4: b,X5: a,X6: a] :
( ( ( f @ X6 @ X4 )
& ( f @ X5 @ X4 ) )
=> ( cR @ X5 @ X6 ) )
& ! [X7: a] :
? [X8: b] : ( f @ X7 @ X8 )
& ! [X9: a,X10: b,X11: b] :
( ( ( f @ X9 @ X11 )
& ( f @ X9 @ X10 ) )
=> ( cS @ X10 @ X11 ) ) )
=> ! [X12: b,X13: a,X14: a] :
( ( ! [X15: a] :
( ( ( cR @ X13 @ z )
& ~ ( f @ X15 @ X12 ) )
| ( f @ X13 @ X12 ) )
& ! [X16: a] :
( ( ~ ( f @ X16 @ X12 )
& ( cR @ X14 @ z ) )
| ( f @ X14 @ X12 ) ) )
=> ( cR @ X13 @ X14 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a] : ( cR @ X3 @ X3 )
& ! [X2: a,X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X2 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ( ! [X4: b,X7: a,X8: a] :
( ( ( f @ X8 @ X4 )
& ( f @ X7 @ X4 ) )
=> ( cR @ X7 @ X8 ) )
& ! [X3: a] :
? [X4: b] : ( f @ X3 @ X4 )
& ! [X3: a,X5: b,X6: b] :
( ( ( f @ X3 @ X6 )
& ( f @ X3 @ X5 ) )
=> ( cS @ X5 @ X6 ) ) )
=> ! [X4: b,X7: a,X8: a] :
( ( ! [X2: a] :
( ( ( cR @ X7 @ z )
& ~ ( f @ X2 @ X4 ) )
| ( f @ X7 @ X4 ) )
& ! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X8 @ z ) )
| ( f @ X8 @ X4 ) ) )
=> ( cR @ X7 @ X8 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: a] : ( cR @ X3 @ X3 )
& ! [X2: a,X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
& ( cR @ X2 @ X1 ) )
=> ( cR @ X0 @ X2 ) ) )
=> ( ( ! [X4: b,X7: a,X8: a] :
( ( ( f @ X8 @ X4 )
& ( f @ X7 @ X4 ) )
=> ( cR @ X7 @ X8 ) )
& ! [X3: a] :
? [X4: b] : ( f @ X3 @ X4 )
& ! [X3: a,X5: b,X6: b] :
( ( ( f @ X3 @ X6 )
& ( f @ X3 @ X5 ) )
=> ( cS @ X5 @ X6 ) ) )
=> ! [X4: b,X7: a,X8: a] :
( ( ! [X2: a] :
( ( ( cR @ X7 @ z )
& ~ ( f @ X2 @ X4 ) )
| ( f @ X7 @ X4 ) )
& ! [X2: a] :
( ( ~ ( f @ X2 @ X4 )
& ( cR @ X8 @ z ) )
| ( f @ X8 @ X4 ) ) )
=> ( cR @ X7 @ X8 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E7fv4ZgOzU/DTF2THF_18939.p',cTHM552D_pme) ).
thf(f109,plain,
( ( $true
= ( cR @ sK0 @ sK2 ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true != $true )
| ( $true
= ( cR @ sK0 @ sK2 ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f67,f103]) ).
thf(f103,plain,
( ( $true
= ( cR @ sK2 @ sK0 ) )
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true
= ( cR @ sK2 @ sK0 ) )
| ( $true != $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f87,f43]) ).
thf(f43,plain,
( ( $true
= ( cR @ sK0 @ z ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl4_5
<=> ( $true
= ( cR @ sK0 @ z ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f87,plain,
( ! [X0: a] :
( ( $true
!= ( cR @ X0 @ z ) )
| ( $true
= ( cR @ sK2 @ X0 ) ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X0: a] :
( ( $true
!= ( cR @ X0 @ z ) )
| ( $true
= ( cR @ sK2 @ X0 ) )
| ( $true != $true ) )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f15,f34]) ).
thf(f34,plain,
( ( $true
= ( cR @ sK2 @ z ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl4_3
<=> ( $true
= ( cR @ sK2 @ z ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f15,plain,
! [X10: a,X11: a,X9: a] :
( ( $true
!= ( cR @ X11 @ X10 ) )
| ( $true
= ( cR @ X11 @ X9 ) )
| ( $true
!= ( cR @ X9 @ X10 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f67,plain,
! [X0: a,X1: a] :
( ( $true
!= ( cR @ X1 @ X0 ) )
| ( ( cR @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
!= ( cR @ X1 @ X0 ) )
| ( ( cR @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f15,f22]) ).
thf(f22,plain,
! [X0: a] :
( $true
= ( cR @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f83,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ~ spl4_1
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f25,f38]) ).
thf(f38,plain,
( ( $true
= ( f @ sK2 @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl4_4
<=> ( $true
= ( f @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f80,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f78,f16]) ).
thf(f78,plain,
( ( $true
= ( cR @ sK0 @ sK2 ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true != $true )
| ( $true
= ( cR @ sK0 @ sK2 ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f72,f29]) ).
thf(f72,plain,
( ! [X0: a] :
( ( $true
!= ( f @ X0 @ sK1 ) )
| ( $true
= ( cR @ X0 @ sK2 ) ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true
!= ( f @ X0 @ sK1 ) )
| ( $true
= ( cR @ X0 @ sK2 ) ) )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f21,f38]) ).
thf(f21,plain,
! [X2: a,X3: b,X1: a] :
( ( $true
!= ( f @ X2 @ X3 ) )
| ( ( f @ X1 @ X3 )
!= $true )
| ( $true
= ( cR @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f45,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f18,f24,f36]) ).
thf(f18,plain,
! [X8: a] :
( ( $true
= ( f @ sK2 @ sK1 ) )
| ( $true
!= ( f @ X8 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f44,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f27,f41]) ).
thf(f20,plain,
( ( $true
= ( f @ sK0 @ sK1 ) )
| ( $true
= ( cR @ sK0 @ z ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f39,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f17,f36,f32]) ).
thf(f17,plain,
( ( $true
= ( f @ sK2 @ sK1 ) )
| ( $true
= ( cR @ sK2 @ z ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f30,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f27,f24]) ).
thf(f19,plain,
! [X7: a] :
( ( $true
!= ( f @ X7 @ sK1 ) )
| ( $true
= ( f @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV104^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n019.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 12:40:24 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
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SEV104^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.44 % Domain : Set Theory (Relations)
% 0.19/0.44 % Problem : TPS problem from RELN-THMS
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro09]
% 0.19/0.44 % Names : tps_1108 [Bro09]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % 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
% 0.19/0.44 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.19/0.44 % Number of atoms : 18 ( 0 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 18 ( 18 avg)
% 0.19/0.44 % Number of connectives : 55 ( 2 ~; 2 |; 9 &; 36 @)
% 0.19/0.44 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 14 ( 14 avg)
% 0.19/0.44 % Number of types : 3 ( 2 usr)
% 0.19/0.44 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.19/0.44 % Number of variables : 17 ( 0 ^; 16 !; 1 ?; 17 :)
% 0.19/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(a_type,type,
% 0.19/0.44 a: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(b_type,type,
% 0.19/0.44 b: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(cR,type,
% 0.19/0.44 cR: a > a > $o ).
% 0.19/0.44
% 0.19/0.44 thf(z,type,
% 0.19/0.44 z: a ).
% 0.19/0.44
% 0.19/0.44 thf(f,type,
% 0.19/0.44 f: a > b > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cS,type,
% 0.19/0.44 cS: b > b > $o ).
% 0.19/0.44
% 0.19/0.44 thf(cTHM552D_pme,conjecture,
% 0.19/0.44 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 0.19/0.44 ( ( ( cR @ Xu @ Xv )
% 0.19/0.44 & ( cR @ Xw @ Xv ) )
% 0.19/0.44 => ( cR @ Xu @ Xw ) )
% 0.19/0.44 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 0.19/0.44 => ( ( ! [Xx: a] :
% 0.19/0.44 ? [Xy: b] : ( f @ Xx @ Xy )
% 0.19/0.44 & ! [Xx: a,Xy1: b,Xy2: b] :
% 0.19/0.44 ( ( ( f @ Xx @ Xy1 )
% 0.19/0.44 & ( f @ Xx @ Xy2 ) )
% 0.19/0.44 => ( cS @ Xy1 @ Xy2 ) )
% 0.19/0.44 & ! [Xx1: a,Xx2: a,Xy: b] :
% 0.19/0.44 ( ( ( f @ Xx1 @ Xy )
% 0.19/0.44 & ( f @ Xx2 @ Xy ) )
% 0.19/0.44 => ( cR @ Xx1 @ Xx2 ) ) )
% 0.19/0.44 => ! [Xy: b,Xx1: a,Xx2: a] :
% 0.19/0.44 ( ( ! [Xw: a] :
% 0.19/0.44 ( ( f @ Xx1 @ Xy )
% 0.19/0.44 | ( ~ ( f @ Xw @ Xy )
% 0.19/0.44 & ( cR @ Xx1 @ z ) ) )
% 0.19/0.44 & ! [Xw: a] :
% 0.19/0.44 ( ( f @ Xx2 @ Xy )
% 0.19/0.44 | ( ~ ( f @ Xw @ Xy )
% 0.19/0.44 & ( cR @ Xx2 @ z ) ) ) )
% 0.19/0.44 => ( cR @ Xx1 @ Xx2 ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.53/1.28 ---- Embedded in THF ---
% 1.53/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.29 %%% Generated on Tue Feb 24 12:40:25 EST 2026
% 1.53/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.29 %%% Logic specification used:
% 1.53/1.29 %%% thf(spec, logic, $$dhol).
% 1.53/1.29
% 1.53/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.E7fv4ZgOzU/DTF2DTF18939.p
% See solution above
% 1.53/1.29 ------------------------
% 1.70/1.30 ---- Cleaned THF ---
% 1.70/1.30 thf(a_type,type,
% 1.70/1.30 a: $tType ).
% 1.70/1.30
% 1.70/1.30 thf(b_type,type,
% 1.70/1.30 b: $tType ).
% 1.70/1.30
% 1.70/1.30 thf(cR,type,
% 1.70/1.30 cR: a > a > $o ).
% 1.70/1.30
% 1.70/1.30 thf(z,type,
% 1.70/1.30 z: a ).
% 1.70/1.30
% 1.70/1.30 thf(f,type,
% 1.70/1.30 f: a > b > $o ).
% 1.70/1.30
% 1.70/1.30 thf(cS,type,
% 1.70/1.30 cS: b > b > $o ).
% 1.70/1.30
% 1.70/1.30 thf(cTHM552D_pme,conjecture,
% 1.70/1.30 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 1.70/1.30 ( ( ( cR @ Xu @ Xv )
% 1.70/1.30 & ( cR @ Xw @ Xv ) )
% 1.70/1.30 => ( cR @ Xu @ Xw ) )
% 1.70/1.30 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 1.70/1.30 => ( ( ! [Xx: a] :
% 1.70/1.30 ? [Xy: b] : ( f @ Xx @ Xy )
% 1.70/1.30 & ! [Xx: a,Xy1: b,Xy2: b] :
% 1.70/1.30 ( ( ( f @ Xx @ Xy1 )
% 1.70/1.30 & ( f @ Xx @ Xy2 ) )
% 1.70/1.30 => ( cS @ Xy1 @ Xy2 ) )
% 1.70/1.30 & ! [Xx1: a,Xx2: a,Xy: b] :
% 1.70/1.30 ( ( ( f @ Xx1 @ Xy )
% 1.70/1.30 & ( f @ Xx2 @ Xy ) )
% 1.70/1.30 => ( cR @ Xx1 @ Xx2 ) ) )
% 1.70/1.30 => ! [Xy: b,Xx1: a,Xx2: a] :
% 1.70/1.30 ( ( ! [Xw: a] :
% 1.70/1.30 ( ( f @ Xx1 @ Xy )
% 1.70/1.30 | ( ~ ( f @ Xw @ Xy )
% 1.70/1.30 & ( cR @ Xx1 @ z ) ) )
% 1.70/1.30 & ! [Xw: a] :
% 1.70/1.30 ( ( f @ Xx2 @ Xy )
% 1.70/1.30 | ( ~ ( f @ Xw @ Xy )
% 1.70/1.30 & ( cR @ Xx2 @ z ) ) ) )
% 1.70/1.30 => ( cR @ Xx1 @ Xx2 ) ) ) ) ).
% 1.70/1.30 ------------------------
% 1.70/1.31 % (19128)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_18939 for (2999ds/4Mi)
% 1.70/1.31 % (19131)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_18939 for (2999ds/2Mi)
% 1.70/1.31 % (19130)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18939 for (2999ds/2Mi)
% 1.70/1.31 % (19131)Instruction limit reached!
% 1.70/1.31 % (19131)------------------------------
% 1.70/1.31 % (19131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.31 % (19131)Termination reason: Unknown
% 1.70/1.31 % (19131)Termination phase: Saturation
% 1.70/1.31
% 1.70/1.31 % (19131)Memory used [KB]: 1023
% 1.70/1.31 % (19131)Time elapsed: 0.002 s
% 1.70/1.31 % (19131)Instructions burned: 3 (million)
% 1.70/1.31 % (19131)------------------------------
% 1.70/1.31 % (19131)------------------------------
% 1.70/1.31 % (19128)Instruction limit reached!
% 1.70/1.31 % (19128)------------------------------
% 1.70/1.31 % (19128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.31 % (19128)Termination reason: Unknown
% 1.70/1.31 % (19128)Termination phase: Saturation
% 1.70/1.31
% 1.70/1.31 % (19128)Memory used [KB]: 5500
% 1.70/1.31 % (19128)Time elapsed: 0.003 s
% 1.70/1.31 % (19128)Instructions burned: 4 (million)
% 1.70/1.31 % (19128)------------------------------
% 1.70/1.31 % (19128)------------------------------
% 1.70/1.31 % (19130)Instruction limit reached!
% 1.70/1.31 % (19130)------------------------------
% 1.70/1.31 % (19130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.31 % (19130)Termination reason: Unknown
% 1.70/1.31 % (19130)Termination phase: Saturation
% 1.70/1.31
% 1.70/1.31 % (19130)Memory used [KB]: 5500
% 1.70/1.31 % (19130)Time elapsed: 0.002 s
% 1.70/1.31 % (19130)Instructions burned: 3 (million)
% 1.70/1.31 % (19130)------------------------------
% 1.70/1.31 % (19130)------------------------------
% 1.70/1.32 % (19133)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18939 for (2999ds/18Mi)
% 1.70/1.32 % (19127)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18939 for (2999ds/183Mi)
% 1.70/1.32 % (19129)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_18939 for (2999ds/27Mi)
% 1.70/1.32 % (19132)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_18939 for (2999ds/275Mi)
% 1.70/1.32 % (19134)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18939 for (2999ds/3Mi)
% 1.70/1.32 % (19133)First to succeed.
% 1.70/1.32 % (19135)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_18939 for (2999ds/37Mi)
% 1.70/1.32 % (19134)Instruction limit reached!
% 1.70/1.32 % (19134)------------------------------
% 1.70/1.32 % (19134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.32 % (19134)Termination reason: Unknown
% 1.70/1.32 % (19134)Termination phase: Saturation
% 1.70/1.32
% 1.70/1.32 % (19134)Memory used [KB]: 1023
% 1.70/1.32 % (19134)Time elapsed: 0.002 s
% 1.70/1.32 % (19134)Instructions burned: 3 (million)
% 1.70/1.32 % (19134)------------------------------
% 1.70/1.32 % (19134)------------------------------
% 1.70/1.32 % (19136)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_18939 for (2999ds/15Mi)
% 1.70/1.33 % (19133)Refutation found. Thanks to Tanya!
% 1.70/1.33 % SZS status Theorem for DTF2THF_18939
% 1.70/1.33 % SZS output start Proof for DTF2THF_18939
% 1.70/1.33 thf(type_def_5, type, a: $tType).
% 1.70/1.33 thf(type_def_7, type, b: $tType).
% 1.70/1.33 thf(func_def_0, type, a: $tType).
% 1.70/1.33 thf(func_def_1, type, b: $tType).
% 1.70/1.33 thf(func_def_2, type, cR: a > a > $o).
% 1.70/1.33 thf(func_def_3, type, z: a).
% 1.70/1.33 thf(func_def_4, type, f: a > b > $o).
% 1.70/1.33 thf(func_def_5, type, cS: b > b > $o).
% 1.70/1.33 thf(func_def_9, type, sK0: a).
% 1.70/1.33 thf(func_def_10, type, sK1: b).
% 1.70/1.33 thf(func_def_11, type, sK2: a).
% 1.70/1.33 thf(func_def_12, type, sK3: a > b).
% 1.70/1.33 thf(f114,plain,(
% 1.70/1.33 $false),
% 1.70/1.33 inference(avatar_sat_refutation,[status(thm)],[f30,f39,f44,f45,f80,f83,f111,f113])).
% 1.70/1.33 thf(f113,plain,(
% 1.70/1.33 ~spl4_1 | ~spl4_2),
% 1.70/1.33 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 1.70/1.33 thf(f112,plain,(
% 1.70/1.33 $false | (~spl4_1 | ~spl4_2)),
% 1.70/1.33 inference(subsumption_resolution,[status(thm)],[f29,f25])).
% 1.70/1.33 thf(f25,plain,(
% 1.70/1.33 ( ! [X7 : a] : (($true != (f @ X7 @ sK1))) ) | ~spl4_1),
% 1.70/1.33 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.70/1.33 thf(f24,definition,(
% 1.70/1.33 spl4_1 <=> ! [X7 : a] : ($true != (f @ X7 @ sK1))),
% 1.70/1.33 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.70/1.33 thf(f29,plain,(
% 1.70/1.33 ($true = (f @ sK0 @ sK1)) | ~spl4_2),
% 1.70/1.33 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.70/1.33 thf(f27,definition,(
% 1.70/1.33 spl4_2 <=> ($true = (f @ sK0 @ sK1))),
% 1.70/1.33 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.70/1.33 thf(f111,plain,(
% 1.70/1.33 ~spl4_3 | ~spl4_5),
% 1.70/1.33 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.70/1.33 thf(f110,plain,(
% 1.70/1.33 $false | (~spl4_3 | ~spl4_5)),
% 1.70/1.33 inference(subsumption_resolution,[status(thm)],[f109,f16])).
% 1.70/1.33 thf(f16,plain,(
% 1.70/1.33 ($true != (cR @ sK0 @ sK2))),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f12,plain,(
% 1.70/1.33 ! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X1 : a,X2 : a,X3 : b] : (((f @ X1 @ X3) != $true) | ($true != (f @ X2 @ X3)) | ($true = (cR @ X1 @ X2))) & (! [X7 : a] : ((($true = (cR @ sK0 @ z)) & ($true != (f @ X7 @ sK1))) | ($true = (f @ sK0 @ sK1))) & ! [X8 : a] : (($true = (f @ sK2 @ sK1)) | (($true != (f @ X8 @ sK1)) & ($true = (cR @ sK2 @ z)))) & ($true != (cR @ sK0 @ sK2))) & ! [X9 : a,X10 : a,X11 : a] : (($true != (cR @ X9 @ X10)) | ($true != (cR @ X11 @ X10)) | ($true = (cR @ X11 @ X9))) & ! [X12 : a] : ($true = (f @ X12 @ (sK3 @ X12))) & ! [X14 : b,X15 : b,X16 : a] : (($true != (f @ X16 @ X15)) | ($true != (f @ X16 @ X14)) | ($true = (cS @ X14 @ X15)))),
% 1.70/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10])).
% 1.70/1.33 thf(f10,plain,(
% 1.70/1.33 ? [X4 : a,X5 : b,X6 : a] : (! [X7 : a] : ((($true = (cR @ X4 @ z)) & ($true != (f @ X7 @ X5))) | ($true = (f @ X4 @ X5))) & ! [X8 : a] : (($true = (f @ X6 @ X5)) | (($true != (f @ X8 @ X5)) & ($true = (cR @ X6 @ z)))) & ($true != (cR @ X4 @ X6))) => (! [X7 : a] : ((($true = (cR @ sK0 @ z)) & ($true != (f @ X7 @ sK1))) | ($true = (f @ sK0 @ sK1))) & ! [X8 : a] : (($true = (f @ sK2 @ sK1)) | (($true != (f @ X8 @ sK1)) & ($true = (cR @ sK2 @ z)))) & ($true != (cR @ sK0 @ sK2)))),
% 1.70/1.33 introduced(definition,[],[choice_axiom])).
% 1.70/1.33 thf(f11,plain,(
% 1.70/1.33 ! [X12 : a] : (? [X13 : b] : ($true = (f @ X12 @ X13)) => ($true = (f @ X12 @ (sK3 @ X12))))),
% 1.70/1.33 introduced(definition,[],[choice_axiom])).
% 1.70/1.33 thf(f9,plain,(
% 1.70/1.33 ! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X1 : a,X2 : a,X3 : b] : (((f @ X1 @ X3) != $true) | ($true != (f @ X2 @ X3)) | ($true = (cR @ X1 @ X2))) & ? [X4 : a,X5 : b,X6 : a] : (! [X7 : a] : ((($true = (cR @ X4 @ z)) & ($true != (f @ X7 @ X5))) | ($true = (f @ X4 @ X5))) & ! [X8 : a] : (($true = (f @ X6 @ X5)) | (($true != (f @ X8 @ X5)) & ($true = (cR @ X6 @ z)))) & ($true != (cR @ X4 @ X6))) & ! [X9 : a,X10 : a,X11 : a] : (($true != (cR @ X9 @ X10)) | ($true != (cR @ X11 @ X10)) | ($true = (cR @ X11 @ X9))) & ! [X12 : a] : ? [X13 : b] : ($true = (f @ X12 @ X13)) & ! [X14 : b,X15 : b,X16 : a] : (($true != (f @ X16 @ X15)) | ($true != (f @ X16 @ X14)) | ($true = (cS @ X14 @ X15)))),
% 1.70/1.33 inference(rectify,[status(thm)],[f8])).
% 1.70/1.33 thf(f8,plain,(
% 1.70/1.33 ! [X0 : a] : ($true = (cR @ X0 @ X0)) & ! [X5 : a,X6 : a,X4 : b] : (($true != (f @ X5 @ X4)) | ($true != (f @ X6 @ X4)) | ($true = (cR @ X5 @ X6))) & ? [X13 : a,X12 : b,X14 : a] : (! [X15 : a] : ((($true = (cR @ X13 @ z)) & ($true != (f @ X15 @ X12))) | ($true = (f @ X13 @ X12))) & ! [X16 : a] : (($true = (f @ X14 @ X12)) | (($true != (f @ X16 @ X12)) & ($true = (cR @ X14 @ z)))) & ($true != (cR @ X13 @ X14))) & ! [X1 : a,X3 : a,X2 : a] : (($true != (cR @ X1 @ X3)) | ($true != (cR @ X2 @ X3)) | ((cR @ X2 @ X1) = $true)) & ! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8)) & ! [X10 : b,X11 : b,X9 : a] : (($true != (f @ X9 @ X11)) | ($true != (f @ X9 @ X10)) | ($true = (cS @ X10 @ X11)))),
% 1.70/1.33 inference(flattening,[status(thm)],[f7])).
% 1.70/1.33 thf(f7,plain,(
% 1.70/1.33 (? [X12 : b,X14 : a,X13 : a] : (($true != (cR @ X13 @ X14)) & (! [X16 : a] : (($true = (f @ X14 @ X12)) | (($true != (f @ X16 @ X12)) & ($true = (cR @ X14 @ z)))) & ! [X15 : a] : ((($true = (cR @ X13 @ z)) & ($true != (f @ X15 @ X12))) | ($true = (f @ X13 @ X12))))) & (! [X5 : a,X4 : b,X6 : a] : (($true = (cR @ X5 @ X6)) | (($true != (f @ X5 @ X4)) | ($true != (f @ X6 @ X4)))) & ! [X11 : b,X10 : b,X9 : a] : (($true = (cS @ X10 @ X11)) | (($true != (f @ X9 @ X11)) | ($true != (f @ X9 @ X10)))) & ! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8)))) & (! [X1 : a,X2 : a,X3 : a] : (((cR @ X2 @ X1) = $true) | (($true != (cR @ X2 @ X3)) | ($true != (cR @ X1 @ X3)))) & ! [X0 : a] : ($true = (cR @ X0 @ X0)))),
% 1.70/1.33 inference(ennf_transformation,[status(thm)],[f6])).
% 1.70/1.33 thf(f6,plain,(
% 1.70/1.33 ~((! [X1 : a,X2 : a,X3 : a] : ((($true = (cR @ X2 @ X3)) & ($true = (cR @ X1 @ X3))) => ((cR @ X2 @ X1) = $true)) & ! [X0 : a] : ($true = (cR @ X0 @ X0))) => ((! [X5 : a,X4 : b,X6 : a] : ((($true = (f @ X5 @ X4)) & ($true = (f @ X6 @ X4))) => ($true = (cR @ X5 @ X6))) & ! [X11 : b,X10 : b,X9 : a] : ((($true = (f @ X9 @ X11)) & ($true = (f @ X9 @ X10))) => ($true = (cS @ X10 @ X11))) & ! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8))) => ! [X12 : b,X14 : a,X13 : a] : ((! [X16 : a] : (($true = (f @ X14 @ X12)) | (($true != (f @ X16 @ X12)) & ($true = (cR @ X14 @ z)))) & ! [X15 : a] : ((($true = (cR @ X13 @ z)) & ($true != (f @ X15 @ X12))) | ($true = (f @ X13 @ X12)))) => ($true = (cR @ X13 @ X14)))))),
% 1.70/1.33 inference(flattening,[status(thm)],[f5])).
% 1.70/1.33 thf(f5,plain,(
% 1.70/1.33 ~((! [X1 : a,X2 : a,X3 : a] : ((($true = (cR @ X2 @ X3)) & ($true = (cR @ X1 @ X3))) => ((cR @ X2 @ X1) = $true)) & ! [X0 : a] : ($true = (cR @ X0 @ X0))) => ((! [X5 : a,X4 : b,X6 : a] : ((($true = (f @ X5 @ X4)) & ($true = (f @ X6 @ X4))) => ($true = (cR @ X5 @ X6))) & ! [X11 : b,X10 : b,X9 : a] : ((($true = (f @ X9 @ X11)) & ($true = (f @ X9 @ X10))) => ($true = (cS @ X10 @ X11))) & ! [X7 : a] : ? [X8 : b] : ($true = (f @ X7 @ X8))) => ! [X12 : b,X13 : a,X14 : a] : ((! [X15 : a] : ((($true = (cR @ X13 @ z)) & ~($true = (f @ X15 @ X12))) | ($true = (f @ X13 @ X12))) & ! [X16 : a] : ((~($true = (f @ X16 @ X12)) & ($true = (cR @ X14 @ z))) | ($true = (f @ X14 @ X12)))) => ($true = (cR @ X13 @ X14)))))),
% 1.70/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.70/1.33 thf(f4,plain,(
% 1.70/1.33 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X2 @ X3) & (cR @ X1 @ X3)) => (cR @ X2 @ X1))) => ((! [X4 : b,X5 : a,X6 : a] : (((f @ X6 @ X4) & (f @ X5 @ X4)) => (cR @ X5 @ X6)) & ! [X7 : a] : ? [X8 : b] : (f @ X7 @ X8) & ! [X9 : a,X10 : b,X11 : b] : (((f @ X9 @ X11) & (f @ X9 @ X10)) => (cS @ X10 @ X11))) => ! [X12 : b,X13 : a,X14 : a] : ((! [X15 : a] : (((cR @ X13 @ z) & ~(f @ X15 @ X12)) | (f @ X13 @ X12)) & ! [X16 : a] : ((~(f @ X16 @ X12) & (cR @ X14 @ z)) | (f @ X14 @ X12))) => (cR @ X13 @ X14))))),
% 1.70/1.33 inference(rectify,[status(thm)],[f2])).
% 1.70/1.33 thf(f2,negated_conjecture,(
% 1.70/1.33 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X2 : a,X0 : a,X1 : a] : (((cR @ X0 @ X1) & (cR @ X2 @ X1)) => (cR @ X0 @ X2))) => ((! [X4 : b,X7 : a,X8 : a] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6))) => ! [X4 : b,X7 : a,X8 : a] : ((! [X2 : a] : (((cR @ X7 @ z) & ~(f @ X2 @ X4)) | (f @ X7 @ X4)) & ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X8 @ z)) | (f @ X8 @ X4))) => (cR @ X7 @ X8))))),
% 1.70/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.70/1.33 thf(f1,conjecture,(
% 1.70/1.33 (! [X3 : a] : (cR @ X3 @ X3) & ! [X2 : a,X0 : a,X1 : a] : (((cR @ X0 @ X1) & (cR @ X2 @ X1)) => (cR @ X0 @ X2))) => ((! [X4 : b,X7 : a,X8 : a] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6))) => ! [X4 : b,X7 : a,X8 : a] : ((! [X2 : a] : (((cR @ X7 @ z) & ~(f @ X2 @ X4)) | (f @ X7 @ X4)) & ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X8 @ z)) | (f @ X8 @ X4))) => (cR @ X7 @ X8)))),
% 1.70/1.33 file('/export/starexec/sandbox/tmp/tmp.E7fv4ZgOzU/DTF2THF_18939.p',cTHM552D_pme)).
% 1.70/1.33 thf(f109,plain,(
% 1.70/1.33 ($true = (cR @ sK0 @ sK2)) | (~spl4_3 | ~spl4_5)),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.70/1.33 thf(f106,plain,(
% 1.70/1.33 ($true != $true) | ($true = (cR @ sK0 @ sK2)) | (~spl4_3 | ~spl4_5)),
% 1.70/1.33 inference(superposition,[status(thm)],[f67,f103])).
% 1.70/1.33 thf(f103,plain,(
% 1.70/1.33 ($true = (cR @ sK2 @ sK0)) | (~spl4_3 | ~spl4_5)),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.70/1.33 thf(f101,plain,(
% 1.70/1.33 ($true = (cR @ sK2 @ sK0)) | ($true != $true) | (~spl4_3 | ~spl4_5)),
% 1.70/1.33 inference(superposition,[status(thm)],[f87,f43])).
% 1.70/1.33 thf(f43,plain,(
% 1.70/1.33 ($true = (cR @ sK0 @ z)) | ~spl4_5),
% 1.70/1.33 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.70/1.33 thf(f41,definition,(
% 1.70/1.33 spl4_5 <=> ($true = (cR @ sK0 @ z))),
% 1.70/1.33 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.70/1.33 thf(f87,plain,(
% 1.70/1.33 ( ! [X0 : a] : (($true != (cR @ X0 @ z)) | ($true = (cR @ sK2 @ X0))) ) | ~spl4_3),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.70/1.33 thf(f85,plain,(
% 1.70/1.33 ( ! [X0 : a] : (($true != (cR @ X0 @ z)) | ($true = (cR @ sK2 @ X0)) | ($true != $true)) ) | ~spl4_3),
% 1.70/1.33 inference(superposition,[status(thm)],[f15,f34])).
% 1.70/1.33 thf(f34,plain,(
% 1.70/1.33 ($true = (cR @ sK2 @ z)) | ~spl4_3),
% 1.70/1.33 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.70/1.33 thf(f32,definition,(
% 1.70/1.33 spl4_3 <=> ($true = (cR @ sK2 @ z))),
% 1.70/1.33 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.70/1.33 thf(f15,plain,(
% 1.70/1.33 ( ! [X10 : a,X11 : a,X9 : a] : (($true != (cR @ X11 @ X10)) | ($true = (cR @ X11 @ X9)) | ($true != (cR @ X9 @ X10))) )),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f67,plain,(
% 1.70/1.33 ( ! [X0 : a,X1 : a] : (($true != (cR @ X1 @ X0)) | ((cR @ X0 @ X1) = $true)) )),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.70/1.33 thf(f66,plain,(
% 1.70/1.33 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != (cR @ X1 @ X0)) | ((cR @ X0 @ X1) = $true)) )),
% 1.70/1.33 inference(superposition,[status(thm)],[f15,f22])).
% 1.70/1.33 thf(f22,plain,(
% 1.70/1.33 ( ! [X0 : a] : (($true = (cR @ X0 @ X0))) )),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f83,plain,(
% 1.70/1.33 ~spl4_1 | ~spl4_4),
% 1.70/1.33 inference(avatar_contradiction_clause,[status(thm)],[f82])).
% 1.70/1.33 thf(f82,plain,(
% 1.70/1.33 $false | (~spl4_1 | ~spl4_4)),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.70/1.33 thf(f81,plain,(
% 1.70/1.33 ($true != $true) | (~spl4_1 | ~spl4_4)),
% 1.70/1.33 inference(superposition,[status(thm)],[f25,f38])).
% 1.70/1.33 thf(f38,plain,(
% 1.70/1.33 ($true = (f @ sK2 @ sK1)) | ~spl4_4),
% 1.70/1.33 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.70/1.33 thf(f36,definition,(
% 1.70/1.33 spl4_4 <=> ($true = (f @ sK2 @ sK1))),
% 1.70/1.33 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.70/1.33 thf(f80,plain,(
% 1.70/1.33 ~spl4_2 | ~spl4_4),
% 1.70/1.33 inference(avatar_contradiction_clause,[status(thm)],[f79])).
% 1.70/1.33 thf(f79,plain,(
% 1.70/1.33 $false | (~spl4_2 | ~spl4_4)),
% 1.70/1.33 inference(subsumption_resolution,[status(thm)],[f78,f16])).
% 1.70/1.33 thf(f78,plain,(
% 1.70/1.33 ($true = (cR @ sK0 @ sK2)) | (~spl4_2 | ~spl4_4)),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.70/1.33 thf(f75,plain,(
% 1.70/1.33 ($true != $true) | ($true = (cR @ sK0 @ sK2)) | (~spl4_2 | ~spl4_4)),
% 1.70/1.33 inference(superposition,[status(thm)],[f72,f29])).
% 1.70/1.33 thf(f72,plain,(
% 1.70/1.33 ( ! [X0 : a] : (($true != (f @ X0 @ sK1)) | ($true = (cR @ X0 @ sK2))) ) | ~spl4_4),
% 1.70/1.33 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.70/1.33 thf(f70,plain,(
% 1.70/1.33 ( ! [X0 : a] : (($true != $true) | ($true != (f @ X0 @ sK1)) | ($true = (cR @ X0 @ sK2))) ) | ~spl4_4),
% 1.70/1.33 inference(superposition,[status(thm)],[f21,f38])).
% 1.70/1.33 thf(f21,plain,(
% 1.70/1.33 ( ! [X2 : a,X3 : b,X1 : a] : (($true != (f @ X2 @ X3)) | ((f @ X1 @ X3) != $true) | ($true = (cR @ X1 @ X2))) )),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f45,plain,(
% 1.70/1.33 spl4_4 | spl4_1),
% 1.70/1.33 inference(avatar_split_clause,[status(thm)],[f18,f24,f36])).
% 1.70/1.33 thf(f18,plain,(
% 1.70/1.33 ( ! [X8 : a] : (($true = (f @ sK2 @ sK1)) | ($true != (f @ X8 @ sK1))) )),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f44,plain,(
% 1.70/1.33 spl4_5 | spl4_2),
% 1.70/1.33 inference(avatar_split_clause,[status(thm)],[f20,f27,f41])).
% 1.70/1.33 thf(f20,plain,(
% 1.70/1.33 ($true = (f @ sK0 @ sK1)) | ($true = (cR @ sK0 @ z))),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f39,plain,(
% 1.70/1.33 spl4_3 | spl4_4),
% 1.70/1.33 inference(avatar_split_clause,[status(thm)],[f17,f36,f32])).
% 1.70/1.33 thf(f17,plain,(
% 1.70/1.33 ($true = (f @ sK2 @ sK1)) | ($true = (cR @ sK2 @ z))),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 thf(f30,plain,(
% 1.70/1.33 spl4_1 | spl4_2),
% 1.70/1.33 inference(avatar_split_clause,[status(thm)],[f19,f27,f24])).
% 1.70/1.33 thf(f19,plain,(
% 1.70/1.33 ( ! [X7 : a] : (($true != (f @ X7 @ sK1)) | ($true = (f @ sK0 @ sK1))) )),
% 1.70/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.70/1.33 % SZS output end Proof for DTF2THF_18939
% 1.70/1.33 % (19133)------------------------------
% 1.70/1.33 % (19133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (19133)Termination reason: Refutation
% 1.70/1.33
% 1.70/1.33 % (19133)Memory used [KB]: 5628
% 1.70/1.33 % (19133)Time elapsed: 0.011 s
% 1.70/1.33 % (19133)Instructions burned: 14 (million)
% 1.70/1.33 % (19133)------------------------------
% 1.70/1.33 % (19133)------------------------------
% 1.70/1.33 % (19126)Success in time 0.017 s
%------------------------------------------------------------------------------