%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU987^5 : 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 : n010.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 09:37:54 AM UTC 2026
% Result : Theorem 1.59s 1.46s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 155 ( 78 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 736 ( 60 ~; 35 |; 10 &; 613 @)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 252 ( 160 ^; 82 !; 10 ?; 252 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
g: b > b ).
thf(func_def_3,type,
f: a > a ).
thf(func_def_4,type,
cS: a > b > $o ).
thf(func_def_8,type,
sK0: ( a > b > $o ) > b ).
thf(func_def_9,type,
sK1: ( a > b > $o ) > a ).
thf(func_def_12,type,
inv_g_3: b > b ).
thf(func_def_13,type,
inv_f_4: a > a ).
thf(func_def_14,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f57,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f52,f54,f56]) ).
thf(f56,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f48]) ).
thf(f48,plain,
( ! [X0: b] :
( ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ Y1 ) ) )
!= X0 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl2_1
<=> ! [X0: b] :
( ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ Y1 ) ) )
!= X0 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f54,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X1: a] :
( ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ Y1 ) ) )
!= X1 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl2_2
<=> ! [X1: a] :
( ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ Y1 ) ) )
!= X1 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f52,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f44,f50,f47]) ).
thf(f44,plain,
! [X0: b,X1: a] :
( ( ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ Y1 ) ) )
!= X0 )
| ( ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ Y1 ) ) )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: b,X1: a] :
( ( ( sK0
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ Y0 )
@ ( inv_g_3
@ ( ^ [Y2: a,Y3: b] : Y3
@ Y0
@ Y1 ) ) ) )
!= X0 )
| ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ Y0 )
@ ( inv_g_3
@ ( ^ [Y2: a,Y3: b] : Y3
@ Y0
@ Y1 ) ) ) )
!= X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: b,X1: a] :
( ( ( sK0
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ Y0 )
@ ( inv_g_3
@ ( ^ [Y2: a,Y3: b] : Y3
@ Y0
@ Y1 ) ) ) )
!= X0 )
| ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ Y0 )
@ ( inv_g_3
@ ( ^ [Y2: a,Y3: b] : Y3
@ Y0
@ Y1 ) ) ) )
!= X1 )
| ( ( sK0
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ Y0 )
@ ( inv_g_3
@ ( ^ [Y2: a,Y3: b] : Y3
@ Y0
@ Y1 ) ) ) )
!= X0 ) ),
inference(equality_resolution,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: b,X0: a > b > b,X1: a] :
( ( ( g @ X2 )
!= ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 )
| ( ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ Y0 ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: b,X0: a > b > b,X1: a] :
( ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 )
| ( ( g @ X2 )
!= ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: b,X0: a > b > b,X1: a] :
( ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 )
| ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X1 )
| ( ( g @ X2 )
!= ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( inv_f_4
@ ( ^ [Y2: a,Y3: b] : Y2
@ Y0
@ Y1 ) )
@ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 ) ),
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: b,X3: a,X0: a > b > b,X1: a > b > a] :
( ( ( X1
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
!= ( f @ X3 ) )
| ( ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 )
| ( ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) ) @ ( inv_g_3 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
!= ( g @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: b,X3: a,X0: a > b > b,X1: a > b > a] :
( ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) )
@ ( ^ [Y2: a,Y3: b] : ( inv_g_3 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) )
!= X3 )
| ( ( sK0
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) )
@ ( ^ [Y2: a,Y3: b] : ( inv_g_3 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) )
!= X2 )
| ( ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) )
@ ( ^ [Y2: a,Y3: b] : ( inv_g_3 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) )
@ ( ^ [Y2: a,Y3: b] : ( inv_g_3 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( g @ X2 ) )
| ( ( f @ X3 )
!= ( X1
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) )
@ ( ^ [Y2: a,Y3: b] : ( inv_g_3 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] :
( cS @ ( inv_f_4 @ ( X1 @ Y0 @ Y1 ) )
@ ( ^ [Y2: a,Y3: b] : ( inv_g_3 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 ) ) ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f27,f13]) ).
thf(f13,plain,
! [X2: b] :
( ( inv_g_3 @ ( g @ X2 ) )
= X2 ),
inference(injectivity,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: b,X3: b] :
( ( ( g @ X2 )
!= ( g @ X3 ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: a,X1: a] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) )
& ! [X2: b,X3: b] :
( ( ( g @ X2 )
!= ( g @ X3 ) )
| ( X2 = X3 ) )
& ! [X4: a > b > $o] :
( ( cS @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) )
!= ( X4 @ ( f @ ( sK1 @ X4 ) ) @ ( g @ ( sK0 @ X4 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
! [X4: a > b > $o] :
( ? [X5: b,X6: a] :
( ( cS @ X6 @ X5 )
!= ( X4 @ ( f @ X6 ) @ ( g @ X5 ) ) )
=> ( ( cS @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) )
!= ( X4 @ ( f @ ( sK1 @ X4 ) ) @ ( g @ ( sK0 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: a,X1: a] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) )
& ! [X2: b,X3: b] :
( ( ( g @ X2 )
!= ( g @ X3 ) )
| ( X2 = X3 ) )
& ! [X4: a > b > $o] :
? [X5: b,X6: a] :
( ( cS @ X6 @ X5 )
!= ( X4 @ ( f @ X6 ) @ ( g @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X4: a > b > $o] :
? [X5: b,X6: a] :
( ( cS @ X6 @ X5 )
!= ( X4 @ ( f @ X6 ) @ ( g @ X5 ) ) )
& ! [X2: b,X3: b] :
( ( ( g @ X2 )
!= ( g @ X3 ) )
| ( X2 = X3 ) )
& ! [X0: a,X1: a] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X3: b,X2: b] :
( ( ( g @ X2 )
= ( g @ X3 ) )
=> ( X2 = X3 ) )
& ! [X1: a,X0: a] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) ) )
=> ? [X4: a > b > $o] :
! [X5: b,X6: a] :
( ( cS @ X6 @ X5 )
= ( X4 @ ( f @ X6 ) @ ( g @ X5 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a,X1: a] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
& ! [X2: b,X3: b] :
( ( ( g @ X2 )
= ( g @ X3 ) )
=> ( X2 = X3 ) ) )
=> ? [X4: a > b > $o] :
! [X5: b,X6: a] :
( ( X4 @ ( f @ X6 ) @ ( g @ X5 ) )
<=> ( cS @ X6 @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
& ! [X1: b,X0: b] :
( ( ( g @ X0 )
= ( g @ X1 ) )
=> ( X0 = X1 ) ) )
=> ? [X2: a > b > $o] :
! [X1: b,X0: a] :
( ( X2 @ ( f @ X0 ) @ ( g @ X1 ) )
<=> ( cS @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
& ! [X1: b,X0: b] :
( ( ( g @ X0 )
= ( g @ X1 ) )
=> ( X0 = X1 ) ) )
=> ? [X2: a > b > $o] :
! [X1: b,X0: a] :
( ( X2 @ ( f @ X0 ) @ ( g @ X1 ) )
<=> ( cS @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bxtqAGdCHl/DTF2THF_2210.p',cSV7_pme) ).
thf(f27,plain,
! [X2: a,X0: a > b > a,X1: a > b > b] :
( ( ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X0 @ Y0 @ Y1 ) ) @ ( X1 @ Y0 @ Y1 ) ) )
!= ( X1
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X0 @ Y0 @ Y1 ) ) @ ( X1 @ Y0 @ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X0 @ Y0 @ Y1 ) ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( f @ X2 )
!= ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X0 @ Y0 @ Y1 ) ) @ ( X1 @ Y0 @ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X0 @ Y0 @ Y1 ) ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( inv_f_4 @ ( X0 @ Y0 @ Y1 ) ) @ ( X1 @ Y0 @ Y1 ) ) )
!= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: a,X0: a > b > a,X1: a > b > b] :
( ( ( X1
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( ^ [Y2: a,Y3: b] : ( inv_f_4 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( ^ [Y2: a,Y3: b] : ( inv_f_4 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) ) )
!= ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( ^ [Y2: a,Y3: b] : ( inv_f_4 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( ^ [Y2: a,Y3: b] : ( inv_f_4 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) )
!= X2 )
| ( ( f @ X2 )
!= ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] :
( cS
@ ( ^ [Y2: a,Y3: b] : ( inv_f_4 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] :
( cS
@ ( ^ [Y2: a,Y3: b] : ( inv_f_4 @ ( X0 @ Y2 @ Y3 ) )
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f20,f15]) ).
thf(f15,plain,
! [X0: a] :
( ( inv_f_4 @ ( f @ X0 ) )
= X0 ),
inference(injectivity,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: a,X1: a] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f20,plain,
! [X0: a > b > a,X1: a > b > b] :
( ( ( X0
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) )
!= ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( X1
@ ( f
@ ( sK1
@ ^ [Y0: a,Y1: b] : ( cS @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) )
@ ( g
@ ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) )
!= ( sK0
@ ^ [Y0: a,Y1: b] : ( cS @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f10]) ).
thf(f10,plain,
! [X4: a > b > $o] :
( ( cS @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) )
!= ( X4 @ ( f @ ( sK1 @ X4 ) ) @ ( g @ ( sK0 @ X4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU987^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n010.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 12:37:48 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SEU987^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.49 % Domain : Set Theory (Relations)
% 0.29/0.49 % Problem : TPS problem from FUNS-AND-RELNS-THMS
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English :
% 0.29/0.49
% 0.29/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Bro09]
% 0.29/0.49 % Names : tps_0910 [Bro09]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.89 v9.1.0, 0.88 v9.0.0, 1.00 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v4.0.0
% 0.29/0.49 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.29/0.49 % Number of atoms : 5 ( 4 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 5 ( 5 avg)
% 0.29/0.49 % Number of connectives : 15 ( 0 ~; 0 |; 1 &; 10 @)
% 0.29/0.49 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.49 % Number of types : 3 ( 2 usr)
% 0.29/0.49 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.29/0.49 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.29/0.49 % SPC : TH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(b_type,type,
% 0.29/0.49 b: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(a_type,type,
% 0.29/0.49 a: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(g,type,
% 0.29/0.49 g: b > b ).
% 0.29/0.49
% 0.29/0.49 thf(f,type,
% 0.29/0.49 f: a > a ).
% 0.29/0.49
% 0.29/0.49 thf(cS,type,
% 0.29/0.49 cS: a > b > $o ).
% 0.29/0.49
% 0.29/0.49 thf(cSV7_pme,conjecture,
% 0.29/0.49 ( ( ! [Xx: a,Xy: a] :
% 0.29/0.49 ( ( ( f @ Xx )
% 0.29/0.49 = ( f @ Xy ) )
% 0.29/0.49 => ( Xx = Xy ) )
% 0.29/0.49 & ! [Xx: b,Xy: b] :
% 0.29/0.49 ( ( ( g @ Xx )
% 0.29/0.49 = ( g @ Xy ) )
% 0.29/0.49 => ( Xx = Xy ) ) )
% 0.29/0.49 => ? [Xu: a > b > $o] :
% 0.29/0.49 ! [Xx: a,Xy: b] :
% 0.29/0.49 ( ( cS @ Xx @ Xy )
% 0.29/0.49 <=> ( Xu @ ( f @ Xx ) @ ( g @ Xy ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.54/1.32 ---- Embedded in THF ---
% 1.54/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.32 %%% Generated on Tue Feb 24 12:37:49 EST 2026
% 1.54/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.32 %%% Logic specification used:
% 1.54/1.32 %%% thf(spec, logic, $$dhol).
% 1.54/1.32
% 1.54/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bxtqAGdCHl/DTF2DTF2210.p
% See solution above
% 1.54/1.32 ------------------------
% 1.54/1.32 ---- Cleaned THF ---
% 1.54/1.32 thf(b_type,type,
% 1.54/1.32 b: $tType ).
% 1.54/1.32
% 1.54/1.32 thf(a_type,type,
% 1.54/1.32 a: $tType ).
% 1.54/1.32
% 1.54/1.32 thf(g,type,
% 1.54/1.32 g: b > b ).
% 1.54/1.32
% 1.54/1.32 thf(f,type,
% 1.54/1.32 f: a > a ).
% 1.54/1.32
% 1.54/1.32 thf(cS,type,
% 1.54/1.32 cS: a > b > $o ).
% 1.54/1.32
% 1.54/1.32 thf(cSV7_pme,conjecture,
% 1.54/1.32 ( ( ! [Xx: a,Xy: a] :
% 1.54/1.32 ( ( ( f @ Xx )
% 1.54/1.32 = ( f @ Xy ) )
% 1.54/1.32 => ( Xx = Xy ) )
% 1.54/1.32 & ! [Xx: b,Xy: b] :
% 1.54/1.32 ( ( ( g @ Xx )
% 1.54/1.32 = ( g @ Xy ) )
% 1.54/1.32 => ( Xx = Xy ) ) )
% 1.54/1.32 => ? [Xu: a > b > $o] :
% 1.54/1.32 ! [Xx: a,Xy: b] :
% 1.54/1.32 ( ( cS @ Xx @ Xy )
% 1.54/1.32 <=> ( Xu @ ( f @ Xx ) @ ( g @ Xy ) ) ) ) ).
% 1.54/1.32 ------------------------
% 1.54/1.34 % (2339)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2210 for (3000ds/183Mi)
% 1.54/1.34 % (2341)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_2210 for (3000ds/27Mi)
% 1.54/1.34 % (2341)Refutation not found, incomplete strategy
% 1.54/1.34 % (2341)------------------------------
% 1.54/1.34 % (2341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.34 % (2341)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.34
% 1.54/1.34
% 1.54/1.34 % (2341)Memory used [KB]: 5500
% 1.54/1.34 % (2341)Time elapsed: 0.002 s
% 1.54/1.34 % (2341)Instructions burned: 2 (million)
% 1.54/1.34 % (2341)------------------------------
% 1.54/1.34 % (2341)------------------------------
% 1.54/1.34 % (2343)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_2210 for (3000ds/2Mi)
% 1.54/1.34 % (2343)Instruction limit reached!
% 1.54/1.34 % (2343)------------------------------
% 1.54/1.34 % (2343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.34 % (2343)Termination reason: Unknown
% 1.54/1.34 % (2343)Termination phase: Saturation
% 1.54/1.34
% 1.54/1.34 % (2343)Memory used [KB]: 895
% 1.54/1.34 % (2343)Time elapsed: 0.002 s
% 1.54/1.34 % (2343)Instructions burned: 2 (million)
% 1.54/1.34 % (2343)------------------------------
% 1.54/1.34 % (2343)------------------------------
% 1.54/1.34 % (2342)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2210 for (3000ds/2Mi)
% 1.54/1.34 % (2344)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_2210 for (3000ds/275Mi)
% 1.54/1.34 % (2345)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2210 for (3000ds/18Mi)
% 1.54/1.34 % (2342)Instruction limit reached!
% 1.54/1.34 % (2342)------------------------------
% 1.54/1.34 % (2342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.34 % (2342)Termination reason: Unknown
% 1.54/1.34 % (2342)Termination phase: Saturation
% 1.54/1.34
% 1.54/1.34 % (2342)Memory used [KB]: 5500
% 1.54/1.34 % (2342)Time elapsed: 0.003 s
% 1.54/1.34 % (2342)Instructions burned: 2 (million)
% 1.54/1.34 % (2342)------------------------------
% 1.54/1.34 % (2342)------------------------------
% 1.54/1.34 % (2340)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_2210 for (3000ds/4Mi)
% 1.54/1.35 % (2340)Instruction limit reached!
% 1.54/1.35 % (2340)------------------------------
% 1.54/1.35 % (2340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (2340)Termination reason: Unknown
% 1.54/1.35 % (2340)Termination phase: Saturation
% 1.54/1.35
% 1.54/1.35 % (2340)Memory used [KB]: 5500
% 1.54/1.35 % (2340)Time elapsed: 0.003 s
% 1.54/1.35 % (2340)Instructions burned: 6 (million)
% 1.54/1.35 % (2340)------------------------------
% 1.54/1.35 % (2340)------------------------------
% 1.54/1.35 % (2346)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/3Mi)
% 1.54/1.35 % (2344)Refutation not found, incomplete strategy
% 1.54/1.35 % (2344)------------------------------
% 1.54/1.35 % (2344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (2344)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.35
% 1.54/1.35
% 1.54/1.35 % (2344)Memory used [KB]: 5500
% 1.54/1.35 % (2344)Time elapsed: 0.007 s
% 1.54/1.35 % (2344)Instructions burned: 8 (million)
% 1.54/1.35 % (2344)------------------------------
% 1.54/1.35 % (2344)------------------------------
% 1.54/1.35 % (2346)Instruction limit reached!
% 1.54/1.35 % (2346)------------------------------
% 1.54/1.35 % (2346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (2346)Termination reason: Unknown
% 1.54/1.35 % (2346)Termination phase: Saturation
% 1.54/1.35
% 1.54/1.35 % (2346)Memory used [KB]: 5500
% 1.54/1.35 % (2346)Time elapsed: 0.003 s
% 1.54/1.35 % (2346)Instructions burned: 6 (million)
% 1.54/1.35 % (2346)------------------------------
% 1.54/1.35 % (2346)------------------------------
% 1.54/1.35 % (2345)Instruction limit reached!
% 1.54/1.35 % (2345)------------------------------
% 1.54/1.35 % (2345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.35 % (2345)Termination reason: Unknown
% 1.54/1.35 % (2345)Termination phase: Saturation
% 1.54/1.35
% 1.54/1.35 % (2345)Memory used [KB]: 5628
% 1.54/1.35 % (2345)Time elapsed: 0.011 s
% 1.54/1.35 % (2345)Instructions burned: 19 (million)
% 1.54/1.35 % (2345)------------------------------
% 1.54/1.35 % (2345)------------------------------
% 1.54/1.36 % (2349)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/3Mi)
% 1.54/1.36 % (2347)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_2210 for (2999ds/37Mi)
% 1.54/1.36 % (2349)Instruction limit reached!
% 1.54/1.36 % (2349)------------------------------
% 1.54/1.36 % (2349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (2349)Termination reason: Unknown
% 1.54/1.36 % (2349)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (2349)Memory used [KB]: 5500
% 1.54/1.36 % (2349)Time elapsed: 0.002 s
% 1.54/1.36 % (2349)Instructions burned: 3 (million)
% 1.54/1.36 % (2349)------------------------------
% 1.54/1.36 % (2349)------------------------------
% 1.54/1.36 % (2351)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/7Mi)
% 1.54/1.36 % (2348)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_2210 for (2999ds/15Mi)
% 1.54/1.36 % (2351)Instruction limit reached!
% 1.54/1.36 % (2351)------------------------------
% 1.54/1.36 % (2351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (2351)Termination reason: Unknown
% 1.54/1.36 % (2351)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (2351)Memory used [KB]: 1023
% 1.54/1.36 % (2351)Time elapsed: 0.004 s
% 1.54/1.36 % (2351)Instructions burned: 10 (million)
% 1.54/1.36 % (2351)------------------------------
% 1.54/1.36 % (2351)------------------------------
% 1.54/1.36 % (2350)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/1041Mi)
% 1.54/1.37 % (2348)Refutation not found, incomplete strategy
% 1.54/1.37 % (2348)------------------------------
% 1.54/1.37 % (2348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.37 % (2348)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.37
% 1.54/1.37
% 1.54/1.37 % (2348)Memory used [KB]: 5628
% 1.54/1.37 % (2348)Time elapsed: 0.007 s
% 1.54/1.37 % (2348)Instructions burned: 10 (million)
% 1.54/1.37 % (2348)------------------------------
% 1.54/1.37 % (2348)------------------------------
% 1.54/1.37 % (2353)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/3Mi)
% 1.54/1.37 % (2353)Instruction limit reached!
% 1.54/1.37 % (2353)------------------------------
% 1.54/1.37 % (2353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.37 % (2353)Termination reason: Unknown
% 1.54/1.37 % (2353)Termination phase: Saturation
% 1.54/1.37
% 1.54/1.37 % (2353)Memory used [KB]: 5500
% 1.54/1.37 % (2353)Time elapsed: 0.002 s
% 1.54/1.37 % (2353)Instructions burned: 3 (million)
% 1.54/1.37 % (2353)------------------------------
% 1.54/1.37 % (2353)------------------------------
% 1.54/1.37 % (2352)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/16Mi)
% 1.54/1.37 % (2354)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/3Mi)
% 1.54/1.37 % (2354)Instruction limit reached!
% 1.54/1.37 % (2354)------------------------------
% 1.54/1.37 % (2354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.37 % (2354)Termination reason: Unknown
% 1.54/1.37 % (2354)Termination phase: Saturation
% 1.54/1.37
% 1.54/1.37 % (2354)Memory used [KB]: 5500
% 1.54/1.37 % (2354)Time elapsed: 0.002 s
% 1.54/1.37 % (2354)Instructions burned: 3 (million)
% 1.54/1.37 % (2354)------------------------------
% 1.54/1.37 % (2354)------------------------------
% 1.54/1.37 % (2347)Instruction limit reached!
% 1.54/1.37 % (2347)------------------------------
% 1.54/1.37 % (2347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.37 % (2347)Termination reason: Unknown
% 1.54/1.37 % (2347)Termination phase: Saturation
% 1.54/1.37
% 1.54/1.37 % (2347)Memory used [KB]: 6012
% 1.54/1.37 % (2347)Time elapsed: 0.019 s
% 1.54/1.37 % (2347)Instructions burned: 38 (million)
% 1.54/1.37 % (2347)------------------------------
% 1.54/1.37 % (2347)------------------------------
% 1.54/1.38 % (2352)Instruction limit reached!
% 1.54/1.38 % (2352)------------------------------
% 1.54/1.38 % (2352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.38 % (2352)Termination reason: Unknown
% 1.54/1.38 % (2352)Termination phase: Saturation
% 1.54/1.38
% 1.54/1.38 % (2352)Memory used [KB]: 5628
% 1.54/1.38 % (2352)Time elapsed: 0.010 s
% 1.54/1.38 % (2352)Instructions burned: 16 (million)
% 1.54/1.38 % (2352)------------------------------
% 1.54/1.38 % (2352)------------------------------
% 1.54/1.38 % (2356)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/3Mi)
% 1.54/1.38 % (2356)Instruction limit reached!
% 1.54/1.38 % (2356)------------------------------
% 1.54/1.38 % (2356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.38 % (2356)Termination reason: Unknown
% 1.54/1.38 % (2356)Termination phase: Saturation
% 1.54/1.38
% 1.54/1.38 % (2356)Memory used [KB]: 5500
% 1.54/1.38 % (2356)Time elapsed: 0.002 s
% 1.54/1.38 % (2356)Instructions burned: 3 (million)
% 1.54/1.38 % (2356)------------------------------
% 1.54/1.38 % (2356)------------------------------
% 1.54/1.38 % (2357)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/4Mi)
% 1.54/1.38 % (2357)Instruction limit reached!
% 1.54/1.38 % (2357)------------------------------
% 1.54/1.38 % (2357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.38 % (2357)Termination reason: Unknown
% 1.54/1.38 % (2357)Termination phase: Saturation
% 1.54/1.38
% 1.54/1.38 % (2357)Memory used [KB]: 5500
% 1.54/1.38 % (2357)Time elapsed: 0.003 s
% 1.54/1.38 % (2357)Instructions burned: 6 (million)
% 1.54/1.38 % (2357)------------------------------
% 1.54/1.38 % (2357)------------------------------
% 1.54/1.38 % (2355)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/7Mi)
% 1.54/1.39 % (2355)Refutation not found, incomplete strategy
% 1.54/1.39 % (2355)------------------------------
% 1.54/1.39 % (2355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (2355)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.39
% 1.54/1.39
% 1.54/1.39 % (2355)Memory used [KB]: 5500
% 1.54/1.39 % (2355)Time elapsed: 0.003 s
% 1.54/1.39 % (2355)Instructions burned: 3 (million)
% 1.54/1.39 % (2355)------------------------------
% 1.54/1.39 % (2355)------------------------------
% 1.54/1.39 % (2360)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/6Mi)
% 1.54/1.39 % (2360)Instruction limit reached!
% 1.54/1.39 % (2360)------------------------------
% 1.54/1.39 % (2360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (2360)Termination reason: Unknown
% 1.54/1.39 % (2360)Termination phase: Saturation
% 1.54/1.39
% 1.54/1.39 % (2360)Memory used [KB]: 5500
% 1.54/1.39 % (2360)Time elapsed: 0.003 s
% 1.54/1.39 % (2360)Instructions burned: 6 (million)
% 1.54/1.39 % (2360)------------------------------
% 1.54/1.39 % (2360)------------------------------
% 1.54/1.39 % (2358)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/18Mi)
% 1.54/1.39 % (2359)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/710Mi)
% 1.54/1.39 % (2339)Instruction limit reached!
% 1.54/1.39 % (2339)------------------------------
% 1.54/1.39 % (2339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (2339)Termination reason: Unknown
% 1.54/1.39 % (2339)Termination phase: Saturation
% 1.54/1.39 % (2358)Refutation not found, incomplete strategy
% 1.54/1.39 % (2358)------------------------------
% 1.54/1.39 % (2358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (2358)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.39
% 1.54/1.39
% 1.54/1.39 % (2358)Memory used [KB]: 5500
% 1.54/1.39 % (2358)Time elapsed: 0.002 s
% 1.54/1.39 % (2358)Instructions burned: 1 (million)
% 1.54/1.39 % (2358)------------------------------
% 1.54/1.39 % (2358)------------------------------
% 1.54/1.39 % (2361)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/902Mi)
% 1.54/1.39
% 1.54/1.39 % (2339)Memory used [KB]: 6268
% 1.54/1.39 % (2339)Time elapsed: 0.054 s
% 1.54/1.39 % (2339)Instructions burned: 185 (million)
% 1.54/1.39 % (2339)------------------------------
% 1.54/1.39 % (2339)------------------------------
% 1.59/1.40 % (2362)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/21Mi)
% 1.59/1.40 % (2364)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/6Mi)
% 1.59/1.40 % (2365)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/377Mi)
% 1.59/1.40 % (2364)Instruction limit reached!
% 1.59/1.40 % (2364)------------------------------
% 1.59/1.40 % (2364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.40 % (2364)Termination reason: Unknown
% 1.59/1.40 % (2364)Termination phase: Saturation
% 1.59/1.40
% 1.59/1.40 % (2364)Memory used [KB]: 5500
% 1.59/1.40 % (2364)Time elapsed: 0.003 s
% 1.59/1.40 % (2364)Instructions burned: 8 (million)
% 1.59/1.40 % (2364)------------------------------
% 1.59/1.40 % (2364)------------------------------
% 1.59/1.41 % (2363)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/5Mi)
% 1.59/1.41 % (2362)Instruction limit reached!
% 1.59/1.41 % (2362)------------------------------
% 1.59/1.41 % (2362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.41 % (2362)Termination reason: Unknown
% 1.59/1.41 % (2362)Termination phase: Saturation
% 1.59/1.41
% 1.59/1.41 % (2362)Memory used [KB]: 5628
% 1.59/1.41 % (2362)Time elapsed: 0.033 s
% 1.59/1.41 % (2362)Instructions burned: 22 (million)
% 1.59/1.41 % (2362)------------------------------
% 1.59/1.41 % (2362)------------------------------
% 1.59/1.41 % (2363)Instruction limit reached!
% 1.59/1.41 % (2363)------------------------------
% 1.59/1.41 % (2363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.41 % (2363)Termination reason: Unknown
% 1.59/1.41 % (2363)Termination phase: Saturation
% 1.59/1.41
% 1.59/1.41 % (2363)Memory used [KB]: 5500
% 1.59/1.41 % (2363)Time elapsed: 0.026 s
% 1.59/1.41 % (2363)Instructions burned: 5 (million)
% 1.59/1.41 % (2363)------------------------------
% 1.59/1.41 % (2363)------------------------------
% 1.59/1.41 % (2366)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/779Mi)
% 1.59/1.42 % (2367)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/19Mi)
% 1.59/1.42 % (2367)Instruction limit reached!
% 1.59/1.42 % (2367)------------------------------
% 1.59/1.42 % (2367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.42 % (2367)Termination reason: Unknown
% 1.59/1.42 % (2367)Termination phase: Saturation
% 1.59/1.42
% 1.59/1.42 % (2367)Memory used [KB]: 5628
% 1.59/1.42 % (2367)Time elapsed: 0.007 s
% 1.59/1.42 % (2367)Instructions burned: 20 (million)
% 1.59/1.42 % (2367)------------------------------
% 1.59/1.42 % (2367)------------------------------
% 1.59/1.43 % (2368)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2210 for (2999ds/879Mi)
% 1.59/1.43 % (2369)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2210 for (2998ds/17Mi)
% 1.59/1.43 % (2368)Refutation not found, incomplete strategy
% 1.59/1.43 % (2368)------------------------------
% 1.59/1.43 % (2368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.43 % (2368)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.43
% 1.59/1.43
% 1.59/1.43 % (2368)Memory used [KB]: 5500
% 1.59/1.43 % (2368)Time elapsed: 0.007 s
% 1.59/1.43 % (2368)Instructions burned: 11 (million)
% 1.59/1.43 % (2368)------------------------------
% 1.59/1.43 % (2368)------------------------------
% 1.59/1.44 % (2369)Instruction limit reached!
% 1.59/1.44 % (2369)------------------------------
% 1.59/1.44 % (2369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.44 % (2369)Termination reason: Unknown
% 1.59/1.44 % (2369)Termination phase: Saturation
% 1.59/1.44
% 1.59/1.44 % (2369)Memory used [KB]: 5628
% 1.59/1.44 % (2369)Time elapsed: 0.007 s
% 1.59/1.44 % (2369)Instructions burned: 19 (million)
% 1.59/1.44 % (2369)------------------------------
% 1.59/1.44 % (2369)------------------------------
% 1.59/1.45 % (2371)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2210 for (2998ds/30Mi)
% 1.59/1.45 % (2370)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2210 for (2998ds/3Mi)
% 1.59/1.45 % (2370)Instruction limit reached!
% 1.59/1.45 % (2370)------------------------------
% 1.59/1.45 % (2370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.45 % (2370)Termination reason: Unknown
% 1.59/1.45 % (2370)Termination phase: Saturation
% 1.59/1.45
% 1.59/1.45 % (2370)Memory used [KB]: 1023
% 1.59/1.45 % (2370)Time elapsed: 0.003 s
% 1.59/1.45 % (2370)Instructions burned: 3 (million)
% 1.59/1.45 % (2370)------------------------------
% 1.59/1.45 % (2370)------------------------------
% 1.59/1.45 % (2371)First to succeed.
% 1.59/1.46 % (2371)Refutation found. Thanks to Tanya!
% 1.59/1.46 % SZS status Theorem for DTF2THF_2210
% 1.59/1.46 % SZS output start Proof for DTF2THF_2210
% 1.59/1.46 thf(type_def_5, type, b: $tType).
% 1.59/1.46 thf(type_def_7, type, a: $tType).
% 1.59/1.46 thf(func_def_0, type, b: $tType).
% 1.59/1.46 thf(func_def_1, type, a: $tType).
% 1.59/1.46 thf(func_def_2, type, g: b > b).
% 1.59/1.46 thf(func_def_3, type, f: a > a).
% 1.59/1.46 thf(func_def_4, type, cS: a > b > $o).
% 1.59/1.46 thf(func_def_8, type, sK0: (a > b > $o) > b).
% 1.59/1.46 thf(func_def_9, type, sK1: (a > b > $o) > a).
% 1.59/1.46 thf(func_def_12, type, inv_g_3: b > b).
% 1.59/1.46 thf(func_def_13, type, inv_f_4: a > a).
% 1.59/1.46 thf(func_def_14, type, ph5: !>[X0: $tType]:(X0)).
% 1.59/1.46 thf(f57,plain,(
% 1.59/1.46 $false),
% 1.59/1.46 inference(avatar_sat_refutation,[status(thm)],[f52,f54,f56])).
% 1.59/1.46 thf(f56,plain,(
% 1.59/1.46 ~spl2_1),
% 1.59/1.46 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 1.59/1.46 thf(f55,plain,(
% 1.59/1.46 $false | ~spl2_1),
% 1.59/1.46 inference(equality_resolution,[status(thm)],[f48])).
% 1.59/1.46 thf(f48,plain,(
% 1.59/1.46 ( ! [X0 : b] : (((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ Y1)))))) != X0)) ) | ~spl2_1),
% 1.59/1.46 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.59/1.46 thf(f47,definition,(
% 1.59/1.46 spl2_1 <=> ! [X0 : b] : ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ Y1)))))) != X0)),
% 1.59/1.46 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.59/1.46 thf(f54,plain,(
% 1.59/1.46 ~spl2_2),
% 1.59/1.46 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.59/1.46 thf(f53,plain,(
% 1.59/1.46 $false | ~spl2_2),
% 1.59/1.46 inference(equality_resolution,[status(thm)],[f51])).
% 1.59/1.46 thf(f51,plain,(
% 1.59/1.46 ( ! [X1 : a] : (((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ Y1)))))) != X1)) ) | ~spl2_2),
% 1.59/1.46 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.59/1.46 thf(f50,definition,(
% 1.59/1.46 spl2_2 <=> ! [X1 : a] : ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ Y1)))))) != X1)),
% 1.59/1.46 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.59/1.46 thf(f52,plain,(
% 1.59/1.46 spl2_1 | spl2_2),
% 1.59/1.46 inference(avatar_split_clause,[status(thm)],[f44,f50,f47])).
% 1.59/1.46 thf(f44,plain,(
% 1.59/1.46 ( ! [X0 : b,X1 : a] : (((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ Y1)))))) != X0) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ Y1)))))) != X1)) )),
% 1.59/1.46 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.59/1.46 thf(f43,plain,(
% 1.59/1.46 ( ! [X0 : b,X1 : a] : (((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))) != X0) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))) != X1)) )),
% 1.59/1.46 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.59/1.46 thf(f40,plain,(
% 1.59/1.46 ( ! [X0 : b,X1 : a] : (((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))) != X0) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))) != X1) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y3)))) @ Y0 @ Y1))))))) != X0)) )),
% 1.59/1.46 inference(equality_resolution,[status(thm)],[f36])).
% 1.59/1.46 thf(f36,plain,(
% 1.59/1.46 ( ! [X2 : b,X0 : a > b > b,X1 : a] : (((g @ X2) != (X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))))) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X2) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ Y0) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X1)) )),
% 1.59/1.46 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.59/1.46 thf(f35,plain,(
% 1.59/1.46 ( ! [X2 : b,X0 : a > b > b,X1 : a] : (((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X1) | ((g @ X2) != (X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))))) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X2)) )),
% 1.59/1.46 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.59/1.46 thf(f33,plain,(
% 1.59/1.46 ( ! [X2 : b,X0 : a > b > b,X1 : a] : (((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X1) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X1) | ((g @ X2) != (X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))))) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ ((^[Y2 : a]: ((^[Y3 : b]: (Y2)))) @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X2)) )),
% 1.59/1.46 inference(equality_resolution,[status(thm)],[f31])).
% 1.59/1.46 thf(f31,plain,(
% 1.59/1.46 ( ! [X2 : b,X3 : a,X0 : a > b > b,X1 : a > b > a] : (((X1 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))))) != (f @ X3)) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X3) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))) != X2) | ((X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1)))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ (inv_g_3 @ (X0 @ Y0 @ Y1))))))))) != (g @ X2))) )),
% 1.59/1.46 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.59/1.46 thf(f28,plain,(
% 1.59/1.46 ( ! [X2 : b,X3 : a,X0 : a > b > b,X1 : a > b > a] : (((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_g_3 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1)))))) != X3) | ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_g_3 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1)))))) != X2) | ((X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_g_3 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_g_3 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1)))))))) != (g @ X2)) | ((f @ X3) != (X1 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_g_3 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X1 @ Y0 @ Y1)) @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_g_3 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1)))))))))) )),
% 1.59/1.46 inference(constrained_superposition,[status(thm)],[f27,f13])).
% 1.59/1.46 thf(f13,plain,(
% 1.59/1.46 ( ! [X2 : b] : (((inv_g_3 @ (g @ X2)) = X2)) )),
% 1.59/1.46 inference(injectivity,[status(thm)],[f11])).
% 1.59/1.46 thf(f11,plain,(
% 1.59/1.46 ( ! [X2 : b,X3 : b] : (((g @ X2) != (g @ X3)) | (X2 = X3)) )),
% 1.59/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.46 thf(f9,plain,(
% 1.59/1.46 ! [X0 : a,X1 : a] : (((f @ X0) != (f @ X1)) | (X0 = X1)) & ! [X2 : b,X3 : b] : (((g @ X2) != (g @ X3)) | (X2 = X3)) & ! [X4 : a > b > $o] : ((cS @ (sK1 @ X4) @ (sK0 @ X4)) != (X4 @ (f @ (sK1 @ X4)) @ (g @ (sK0 @ X4))))),
% 1.59/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.59/1.46 thf(f8,plain,(
% 1.59/1.46 ! [X4 : a > b > $o] : (? [X5 : b,X6 : a] : ((cS @ X6 @ X5) != (X4 @ (f @ X6) @ (g @ X5))) => ((cS @ (sK1 @ X4) @ (sK0 @ X4)) != (X4 @ (f @ (sK1 @ X4)) @ (g @ (sK0 @ X4)))))),
% 1.59/1.46 introduced(definition,[],[choice_axiom])).
% 1.59/1.46 thf(f7,plain,(
% 1.59/1.46 ! [X0 : a,X1 : a] : (((f @ X0) != (f @ X1)) | (X0 = X1)) & ! [X2 : b,X3 : b] : (((g @ X2) != (g @ X3)) | (X2 = X3)) & ! [X4 : a > b > $o] : ? [X5 : b,X6 : a] : ((cS @ X6 @ X5) != (X4 @ (f @ X6) @ (g @ X5)))),
% 1.59/1.46 inference(flattening,[status(thm)],[f6])).
% 1.59/1.46 thf(f6,plain,(
% 1.59/1.46 ! [X4 : a > b > $o] : ? [X5 : b,X6 : a] : ((cS @ X6 @ X5) != (X4 @ (f @ X6) @ (g @ X5))) & (! [X2 : b,X3 : b] : (((g @ X2) != (g @ X3)) | (X2 = X3)) & ! [X0 : a,X1 : a] : (((f @ X0) != (f @ X1)) | (X0 = X1)))),
% 1.59/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.59/1.46 thf(f5,plain,(
% 1.59/1.46 ~((! [X3 : b,X2 : b] : (((g @ X2) = (g @ X3)) => (X2 = X3)) & ! [X1 : a,X0 : a] : (((f @ X0) = (f @ X1)) => (X0 = X1))) => ? [X4 : a > b > $o] : ! [X5 : b,X6 : a] : ((cS @ X6 @ X5) = (X4 @ (f @ X6) @ (g @ X5))))),
% 1.59/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.46 thf(f4,plain,(
% 1.59/1.46 ~((! [X0 : a,X1 : a] : (((f @ X0) = (f @ X1)) => (X0 = X1)) & ! [X2 : b,X3 : b] : (((g @ X2) = (g @ X3)) => (X2 = X3))) => ? [X4 : a > b > $o] : ! [X5 : b,X6 : a] : ((X4 @ (f @ X6) @ (g @ X5)) <=> (cS @ X6 @ X5)))),
% 1.59/1.46 inference(rectify,[status(thm)],[f2])).
% 1.59/1.46 thf(f2,negated_conjecture,(
% 1.59/1.46 ~((! [X1 : a,X0 : a] : (((f @ X0) = (f @ X1)) => (X0 = X1)) & ! [X1 : b,X0 : b] : (((g @ X0) = (g @ X1)) => (X0 = X1))) => ? [X2 : a > b > $o] : ! [X1 : b,X0 : a] : ((X2 @ (f @ X0) @ (g @ X1)) <=> (cS @ X0 @ X1)))),
% 1.59/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.46 thf(f1,conjecture,(
% 1.59/1.46 (! [X1 : a,X0 : a] : (((f @ X0) = (f @ X1)) => (X0 = X1)) & ! [X1 : b,X0 : b] : (((g @ X0) = (g @ X1)) => (X0 = X1))) => ? [X2 : a > b > $o] : ! [X1 : b,X0 : a] : ((X2 @ (f @ X0) @ (g @ X1)) <=> (cS @ X0 @ X1))),
% 1.59/1.46 file('/export/starexec/sandbox/tmp/tmp.bxtqAGdCHl/DTF2THF_2210.p',cSV7_pme)).
% 1.59/1.46 thf(f27,plain,(
% 1.59/1.46 ( ! [X2 : a,X0 : a > b > a,X1 : a > b > b] : (((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X0 @ Y0 @ Y1)) @ (X1 @ Y0 @ Y1)))))) != (X1 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X0 @ Y0 @ Y1)) @ (X1 @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X0 @ Y0 @ Y1)) @ (X1 @ Y0 @ Y1))))))))) | ((f @ X2) != (X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X0 @ Y0 @ Y1)) @ (X1 @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X0 @ Y0 @ Y1)) @ (X1 @ Y0 @ Y1))))))))) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (inv_f_4 @ (X0 @ Y0 @ Y1)) @ (X1 @ Y0 @ Y1)))))) != X2)) )),
% 1.59/1.46 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.59/1.46 thf(f24,plain,(
% 1.59/1.46 ( ! [X2 : a,X0 : a > b > a,X1 : a > b > b] : (((X1 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_f_4 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_f_4 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_f_4 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) | ((sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_f_4 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))) != X2) | ((f @ X2) != (X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_f_4 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ ((^[Y2 : a]: ((^[Y3 : b]: (inv_f_4 @ (X0 @ Y2 @ Y3))))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))))))) )),
% 1.59/1.46 inference(constrained_superposition,[status(thm)],[f20,f15])).
% 1.59/1.46 thf(f15,plain,(
% 1.59/1.46 ( ! [X0 : a] : (((inv_f_4 @ (f @ X0)) = X0)) )),
% 1.59/1.46 inference(injectivity,[status(thm)],[f12])).
% 1.59/1.46 thf(f12,plain,(
% 1.59/1.46 ( ! [X0 : a,X1 : a] : (((f @ X0) != (f @ X1)) | (X0 = X1)) )),
% 1.59/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.46 thf(f20,plain,(
% 1.59/1.46 ( ! [X0 : a > b > a,X1 : a > b > b] : (((X0 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))))) != (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) | ((X1 @ (f @ (sK1 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))))) @ (g @ (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))))) != (sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (cS @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))))))) )),
% 1.59/1.46 inference(equality_resolution,[status(thm)],[f10])).
% 1.59/1.46 thf(f10,plain,(
% 1.59/1.46 ( ! [X4 : a > b > $o] : (((cS @ (sK1 @ X4) @ (sK0 @ X4)) != (X4 @ (f @ (sK1 @ X4)) @ (g @ (sK0 @ X4))))) )),
% 1.59/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.46 % SZS output end Proof for DTF2THF_2210
% 1.59/1.46 % (2371)------------------------------
% 1.59/1.46 % (2371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.46 % (2371)Termination reason: Refutation
% 1.59/1.46
% 1.59/1.46 % (2371)Memory used [KB]: 5756
% 1.59/1.46 % (2371)Time elapsed: 0.009 s
% 1.59/1.46 % (2371)Instructions burned: 23 (million)
% 1.59/1.46 % (2371)------------------------------
% 1.59/1.46 % (2371)------------------------------
% 1.59/1.46 % (2338)Success in time 0.137 s
%------------------------------------------------------------------------------