%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO274^5 : 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 : n027.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 09:53:49 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 396 ( 154 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 600 ( 77 ~; 83 |; 38 &; 354 @)
% ( 4 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 141 ( 0 ^; 119 !; 22 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
c: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
cG: c > b ).
thf(func_def_4,type,
cF: b > a ).
thf(func_def_6,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: c > c > b > $o ).
thf(func_def_10,type,
sK1: b > b > a > $o ).
thf(func_def_11,type,
sK2: c ).
thf(func_def_12,type,
sK3: c ).
thf(func_def_13,type,
sK4: c > $o ).
thf(func_def_15,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f40,f52,f56,f60]) ).
thf(f60,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f59,f50,f46]) ).
thf(f46,definition,
( spl5_3
<=> ( ( sK4 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f50,definition,
( spl5_4
<=> ! [X0: c > $o] :
( ( ( X0 @ sK2 )
!= $true )
| ( $true
= ( X0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f59,plain,
( ( ( sK4 @ sK3 )
= $true )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( sK4 @ sK3 )
= $true )
| ( $true != $true )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f51,f15]) ).
thf(f15,plain,
( $true
= ( sK4 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: c,X1: c] :
( ! [X2: c > $o] :
( ( ( X2 @ X0 )
= $true )
| ( ( X2 @ X1 )
!= $true ) )
| ( ( $true
!= ( sK0 @ X1 @ X0 @ ( cG @ X0 ) ) )
& ( $true
= ( sK0 @ X1 @ X0 @ ( cG @ X1 ) ) ) ) )
& ! [X4: b,X5: b] :
( ( ( $true
!= ( sK1 @ X5 @ X4 @ ( cF @ X5 ) ) )
& ( $true
= ( sK1 @ X5 @ X4 @ ( cF @ X4 ) ) ) )
| ! [X7: b > $o] :
( ( $true
!= ( X7 @ X4 ) )
| ( $true
= ( X7 @ X5 ) ) ) )
& ( ( sK4 @ sK3 )
!= $true )
& ( $true
= ( sK4 @ sK2 ) )
& ! [X11: a > $o] :
( ( $true
= ( X11 @ ( cF @ ( cG @ sK3 ) ) ) )
| ( $true
!= ( X11 @ ( cF @ ( cG @ sK2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: c,X1: c] :
( ? [X3: b > $o] :
( ( ( X3 @ ( cG @ X0 ) )
!= $true )
& ( $true
= ( X3 @ ( cG @ X1 ) ) ) )
=> ( ( $true
!= ( sK0 @ X1 @ X0 @ ( cG @ X0 ) ) )
& ( $true
= ( sK0 @ X1 @ X0 @ ( cG @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X4: b,X5: b] :
( ? [X6: a > $o] :
( ( $true
!= ( X6 @ ( cF @ X5 ) ) )
& ( $true
= ( X6 @ ( cF @ X4 ) ) ) )
=> ( ( $true
!= ( sK1 @ X5 @ X4 @ ( cF @ X5 ) ) )
& ( $true
= ( sK1 @ X5 @ X4 @ ( cF @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X8: c,X9: c] :
( ? [X10: c > $o] :
( ( $true
!= ( X10 @ X9 ) )
& ( $true
= ( X10 @ X8 ) ) )
& ! [X11: a > $o] :
( ( $true
= ( X11 @ ( cF @ ( cG @ X9 ) ) ) )
| ( $true
!= ( X11 @ ( cF @ ( cG @ X8 ) ) ) ) ) )
=> ( ? [X10: c > $o] :
( ( $true
!= ( X10 @ sK3 ) )
& ( $true
= ( X10 @ sK2 ) ) )
& ! [X11: a > $o] :
( ( $true
= ( X11 @ ( cF @ ( cG @ sK3 ) ) ) )
| ( $true
!= ( X11 @ ( cF @ ( cG @ sK2 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X10: c > $o] :
( ( $true
!= ( X10 @ sK3 ) )
& ( $true
= ( X10 @ sK2 ) ) )
=> ( ( ( sK4 @ sK3 )
!= $true )
& ( $true
= ( sK4 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: c,X1: c] :
( ! [X2: c > $o] :
( ( ( X2 @ X0 )
= $true )
| ( ( X2 @ X1 )
!= $true ) )
| ? [X3: b > $o] :
( ( ( X3 @ ( cG @ X0 ) )
!= $true )
& ( $true
= ( X3 @ ( cG @ X1 ) ) ) ) )
& ! [X4: b,X5: b] :
( ? [X6: a > $o] :
( ( $true
!= ( X6 @ ( cF @ X5 ) ) )
& ( $true
= ( X6 @ ( cF @ X4 ) ) ) )
| ! [X7: b > $o] :
( ( $true
!= ( X7 @ X4 ) )
| ( $true
= ( X7 @ X5 ) ) ) )
& ? [X8: c,X9: c] :
( ? [X10: c > $o] :
( ( $true
!= ( X10 @ X9 ) )
& ( $true
= ( X10 @ X8 ) ) )
& ! [X11: a > $o] :
( ( $true
= ( X11 @ ( cF @ ( cG @ X9 ) ) ) )
| ( $true
!= ( X11 @ ( cF @ ( cG @ X8 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X5: c,X4: c] :
( ! [X7: c > $o] :
( ( ( X7 @ X5 )
= $true )
| ( $true
!= ( X7 @ X4 ) ) )
| ? [X6: b > $o] :
( ( $true
!= ( X6 @ ( cG @ X5 ) ) )
& ( $true
= ( X6 @ ( cG @ X4 ) ) ) ) )
& ! [X1: b,X0: b] :
( ? [X2: a > $o] :
( ( ( X2 @ ( cF @ X0 ) )
!= $true )
& ( ( X2 @ ( cF @ X1 ) )
= $true ) )
| ! [X3: b > $o] :
( ( $true
!= ( X3 @ X1 ) )
| ( $true
= ( X3 @ X0 ) ) ) )
& ? [X8: c,X9: c] :
( ? [X11: c > $o] :
( ( $true
!= ( X11 @ X9 ) )
& ( $true
= ( X11 @ X8 ) ) )
& ! [X10: a > $o] :
( ( $true
= ( X10 @ ( cF @ ( cG @ X9 ) ) ) )
| ( $true
!= ( X10 @ ( cF @ ( cG @ X8 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X8: c,X9: c] :
( ? [X11: c > $o] :
( ( $true
!= ( X11 @ X9 ) )
& ( $true
= ( X11 @ X8 ) ) )
& ! [X10: a > $o] :
( ( $true
= ( X10 @ ( cF @ ( cG @ X9 ) ) ) )
| ( $true
!= ( X10 @ ( cF @ ( cG @ X8 ) ) ) ) ) )
& ! [X1: b,X0: b] :
( ? [X2: a > $o] :
( ( ( X2 @ ( cF @ X0 ) )
!= $true )
& ( ( X2 @ ( cF @ X1 ) )
= $true ) )
| ! [X3: b > $o] :
( ( $true
!= ( X3 @ X1 ) )
| ( $true
= ( X3 @ X0 ) ) ) )
& ! [X5: c,X4: c] :
( ! [X7: c > $o] :
( ( ( X7 @ X5 )
= $true )
| ( $true
!= ( X7 @ X4 ) ) )
| ? [X6: b > $o] :
( ( $true
!= ( X6 @ ( cG @ X5 ) ) )
& ( $true
= ( X6 @ ( cG @ X4 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: b,X1: b] :
( ! [X2: a > $o] :
( ( ( X2 @ ( cF @ X1 ) )
= $true )
=> ( ( X2 @ ( cF @ X0 ) )
= $true ) )
=> ! [X3: b > $o] :
( ( $true
= ( X3 @ X1 ) )
=> ( $true
= ( X3 @ X0 ) ) ) )
& ! [X4: c,X5: c] :
( ! [X6: b > $o] :
( ( $true
= ( X6 @ ( cG @ X4 ) ) )
=> ( $true
= ( X6 @ ( cG @ X5 ) ) ) )
=> ! [X7: c > $o] :
( ( $true
= ( X7 @ X4 ) )
=> ( ( X7 @ X5 )
= $true ) ) ) )
=> ! [X8: c,X9: c] :
( ! [X10: a > $o] :
( ( $true
= ( X10 @ ( cF @ ( cG @ X8 ) ) ) )
=> ( $true
= ( X10 @ ( cF @ ( cG @ X9 ) ) ) ) )
=> ! [X11: c > $o] :
( ( $true
= ( X11 @ X8 ) )
=> ( $true
= ( X11 @ X9 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: b,X1: b] :
( ! [X2: a > $o] :
( ( X2 @ ( cF @ X1 ) )
=> ( X2 @ ( cF @ X0 ) ) )
=> ! [X3: b > $o] :
( ( X3 @ X1 )
=> ( X3 @ X0 ) ) )
& ! [X4: c,X5: c] :
( ! [X6: b > $o] :
( ( X6 @ ( cG @ X4 ) )
=> ( X6 @ ( cG @ X5 ) ) )
=> ! [X7: c > $o] :
( ( X7 @ X4 )
=> ( X7 @ X5 ) ) ) )
=> ! [X8: c,X9: c] :
( ! [X10: a > $o] :
( ( X10 @ ( cF @ ( cG @ X8 ) ) )
=> ( X10 @ ( cF @ ( cG @ X9 ) ) ) )
=> ! [X11: c > $o] :
( ( X11 @ X8 )
=> ( X11 @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: b,X0: b] :
( ! [X2: a > $o] :
( ( X2 @ ( cF @ X0 ) )
=> ( X2 @ ( cF @ X1 ) ) )
=> ! [X2: b > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
& ! [X0: c,X1: c] :
( ! [X2: b > $o] :
( ( X2 @ ( cG @ X0 ) )
=> ( X2 @ ( cG @ X1 ) ) )
=> ! [X2: c > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) )
=> ! [X0: c,X1: c] :
( ! [X2: a > $o] :
( ( X2 @ ( cF @ ( cG @ X0 ) ) )
=> ( X2 @ ( cF @ ( cG @ X1 ) ) ) )
=> ! [X2: c > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: b,X0: b] :
( ! [X2: a > $o] :
( ( X2 @ ( cF @ X0 ) )
=> ( X2 @ ( cF @ X1 ) ) )
=> ! [X2: b > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
& ! [X0: c,X1: c] :
( ! [X2: b > $o] :
( ( X2 @ ( cG @ X0 ) )
=> ( X2 @ ( cG @ X1 ) ) )
=> ! [X2: c > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) )
=> ! [X0: c,X1: c] :
( ! [X2: a > $o] :
( ( X2 @ ( cF @ ( cG @ X0 ) ) )
=> ( X2 @ ( cF @ ( cG @ X1 ) ) ) )
=> ! [X2: c > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YTfFFIfkre/DTF2THF_29950.p',cTHM48_EXPD) ).
thf(f51,plain,
( ! [X0: c > $o] :
( ( ( X0 @ sK2 )
!= $true )
| ( $true
= ( X0 @ sK3 ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f56,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f16,f48]) ).
thf(f48,plain,
( ( ( sK4 @ sK3 )
= $true )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f16,plain,
( ( sK4 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f52,plain,
( spl5_3
| spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f43,f32,f50,f46]) ).
thf(f32,definition,
( spl5_1
<=> ! [X1: c] :
( ( ( sK0 @ sK2 @ X1 @ ( cG @ sK3 ) )
= $true )
| ( $true
= ( sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f43,plain,
( ! [X0: c > $o] :
( ( ( X0 @ sK2 )
!= $true )
| ( $true
= ( X0 @ sK3 ) )
| ( ( sK4 @ sK3 )
= $true ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: c > $o] :
( ( $true
= ( X0 @ sK3 ) )
| ( ( sK4 @ sK3 )
= $true )
| ( $true != $true )
| ( ( X0 @ sK2 )
!= $true ) )
| ~ spl5_1 ),
inference(superposition,[status(thm)],[f20,f33]) ).
thf(f33,plain,
( ! [X1: c] :
( ( ( sK0 @ sK2 @ X1 @ ( cG @ sK3 ) )
= $true )
| ( $true
= ( sK4 @ X1 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f20,plain,
! [X2: c > $o,X0: c,X1: c] :
( ( $true
!= ( sK0 @ X1 @ X0 @ ( cG @ X0 ) ) )
| ( ( X2 @ X1 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f40,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f39,f35,f32]) ).
thf(f35,definition,
( spl5_2
<=> ! [X0: b > $o] :
( ( $true
= ( X0 @ ( cG @ sK3 ) ) )
| ( $true
!= ( X0 @ ( cG @ sK2 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f39,plain,
( ! [X0: c] :
( ( $true
= ( sK4 @ X0 ) )
| ( ( sK0 @ sK2 @ X0 @ ( cG @ sK3 ) )
= $true ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: c] :
( ( $true != $true )
| ( $true
= ( sK4 @ X0 ) )
| ( ( sK0 @ sK2 @ X0 @ ( cG @ sK3 ) )
= $true ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f36,f22]) ).
thf(f22,plain,
! [X0: c] :
( ( ( sK0 @ sK2 @ X0 @ ( cG @ sK2 ) )
= $true )
| ( $true
= ( sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: c] :
( ( $true != $true )
| ( $true
= ( sK4 @ X0 ) )
| ( ( sK0 @ sK2 @ X0 @ ( cG @ sK2 ) )
= $true ) ),
inference(superposition,[status(thm)],[f19,f15]) ).
thf(f19,plain,
! [X2: c > $o,X0: c,X1: c] :
( ( ( X2 @ X1 )
!= $true )
| ( $true
= ( sK0 @ X1 @ X0 @ ( cG @ X1 ) ) )
| ( ( X2 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f36,plain,
( ! [X0: b > $o] :
( ( $true
!= ( X0 @ ( cG @ sK2 ) ) )
| ( $true
= ( X0 @ ( cG @ sK3 ) ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f37,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f35,f32]) ).
thf(f30,plain,
! [X0: b > $o,X1: c] :
( ( ( sK0 @ sK2 @ X1 @ ( cG @ sK3 ) )
= $true )
| ( $true
= ( X0 @ ( cG @ sK3 ) ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
!= ( X0 @ ( cG @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: b > $o,X1: c] :
( ( $true
= ( sK4 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( X0 @ ( cG @ sK2 ) ) )
| ( $true
= ( X0 @ ( cG @ sK3 ) ) )
| ( ( sK0 @ sK2 @ X1 @ ( cG @ sK3 ) )
= $true ) ),
inference(superposition,[status(thm)],[f18,f28]) ).
thf(f28,plain,
! [X0: b,X1: c] :
( ( ( sK1 @ X0 @ ( cG @ sK2 ) @ ( cF @ ( cG @ sK3 ) ) )
= $true )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: b,X1: c] :
( ( $true
= ( sK0 @ sK2 @ X1 @ X0 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true != $true )
| ( ( sK1 @ X0 @ ( cG @ sK2 ) @ ( cF @ ( cG @ sK3 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f14,f24]) ).
thf(f24,plain,
! [X0: c,X1: b] :
( ( $true
= ( sK1 @ X1 @ ( cG @ sK2 ) @ ( cF @ ( cG @ sK2 ) ) ) )
| ( $true
= ( sK4 @ X0 ) )
| ( ( sK0 @ sK2 @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: c,X1: b] :
( ( $true
= ( sK1 @ X1 @ ( cG @ sK2 ) @ ( cF @ ( cG @ sK2 ) ) ) )
| ( $true
= ( sK4 @ X0 ) )
| ( $true != $true )
| ( ( sK0 @ sK2 @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f17,f22]) ).
thf(f17,plain,
! [X7: b > $o,X4: b,X5: b] :
( ( $true
!= ( X7 @ X4 ) )
| ( $true
= ( sK1 @ X5 @ X4 @ ( cF @ X4 ) ) )
| ( $true
= ( X7 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f14,plain,
! [X11: a > $o] :
( ( $true
!= ( X11 @ ( cF @ ( cG @ sK2 ) ) ) )
| ( $true
= ( X11 @ ( cF @ ( cG @ sK3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f18,plain,
! [X7: b > $o,X4: b,X5: b] :
( ( $true
!= ( sK1 @ X5 @ X4 @ ( cF @ X5 ) ) )
| ( $true
= ( X7 @ X5 ) )
| ( $true
!= ( X7 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO274^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n027.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:27:37 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SYO274^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Syntactic
% 0.28/0.47 % Problem : TPS problem THM48-EXPD
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0478 [Bro09]
% 0.28/0.47 % : THM48-EXPD [TPS]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.28/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.47 % Number of connectives : 31 ( 0 ~; 0 |; 1 &; 20 @)
% 0.28/0.47 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 10 ( 10 avg)
% 0.28/0.47 % Number of types : 4 ( 3 usr)
% 0.28/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.28/0.47 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(c_type,type,
% 0.28/0.47 c: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(b_type,type,
% 0.28/0.47 b: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(a_type,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(cG,type,
% 0.28/0.47 cG: c > b ).
% 0.28/0.47
% 0.28/0.47 thf(cF,type,
% 0.28/0.47 cF: b > a ).
% 0.28/0.47
% 0.28/0.47 thf(cTHM48_EXPD,conjecture,
% 0.28/0.47 ( ( ! [Xx: b,Xy: b] :
% 0.28/0.47 ( ! [Xq: a > $o] :
% 0.28/0.47 ( ( Xq @ ( cF @ Xx ) )
% 0.28/0.47 => ( Xq @ ( cF @ Xy ) ) )
% 0.28/0.47 => ! [Xq: b > $o] :
% 0.28/0.47 ( ( Xq @ Xx )
% 0.28/0.47 => ( Xq @ Xy ) ) )
% 0.28/0.47 & ! [Xx: c,Xy: c] :
% 0.28/0.47 ( ! [Xq: b > $o] :
% 0.28/0.47 ( ( Xq @ ( cG @ Xx ) )
% 0.28/0.47 => ( Xq @ ( cG @ Xy ) ) )
% 0.28/0.47 => ! [Xq: c > $o] :
% 0.28/0.47 ( ( Xq @ Xx )
% 0.28/0.47 => ( Xq @ Xy ) ) ) )
% 0.28/0.47 => ! [Xx: c,Xy: c] :
% 0.28/0.47 ( ! [Xq: a > $o] :
% 0.28/0.47 ( ( Xq @ ( cF @ ( cG @ Xx ) ) )
% 0.28/0.47 => ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
% 0.28/0.47 => ! [Xq: c > $o] :
% 0.28/0.47 ( ( Xq @ Xx )
% 0.28/0.47 => ( Xq @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 14:27:38 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YTfFFIfkre/DTF2DTF29950.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(c_type,type,
% 1.48/1.28 c: $tType ).
% 1.48/1.28
% 1.48/1.28 thf(b_type,type,
% 1.48/1.28 b: $tType ).
% 1.48/1.28
% 1.48/1.28 thf(a_type,type,
% 1.48/1.28 a: $tType ).
% 1.48/1.28
% 1.48/1.28 thf(cG,type,
% 1.48/1.28 cG: c > b ).
% 1.48/1.28
% 1.48/1.28 thf(cF,type,
% 1.48/1.28 cF: b > a ).
% 1.48/1.28
% 1.48/1.28 thf(cTHM48_EXPD,conjecture,
% 1.48/1.28 ( ( ! [Xx: b,Xy: b] :
% 1.48/1.28 ( ! [Xq: a > $o] :
% 1.48/1.28 ( ( Xq @ ( cF @ Xx ) )
% 1.48/1.28 => ( Xq @ ( cF @ Xy ) ) )
% 1.48/1.28 => ! [Xq: b > $o] :
% 1.48/1.28 ( ( Xq @ Xx )
% 1.48/1.28 => ( Xq @ Xy ) ) )
% 1.48/1.28 & ! [Xx: c,Xy: c] :
% 1.48/1.28 ( ! [Xq: b > $o] :
% 1.48/1.28 ( ( Xq @ ( cG @ Xx ) )
% 1.48/1.28 => ( Xq @ ( cG @ Xy ) ) )
% 1.48/1.28 => ! [Xq: c > $o] :
% 1.48/1.28 ( ( Xq @ Xx )
% 1.48/1.28 => ( Xq @ Xy ) ) ) )
% 1.48/1.28 => ! [Xx: c,Xy: c] :
% 1.48/1.28 ( ! [Xq: a > $o] :
% 1.48/1.28 ( ( Xq @ ( cF @ ( cG @ Xx ) ) )
% 1.48/1.28 => ( Xq @ ( cF @ ( cG @ Xy ) ) ) )
% 1.48/1.28 => ! [Xq: c > $o] :
% 1.48/1.28 ( ( Xq @ Xx )
% 1.48/1.28 => ( Xq @ Xy ) ) ) ) ).
% 1.48/1.28 ------------------------
% 1.64/1.30 % (30169)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_29950 for (2999ds/27Mi)
% 1.64/1.30 % (30169)First to succeed.
% 1.64/1.30 % (30169)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_29950
% 1.64/1.30 % SZS output start Proof for DTF2THF_29950
% 1.64/1.30 thf(type_def_5, type, c: $tType).
% 1.64/1.30 thf(type_def_6, type, b: $tType).
% 1.64/1.30 thf(type_def_8, type, a: $tType).
% 1.64/1.30 thf(func_def_0, type, c: $tType).
% 1.64/1.30 thf(func_def_1, type, b: $tType).
% 1.64/1.30 thf(func_def_2, type, a: $tType).
% 1.64/1.30 thf(func_def_3, type, cG: c > b).
% 1.64/1.30 thf(func_def_4, type, cF: b > a).
% 1.64/1.30 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.30 thf(func_def_9, type, sK0: c > c > b > $o).
% 1.64/1.30 thf(func_def_10, type, sK1: b > b > a > $o).
% 1.64/1.30 thf(func_def_11, type, sK2: c).
% 1.64/1.30 thf(func_def_12, type, sK3: c).
% 1.64/1.30 thf(func_def_13, type, sK4: c > $o).
% 1.64/1.30 thf(func_def_15, type, ph6: !>[X0: $tType]:(X0)).
% 1.64/1.30 thf(f61,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(avatar_sat_refutation,[status(thm)],[f37,f40,f52,f56,f60])).
% 1.64/1.30 thf(f60,plain,(
% 1.64/1.30 spl5_3 | ~spl5_4),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f59,f50,f46])).
% 1.64/1.30 thf(f46,definition,(
% 1.64/1.30 spl5_3 <=> ((sK4 @ sK3) = $true)),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.64/1.30 thf(f50,definition,(
% 1.64/1.30 spl5_4 <=> ! [X0 : c > $o] : (((X0 @ sK2) != $true) | ($true = (X0 @ sK3)))),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.64/1.30 thf(f59,plain,(
% 1.64/1.30 ((sK4 @ sK3) = $true) | ~spl5_4),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.64/1.30 thf(f58,plain,(
% 1.64/1.30 ((sK4 @ sK3) = $true) | ($true != $true) | ~spl5_4),
% 1.64/1.30 inference(superposition,[status(thm)],[f51,f15])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 ($true = (sK4 @ sK2))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 ! [X0 : c,X1 : c] : (! [X2 : c > $o] : (((X2 @ X0) = $true) | ((X2 @ X1) != $true)) | (($true != (sK0 @ X1 @ X0 @ (cG @ X0))) & ($true = (sK0 @ X1 @ X0 @ (cG @ X1))))) & ! [X4 : b,X5 : b] : ((($true != (sK1 @ X5 @ X4 @ (cF @ X5))) & ($true = (sK1 @ X5 @ X4 @ (cF @ X4)))) | ! [X7 : b > $o] : (($true != (X7 @ X4)) | ($true = (X7 @ X5)))) & ((((sK4 @ sK3) != $true) & ($true = (sK4 @ sK2))) & ! [X11 : a > $o] : (($true = (X11 @ (cF @ (cG @ sK3)))) | ($true != (X11 @ (cF @ (cG @ sK2))))))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f12,f11,f10,f9])).
% 1.64/1.30 thf(f9,plain,(
% 1.64/1.30 ! [X0 : c,X1 : c] : (? [X3 : b > $o] : (((X3 @ (cG @ X0)) != $true) & ($true = (X3 @ (cG @ X1)))) => (($true != (sK0 @ X1 @ X0 @ (cG @ X0))) & ($true = (sK0 @ X1 @ X0 @ (cG @ X1)))))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 ! [X4 : b,X5 : b] : (? [X6 : a > $o] : (($true != (X6 @ (cF @ X5))) & ($true = (X6 @ (cF @ X4)))) => (($true != (sK1 @ X5 @ X4 @ (cF @ X5))) & ($true = (sK1 @ X5 @ X4 @ (cF @ X4)))))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 ? [X8 : c,X9 : c] : (? [X10 : c > $o] : (($true != (X10 @ X9)) & ($true = (X10 @ X8))) & ! [X11 : a > $o] : (($true = (X11 @ (cF @ (cG @ X9)))) | ($true != (X11 @ (cF @ (cG @ X8)))))) => (? [X10 : c > $o] : (($true != (X10 @ sK3)) & ($true = (X10 @ sK2))) & ! [X11 : a > $o] : (($true = (X11 @ (cF @ (cG @ sK3)))) | ($true != (X11 @ (cF @ (cG @ sK2))))))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 ? [X10 : c > $o] : (($true != (X10 @ sK3)) & ($true = (X10 @ sK2))) => (((sK4 @ sK3) != $true) & ($true = (sK4 @ sK2)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f8,plain,(
% 1.64/1.30 ! [X0 : c,X1 : c] : (! [X2 : c > $o] : (((X2 @ X0) = $true) | ((X2 @ X1) != $true)) | ? [X3 : b > $o] : (((X3 @ (cG @ X0)) != $true) & ($true = (X3 @ (cG @ X1))))) & ! [X4 : b,X5 : b] : (? [X6 : a > $o] : (($true != (X6 @ (cF @ X5))) & ($true = (X6 @ (cF @ X4)))) | ! [X7 : b > $o] : (($true != (X7 @ X4)) | ($true = (X7 @ X5)))) & ? [X8 : c,X9 : c] : (? [X10 : c > $o] : (($true != (X10 @ X9)) & ($true = (X10 @ X8))) & ! [X11 : a > $o] : (($true = (X11 @ (cF @ (cG @ X9)))) | ($true != (X11 @ (cF @ (cG @ X8))))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f7])).
% 1.64/1.30 thf(f7,plain,(
% 1.64/1.30 ! [X5 : c,X4 : c] : (! [X7 : c > $o] : (((X7 @ X5) = $true) | ($true != (X7 @ X4))) | ? [X6 : b > $o] : (($true != (X6 @ (cG @ X5))) & ($true = (X6 @ (cG @ X4))))) & ! [X1 : b,X0 : b] : (? [X2 : a > $o] : (((X2 @ (cF @ X0)) != $true) & ((X2 @ (cF @ X1)) = $true)) | ! [X3 : b > $o] : (($true != (X3 @ X1)) | ($true = (X3 @ X0)))) & ? [X8 : c,X9 : c] : (? [X11 : c > $o] : (($true != (X11 @ X9)) & ($true = (X11 @ X8))) & ! [X10 : a > $o] : (($true = (X10 @ (cF @ (cG @ X9)))) | ($true != (X10 @ (cF @ (cG @ X8))))))),
% 1.64/1.30 inference(flattening,[status(thm)],[f6])).
% 1.64/1.30 thf(f6,plain,(
% 1.64/1.30 ? [X8 : c,X9 : c] : (? [X11 : c > $o] : (($true != (X11 @ X9)) & ($true = (X11 @ X8))) & ! [X10 : a > $o] : (($true = (X10 @ (cF @ (cG @ X9)))) | ($true != (X10 @ (cF @ (cG @ X8)))))) & (! [X1 : b,X0 : b] : (? [X2 : a > $o] : (((X2 @ (cF @ X0)) != $true) & ((X2 @ (cF @ X1)) = $true)) | ! [X3 : b > $o] : (($true != (X3 @ X1)) | ($true = (X3 @ X0)))) & ! [X5 : c,X4 : c] : (! [X7 : c > $o] : (((X7 @ X5) = $true) | ($true != (X7 @ X4))) | ? [X6 : b > $o] : (($true != (X6 @ (cG @ X5))) & ($true = (X6 @ (cG @ X4))))))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.30 thf(f5,plain,(
% 1.64/1.30 ~((! [X0 : b,X1 : b] : (! [X2 : a > $o] : (((X2 @ (cF @ X1)) = $true) => ((X2 @ (cF @ X0)) = $true)) => ! [X3 : b > $o] : (($true = (X3 @ X1)) => ($true = (X3 @ X0)))) & ! [X4 : c,X5 : c] : (! [X6 : b > $o] : (($true = (X6 @ (cG @ X4))) => ($true = (X6 @ (cG @ X5)))) => ! [X7 : c > $o] : (($true = (X7 @ X4)) => ((X7 @ X5) = $true)))) => ! [X8 : c,X9 : c] : (! [X10 : a > $o] : (($true = (X10 @ (cF @ (cG @ X8)))) => ($true = (X10 @ (cF @ (cG @ X9))))) => ! [X11 : c > $o] : (($true = (X11 @ X8)) => ($true = (X11 @ X9)))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,plain,(
% 1.64/1.30 ~((! [X0 : b,X1 : b] : (! [X2 : a > $o] : ((X2 @ (cF @ X1)) => (X2 @ (cF @ X0))) => ! [X3 : b > $o] : ((X3 @ X1) => (X3 @ X0))) & ! [X4 : c,X5 : c] : (! [X6 : b > $o] : ((X6 @ (cG @ X4)) => (X6 @ (cG @ X5))) => ! [X7 : c > $o] : ((X7 @ X4) => (X7 @ X5)))) => ! [X8 : c,X9 : c] : (! [X10 : a > $o] : ((X10 @ (cF @ (cG @ X8))) => (X10 @ (cF @ (cG @ X9)))) => ! [X11 : c > $o] : ((X11 @ X8) => (X11 @ X9))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f2])).
% 1.64/1.30 thf(f2,negated_conjecture,(
% 1.64/1.30 ~((! [X1 : b,X0 : b] : (! [X2 : a > $o] : ((X2 @ (cF @ X0)) => (X2 @ (cF @ X1))) => ! [X2 : b > $o] : ((X2 @ X0) => (X2 @ X1))) & ! [X0 : c,X1 : c] : (! [X2 : b > $o] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X2 : c > $o] : ((X2 @ X0) => (X2 @ X1)))) => ! [X0 : c,X1 : c] : (! [X2 : a > $o] : ((X2 @ (cF @ (cG @ X0))) => (X2 @ (cF @ (cG @ X1)))) => ! [X2 : c > $o] : ((X2 @ X0) => (X2 @ X1))))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.30 thf(f1,conjecture,(
% 1.64/1.30 (! [X1 : b,X0 : b] : (! [X2 : a > $o] : ((X2 @ (cF @ X0)) => (X2 @ (cF @ X1))) => ! [X2 : b > $o] : ((X2 @ X0) => (X2 @ X1))) & ! [X0 : c,X1 : c] : (! [X2 : b > $o] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X2 : c > $o] : ((X2 @ X0) => (X2 @ X1)))) => ! [X0 : c,X1 : c] : (! [X2 : a > $o] : ((X2 @ (cF @ (cG @ X0))) => (X2 @ (cF @ (cG @ X1)))) => ! [X2 : c > $o] : ((X2 @ X0) => (X2 @ X1)))),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.YTfFFIfkre/DTF2THF_29950.p',cTHM48_EXPD)).
% 1.64/1.30 thf(f51,plain,(
% 1.64/1.30 ( ! [X0 : c > $o] : (((X0 @ sK2) != $true) | ($true = (X0 @ sK3))) ) | ~spl5_4),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.64/1.30 thf(f56,plain,(
% 1.64/1.30 ~spl5_3),
% 1.64/1.30 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 1.64/1.30 thf(f55,plain,(
% 1.64/1.30 $false | ~spl5_3),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.64/1.30 thf(f53,plain,(
% 1.64/1.30 ($true != $true) | ~spl5_3),
% 1.64/1.30 inference(superposition,[status(thm)],[f16,f48])).
% 1.64/1.30 thf(f48,plain,(
% 1.64/1.30 ((sK4 @ sK3) = $true) | ~spl5_3),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 ((sK4 @ sK3) != $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f52,plain,(
% 1.64/1.30 spl5_3 | spl5_4 | ~spl5_1),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f43,f32,f50,f46])).
% 1.64/1.30 thf(f32,definition,(
% 1.64/1.30 spl5_1 <=> ! [X1 : c] : (((sK0 @ sK2 @ X1 @ (cG @ sK3)) = $true) | ($true = (sK4 @ X1)))),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.64/1.30 thf(f43,plain,(
% 1.64/1.30 ( ! [X0 : c > $o] : (((X0 @ sK2) != $true) | ($true = (X0 @ sK3)) | ((sK4 @ sK3) = $true)) ) | ~spl5_1),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.64/1.30 thf(f41,plain,(
% 1.64/1.30 ( ! [X0 : c > $o] : (($true = (X0 @ sK3)) | ((sK4 @ sK3) = $true) | ($true != $true) | ((X0 @ sK2) != $true)) ) | ~spl5_1),
% 1.64/1.30 inference(superposition,[status(thm)],[f20,f33])).
% 1.64/1.30 thf(f33,plain,(
% 1.64/1.30 ( ! [X1 : c] : (((sK0 @ sK2 @ X1 @ (cG @ sK3)) = $true) | ($true = (sK4 @ X1))) ) | ~spl5_1),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.64/1.30 thf(f20,plain,(
% 1.64/1.30 ( ! [X2 : c > $o,X0 : c,X1 : c] : (($true != (sK0 @ X1 @ X0 @ (cG @ X0))) | ((X2 @ X1) != $true) | ((X2 @ X0) = $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f40,plain,(
% 1.64/1.30 spl5_1 | ~spl5_2),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f39,f35,f32])).
% 1.64/1.30 thf(f35,definition,(
% 1.64/1.30 spl5_2 <=> ! [X0 : b > $o] : (($true = (X0 @ (cG @ sK3))) | ($true != (X0 @ (cG @ sK2))))),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.64/1.30 thf(f39,plain,(
% 1.64/1.30 ( ! [X0 : c] : (($true = (sK4 @ X0)) | ((sK0 @ sK2 @ X0 @ (cG @ sK3)) = $true)) ) | ~spl5_2),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.64/1.30 thf(f38,plain,(
% 1.64/1.30 ( ! [X0 : c] : (($true != $true) | ($true = (sK4 @ X0)) | ((sK0 @ sK2 @ X0 @ (cG @ sK3)) = $true)) ) | ~spl5_2),
% 1.64/1.30 inference(superposition,[status(thm)],[f36,f22])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 ( ! [X0 : c] : (((sK0 @ sK2 @ X0 @ (cG @ sK2)) = $true) | ($true = (sK4 @ X0))) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 ( ! [X0 : c] : (($true != $true) | ($true = (sK4 @ X0)) | ((sK0 @ sK2 @ X0 @ (cG @ sK2)) = $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f19,f15])).
% 1.64/1.30 thf(f19,plain,(
% 1.64/1.30 ( ! [X2 : c > $o,X0 : c,X1 : c] : (((X2 @ X1) != $true) | ($true = (sK0 @ X1 @ X0 @ (cG @ X1))) | ((X2 @ X0) = $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f36,plain,(
% 1.64/1.30 ( ! [X0 : b > $o] : (($true != (X0 @ (cG @ sK2))) | ($true = (X0 @ (cG @ sK3)))) ) | ~spl5_2),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.64/1.30 thf(f37,plain,(
% 1.64/1.30 spl5_1 | spl5_2),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f30,f35,f32])).
% 1.64/1.30 thf(f30,plain,(
% 1.64/1.30 ( ! [X0 : b > $o,X1 : c] : (((sK0 @ sK2 @ X1 @ (cG @ sK3)) = $true) | ($true = (X0 @ (cG @ sK3))) | ($true = (sK4 @ X1)) | ($true != (X0 @ (cG @ sK2)))) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.64/1.30 thf(f29,plain,(
% 1.64/1.30 ( ! [X0 : b > $o,X1 : c] : (($true = (sK4 @ X1)) | ($true != $true) | ($true != (X0 @ (cG @ sK2))) | ($true = (X0 @ (cG @ sK3))) | ((sK0 @ sK2 @ X1 @ (cG @ sK3)) = $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f18,f28])).
% 1.64/1.30 thf(f28,plain,(
% 1.64/1.30 ( ! [X0 : b,X1 : c] : (((sK1 @ X0 @ (cG @ sK2) @ (cF @ (cG @ sK3))) = $true) | ($true = (sK4 @ X1)) | ($true = (sK0 @ sK2 @ X1 @ X0))) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.64/1.30 thf(f27,plain,(
% 1.64/1.30 ( ! [X0 : b,X1 : c] : (($true = (sK0 @ sK2 @ X1 @ X0)) | ($true = (sK4 @ X1)) | ($true != $true) | ((sK1 @ X0 @ (cG @ sK2) @ (cF @ (cG @ sK3))) = $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f14,f24])).
% 1.64/1.30 thf(f24,plain,(
% 1.64/1.30 ( ! [X0 : c,X1 : b] : (($true = (sK1 @ X1 @ (cG @ sK2) @ (cF @ (cG @ sK2)))) | ($true = (sK4 @ X0)) | ((sK0 @ sK2 @ X0 @ X1) = $true)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 ( ! [X0 : c,X1 : b] : (($true = (sK1 @ X1 @ (cG @ sK2) @ (cF @ (cG @ sK2)))) | ($true = (sK4 @ X0)) | ($true != $true) | ((sK0 @ sK2 @ X0 @ X1) = $true)) )),
% 1.64/1.30 inference(superposition,[status(thm)],[f17,f22])).
% 1.64/1.30 thf(f17,plain,(
% 1.64/1.30 ( ! [X7 : b > $o,X4 : b,X5 : b] : (($true != (X7 @ X4)) | ($true = (sK1 @ X5 @ X4 @ (cF @ X4))) | ($true = (X7 @ X5))) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 ( ! [X11 : a > $o] : (($true != (X11 @ (cF @ (cG @ sK2)))) | ($true = (X11 @ (cF @ (cG @ sK3))))) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f18,plain,(
% 1.64/1.30 ( ! [X7 : b > $o,X4 : b,X5 : b] : (($true != (sK1 @ X5 @ X4 @ (cF @ X5))) | ($true = (X7 @ X5)) | ($true != (X7 @ X4))) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 % SZS output end Proof for DTF2THF_29950
% 1.64/1.30 % (30169)------------------------------
% 1.64/1.30 % (30169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (30169)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (30169)Memory used [KB]: 5628
% 1.64/1.30 % (30169)Time elapsed: 0.006 s
% 1.64/1.30 % (30169)Instructions burned: 9 (million)
% 1.64/1.30 % (30169)------------------------------
% 1.64/1.30 % (30169)------------------------------
% 1.64/1.30 % (30166)Success in time 0.015 s
%------------------------------------------------------------------------------