%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT056^2 : TPTP v9.2.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 08:44:45 AM UTC 2026
% Result : Theorem 1.78s 1.64s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 33 unt; 0 typ; 4 def)
% Number of atoms : 228 ( 123 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 1045 ( 39 ~; 42 |; 0 &; 884 @)
% ( 4 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 19 con; 0-2 aty)
% ( 41 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 112 ( 50 ^; 58 !; 4 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
lst: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
lst: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
ap: lst > lst > lst ).
thf(func_def_3,type,
cns: a > lst > lst ).
thf(func_def_4,type,
nl: lst ).
thf(func_def_5,type,
xs: lst ).
thf(func_def_16,type,
sK0: lst ).
thf(func_def_17,type,
sK1: lst ).
thf(func_def_19,type,
sK3: a ).
thf(func_def_20,type,
sK4: lst ).
thf(func_def_21,type,
sK5: ( lst > $o ) > a ).
thf(func_def_22,type,
sK6: ( lst > $o ) > lst ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: lst ).
thf(func_def_25,type,
sK9: a ).
thf(func_def_26,type,
sK10: lst ).
thf(func_def_27,type,
sK11: a ).
thf(func_def_28,type,
sK12: lst ).
thf(func_def_29,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f194,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f122,f131,f175,f183,f191]) ).
thf(f191,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[status(thm)],[f190]) ).
thf(f190,plain,
( $false
| ~ spl2_11 ),
inference(trivial_inequality_removal,[status(thm)],[f189]) ).
thf(f189,plain,
( ( ( ap @ xs @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ xs @ ( ap @ sK1 @ sK0 ) ) )
| ~ spl2_11 ),
inference(superposition,[status(thm)],[f18,f126]) ).
thf(f126,plain,
( ! [X0: lst] :
( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[status(thm)],[f125]) ).
thf(f125,definition,
( spl2_11
<=> ! [X0: lst] :
( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition]) ).
thf(f18,plain,
( ( ap @ xs @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ xs @ sK1 ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ap @ xs @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ xs @ sK1 ) @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: lst,X1: lst] :
( ( ap @ ( ap @ xs @ X1 ) @ X0 )
!= ( ap @ xs @ ( ap @ X1 @ X0 ) ) )
=> ( ( ap @ xs @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ xs @ sK1 ) @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
? [X0: lst,X1: lst] :
( ( ap @ ( ap @ xs @ X1 ) @ X0 )
!= ( ap @ xs @ ( ap @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ! [X0: lst,X1: lst] :
( ( ap @ ( ap @ xs @ X1 ) @ X0 )
= ( ap @ xs @ ( ap @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X8: lst,X7: lst] :
( ( ap @ xs @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ xs @ X7 ) @ X8 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X8: lst,X7: lst] :
( ( ap @ xs @ ( ap @ X7 @ X8 ) )
= ( ap @ ( ap @ xs @ X7 ) @ X8 ) ),
file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',conj_0) ).
thf(f183,plain,
( ~ spl2_9
| spl2_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f182]) ).
thf(f182,plain,
( $false
| ~ spl2_9
| spl2_12 ),
inference(trivial_inequality_removal,[status(thm)],[f181]) ).
thf(f181,plain,
( ( ( cns @ sK9 @ ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) ) )
!= ( cns @ sK9 @ ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) ) ) )
| ~ spl2_9
| spl2_12 ),
inference(forward_demodulation,[status(thm)],[f180,f117]) ).
thf(f117,plain,
( ( ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f115,definition,
( spl2_9
<=> ( ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition]) ).
thf(f180,plain,
( ( ( cns @ sK9 @ ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) )
!= ( cns @ sK9 @ ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) ) ) )
| spl2_12 ),
inference(superposition,[status(thm)],[f178,f168]) ).
thf(f168,plain,
! [X2: a,X3: lst,X1: lst] :
( ( ap @ ( cns @ X2 @ X3 ) @ X1 )
= ( cns @ X2 @ ( ap @ X3 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: a,X3: lst,X1: lst] :
( ( ( ap @ ( cns @ X2 @ X3 ) @ X1 )
= ( cns @ X2 @ ( ap @ X3 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: a,X3: lst,X1: lst] :
( ( ^ [Y0: lst] :
( ( ap @ ( cns @ X2 @ Y0 ) @ X1 )
= ( cns @ X2 @ ( ap @ Y0 @ X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X2: a,X1: lst] :
( ( !! @ lst
@ ^ [Y0: lst] :
( ( ap @ ( cns @ X2 @ Y0 ) @ X1 )
= ( cns @ X2 @ ( ap @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
! [X2: a,X1: lst] :
( $true
= ( ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ap @ ( cns @ Y0 @ Y1 ) @ X1 )
= ( cns @ Y0 @ ( ap @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
! [X1: lst] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ap @ ( cns @ Y0 @ Y1 ) @ X1 )
= ( cns @ Y0 @ ( ap @ Y1 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f162]) ).
thf(f162,plain,
! [X1: lst] :
( $true
= ( ^ [Y0: lst] :
( !! @ a
@ ^ [Y1: a] :
( !! @ lst
@ ^ [Y2: lst] :
( ( ap @ ( cns @ Y1 @ Y2 ) @ Y0 )
= ( cns @ Y1 @ ( ap @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( !! @ lst
@ ^ [Y0: lst] :
( !! @ a
@ ^ [Y1: a] :
( !! @ lst
@ ^ [Y2: lst] :
( ( ap @ ( cns @ Y1 @ Y2 ) @ Y0 )
= ( cns @ Y1 @ ( ap @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ lst
@ ^ [Y0: lst] :
( !! @ a
@ ^ [Y1: a] :
( !! @ lst
@ ^ [Y2: lst] :
( ( ap @ ( cns @ Y1 @ Y2 ) @ Y0 )
= ( cns @ Y1 @ ( ap @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: lst,X1: a,X2: lst] :
( ( ap @ ( cns @ X1 @ X0 ) @ X2 )
= ( cns @ X1 @ ( ap @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X5: lst,X6: a,X4: lst] :
( ( ap @ ( cns @ X6 @ X5 ) @ X4 )
= ( cns @ X6 @ ( ap @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',fact_1p_Osimps_I2_J) ).
thf(f178,plain,
( ( ( cns @ sK9 @ ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) ) )
!= ( ap @ ( cns @ sK9 @ ( ap @ sK10 @ sK1 ) ) @ sK0 ) )
| spl2_12 ),
inference(forward_demodulation,[status(thm)],[f177,f168]) ).
thf(f177,plain,
( ( ( cns @ sK9 @ ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) ) )
!= ( ap @ ( ap @ ( cns @ sK9 @ sK10 ) @ sK1 ) @ sK0 ) )
| spl2_12 ),
inference(forward_demodulation,[status(thm)],[f130,f168]) ).
thf(f130,plain,
( ( ( ap @ ( ap @ ( cns @ sK9 @ sK10 ) @ sK1 ) @ sK0 )
!= ( ap @ ( cns @ sK9 @ sK10 ) @ ( ap @ sK1 @ sK0 ) ) )
| spl2_12 ),
inference(avatar_component_clause,[status(thm)],[f128]) ).
thf(f128,definition,
( spl2_12
<=> ( ( ap @ ( ap @ ( cns @ sK9 @ sK10 ) @ sK1 ) @ sK0 )
= ( ap @ ( cns @ sK9 @ sK10 ) @ ( ap @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_12])],[avatar_definition]) ).
thf(f175,plain,
spl2_10,
inference(avatar_contradiction_clause,[status(thm)],[f174]) ).
thf(f174,plain,
( $false
| spl2_10 ),
inference(subsumption_resolution,[status(thm)],[f173,f171]) ).
thf(f171,plain,
! [X1: lst] :
( ( ap @ nl @ X1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X1: lst] :
( ( ( ap @ nl @ X1 )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f169]) ).
thf(f169,plain,
! [X1: lst] :
( ( ^ [Y0: lst] :
( ( ap @ nl @ Y0 )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ lst
@ ^ [Y0: lst] :
( ( ap @ nl @ Y0 )
= Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( !! @ lst
@ ^ [Y0: lst] :
( ( ap @ nl @ Y0 )
= Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: lst] :
( ( ap @ nl @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: lst] :
( ( ap @ nl @ X4 )
= X4 ),
file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',fact_2p_Osimps_I1_J) ).
thf(f173,plain,
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ sK1 @ sK0 ) )
| spl2_10 ),
inference(forward_demodulation,[status(thm)],[f121,f171]) ).
thf(f121,plain,
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| spl2_10 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl2_10
<=> ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition]) ).
thf(f131,plain,
( spl2_11
| ~ spl2_12
| ~ spl2_10 ),
inference(avatar_split_clause,[status(thm)],[f123,f119,f128,f125]) ).
thf(f123,plain,
! [X0: lst] :
( ( ( ap @ ( ap @ ( cns @ sK9 @ sK10 ) @ sK1 ) @ sK0 )
!= ( ap @ ( cns @ sK9 @ sK10 ) @ ( ap @ sK1 @ sK0 ) ) )
| ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X0: lst] :
( ( ( ( ap @ ( cns @ sK9 @ sK10 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ sK9 @ sK10 ) @ sK1 ) @ sK0 ) )
= $false )
| ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) )
| ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: lst] :
( ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) )
| ( $false
= ( ( ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ sK9 @ sK10 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ sK9 @ sK10 ) @ sK1 ) @ sK0 ) ) ) )
| ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: lst] :
( ( $false
= ( ^ [Y0: lst] :
( ( ( ap @ Y0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y0 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ sK9 @ Y0 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ sK9 @ Y0 ) @ sK1 ) @ sK0 ) ) )
@ sK10 ) )
| ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X0: lst] :
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) )
| ( ( !! @ lst
@ ^ [Y0: lst] :
( ( ( ap @ Y0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y0 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ sK9 @ Y0 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ sK9 @ Y0 ) @ sK1 ) @ sK0 ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X0: lst] :
( ( ( ( ap @ X0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ X0 @ sK1 ) @ sK0 ) )
= $true )
| ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( !! @ lst
@ ^ [Y0: lst] :
( ( ( ap @ Y0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y0 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ sK9 @ Y0 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ sK9 @ Y0 ) @ sK1 ) @ sK0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
! [X0: lst] :
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( $false
= ( ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ( ap @ Y1 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y1 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ Y0 @ Y1 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ Y0 @ Y1 ) @ sK1 ) @ sK0 ) ) ) )
@ sK9 ) )
| ( ( ( ap @ X0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ X0 @ sK1 ) @ sK0 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X0: lst] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ( ap @ Y1 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y1 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ Y0 @ Y1 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ Y0 @ Y1 ) @ sK1 ) @ sK0 ) ) ) ) ) )
| ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( ( ap @ X0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ X0 @ sK1 ) @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: lst] :
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ( ap @ Y1 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y1 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ Y0 @ Y1 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ Y0 @ Y1 ) @ sK1 ) @ sK0 ) ) ) ) )
=> ( ( ap @ X0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ X0 @ sK1 ) @ sK0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: lst] :
( ( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
= $false )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ( ap @ Y1 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y1 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ Y0 @ Y1 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ Y0 @ Y1 ) @ sK1 ) @ sK0 ) ) ) ) )
=> ( ( ap @ X0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ X0 @ sK1 ) @ sK0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: lst] :
( $true
= ( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ lst
@ ^ [Y1: lst] :
( ( ( ap @ Y1 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y1 @ sK1 ) @ sK0 ) )
=> ( ( ap @ ( cns @ Y0 @ Y1 ) @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ ( cns @ Y0 @ Y1 ) @ sK1 ) @ sK0 ) ) ) ) )
=> ( ( ap @ X0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ X0 @ sK1 ) @ sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: lst] :
( $true
= ( ^ [Y0: lst > $o] :
( ( Y0 @ nl )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ lst
@ ^ [Y2: lst] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( cns @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X0 ) ) )
@ ^ [Y0: lst] :
( ( ap @ Y0 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ Y0 @ sK1 ) @ sK0 ) ) ) ),
inference(heuristic_instantiation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: lst] :
( ( !! @ ( lst > $o )
@ ^ [Y0: lst > $o] :
( ( Y0 @ nl )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ lst
@ ^ [Y2: lst] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( cns @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: lst] :
( ( ^ [Y0: lst] :
( !! @ ( lst > $o )
@ ^ [Y1: lst > $o] :
( ( Y1 @ nl )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ lst
@ ^ [Y3: lst] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( cns @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ lst
@ ^ [Y0: lst] :
( !! @ ( lst > $o )
@ ^ [Y1: lst > $o] :
( ( Y1 @ nl )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ lst
@ ^ [Y3: lst] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( cns @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( !! @ lst
@ ^ [Y0: lst] :
( !! @ ( lst > $o )
@ ^ [Y1: lst > $o] :
( ( Y1 @ nl )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ lst
@ ^ [Y3: lst] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( cns @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: lst > $o,X1: lst] :
( ( X0 @ nl )
=> ( ! [X2: lst,X3: a] :
( ( X0 @ X2 )
=> ( X0 @ ( cns @ X3 @ X2 ) ) )
=> ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: lst > $o,X0: lst] :
( ( X1 @ nl )
=> ( ! [X3: lst,X2: a] :
( ( X1 @ X3 )
=> ( X1 @ ( cns @ X2 @ X3 ) ) )
=> ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',fact_0_lst_Oinduct) ).
thf(f122,plain,
( spl2_9
| ~ spl2_10 ),
inference(avatar_split_clause,[status(thm)],[f113,f119,f115]) ).
thf(f113,plain,
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) ) ),
inference(condensation,[status(thm)],[f112]) ).
thf(f112,plain,
! [X0: lst] :
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) )
| ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: lst] :
( ( ( ap @ nl @ ( ap @ sK1 @ sK0 ) )
!= ( ap @ ( ap @ nl @ sK1 ) @ sK0 ) )
| ( $true
= ( ( ap @ sK10 @ ( ap @ sK1 @ sK0 ) )
= ( ap @ ( ap @ sK10 @ sK1 ) @ sK0 ) ) )
| ( ( ap @ ( ap @ X0 @ sK1 ) @ sK0 )
= ( ap @ X0 @ ( ap @ sK1 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT056^2 : TPTP v9.2.1. Released v5.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n029.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 06:06:14 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.42 ---- Original DTF file ---
% 0.18/0.42 thf(spec,logic,$$dhol).
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 % File : DAT056^2 : TPTP v9.2.1. Released v5.4.0.
% 0.18/0.42 % Domain : Data Structures
% 0.18/0.42 % Problem : List operation requiring induction
% 0.18/0.42 % Version : Especial.
% 0.18/0.42 % English :
% 0.18/0.42
% 0.18/0.42 % Refs : [Bla12] Blanchette (2012), Email to Geoff Sutcliffe
% 0.18/0.42 % Source : [Bla12]
% 0.18/0.42 % Names : hard.tptp [Bla12]
% 0.18/0.42
% 0.18/0.42 % Status : Theorem
% 0.18/0.42 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.78 v7.3.0, 0.89 v7.2.0, 1.00 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 1.00 v5.4.0
% 0.18/0.42 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 0 def)
% 0.18/0.42 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.42 % Maximal formula atoms : 1 ( 0 avg)
% 0.18/0.42 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 0.18/0.42 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.42 % Maximal formula depth : 11 ( 5 avg)
% 0.18/0.42 % Number of types : 3 ( 2 usr)
% 0.18/0.42 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.42 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.18/0.42 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.18/0.42 % SPC : TH0_THM_EQU_NAR
% 0.18/0.42
% 0.18/0.42 % Comments :
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 %----Should-be-implicit typings (2)
% 0.18/0.42 thf(ty_n_tc__Foo__Olst_It__J,type,
% 0.18/0.42 lst: $tType ).
% 0.18/0.42
% 0.18/0.42 thf(ty_n_t_,type,
% 0.18/0.42 a: $tType ).
% 0.18/0.42
% 0.18/0.42 %----Explicit typings (4)
% 0.18/0.42 thf(sy_c_Foo_Oap_001t_,type,
% 0.18/0.42 ap: lst > lst > lst ).
% 0.18/0.42
% 0.18/0.42 thf(sy_c_Foo_Olst_OCns_001t_,type,
% 0.18/0.42 cns: a > lst > lst ).
% 0.18/0.42
% 0.18/0.42 thf(sy_c_Foo_Olst_ONl_001t_,type,
% 0.18/0.42 nl: lst ).
% 0.18/0.42
% 0.18/0.42 thf(sy_v_xs,type,
% 0.18/0.42 xs: lst ).
% 0.18/0.42
% 0.18/0.42 %----Relevant facts (3)
% 0.18/0.42 thf(fact_0_lst_Oinduct,axiom,
% 0.18/0.42 ! [Lst: lst,P: lst > $o] :
% 0.18/0.42 ( ( P @ nl )
% 0.18/0.42 => ( ! [A: a,Lst2: lst] :
% 0.18/0.42 ( ( P @ Lst2 )
% 0.18/0.42 => ( P @ ( cns @ A @ Lst2 ) ) )
% 0.18/0.42 => ( P @ Lst ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(fact_1p_Osimps_I2_J,axiom,
% 0.18/0.42 ! [Ys2: lst,Xs: lst,X: a] :
% 0.18/0.42 ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
% 0.18/0.42 = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(fact_2p_Osimps_I1_J,axiom,
% 0.18/0.42 ! [Ys2: lst] :
% 0.18/0.42 ( ( ap @ nl @ Ys2 )
% 0.18/0.42 = Ys2 ) ).
% 0.18/0.42
% 0.18/0.42 %----Conjectures (1)
% 0.18/0.42 thf(conj_0,conjecture,
% 0.18/0.42 ! [Ys: lst,Zs: lst] :
% 0.18/0.42 ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
% 0.18/0.42 = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) ).
% 0.18/0.42
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 ------------------------
% 1.65/1.45 ---- Embedded in THF ---
% 1.65/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.45 %%% Generated on Tue Feb 24 06:06:15 EST 2026
% 1.65/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.45 %%% Logic specification used:
% 1.65/1.45 %%% thf(spec, logic, $$dhol).
% 1.65/1.45
% 1.65/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2DTF6147.p
% See solution above
% 1.65/1.45 ------------------------
% 1.65/1.46 ---- Cleaned THF ---
% 1.65/1.46 thf(ty_n_tc__Foo__Olst_It__J,type,
% 1.65/1.46 lst: $tType ).
% 1.65/1.46
% 1.65/1.46 thf(ty_n_t_,type,
% 1.65/1.46 a: $tType ).
% 1.65/1.46
% 1.65/1.46 thf(sy_c_Foo_Oap_001t_,type,
% 1.65/1.46 ap: lst > lst > lst ).
% 1.65/1.46
% 1.65/1.46 thf(sy_c_Foo_Olst_OCns_001t_,type,
% 1.65/1.46 cns: a > lst > lst ).
% 1.65/1.46
% 1.65/1.46 thf(sy_c_Foo_Olst_ONl_001t_,type,
% 1.65/1.46 nl: lst ).
% 1.65/1.46
% 1.65/1.46 thf(sy_v_xs,type,
% 1.65/1.46 xs: lst ).
% 1.65/1.46
% 1.65/1.46 thf(fact_0_lst_Oinduct,axiom,
% 1.65/1.46 ! [Lst: lst,P: lst > $o] :
% 1.65/1.46 ( ( P @ nl )
% 1.65/1.46 => ( ! [A: a,Lst2: lst] :
% 1.65/1.46 ( ( P @ Lst2 )
% 1.65/1.46 => ( P @ ( cns @ A @ Lst2 ) ) )
% 1.65/1.46 => ( P @ Lst ) ) ) ).
% 1.65/1.46
% 1.65/1.46 thf(fact_1p_Osimps_I2_J,axiom,
% 1.65/1.46 ! [Ys2: lst,Xs: lst,X: a] :
% 1.65/1.46 ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
% 1.65/1.46 = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) ).
% 1.65/1.46
% 1.65/1.46 thf(fact_2p_Osimps_I1_J,axiom,
% 1.65/1.46 ! [Ys2: lst] :
% 1.65/1.46 ( ( ap @ nl @ Ys2 )
% 1.65/1.46 = Ys2 ) ).
% 1.65/1.46
% 1.65/1.46 thf(conj_0,conjecture,
% 1.65/1.46 ! [Ys: lst,Zs: lst] :
% 1.65/1.46 ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
% 1.65/1.46 = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) ).
% 1.65/1.46 ------------------------
% 1.65/1.48 % (6248)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_6147 for (2999ds/2Mi)
% 1.65/1.48 % (6246)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_6147 for (2999ds/27Mi)
% 1.65/1.48 % (6249)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_6147 for (2999ds/275Mi)
% 1.65/1.48 % (6250)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/18Mi)
% 1.65/1.48 % (6248)Instruction limit reached!
% 1.65/1.48 % (6248)------------------------------
% 1.65/1.48 % (6248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (6248)Termination reason: Unknown
% 1.65/1.48 % (6248)Termination phase: Property scanning
% 1.65/1.48
% 1.65/1.48 % (6248)Memory used [KB]: 895
% 1.65/1.48 % (6248)Time elapsed: 0.003 s
% 1.65/1.48 % (6248)Instructions burned: 2 (million)
% 1.65/1.48 % (6248)------------------------------
% 1.65/1.48 % (6248)------------------------------
% 1.65/1.48 % (6245)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_6147 for (2999ds/4Mi)
% 1.65/1.48 % (6244)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/183Mi)
% 1.65/1.48 % (6247)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/2Mi)
% 1.65/1.48 % (6249)Refutation not found, incomplete strategy
% 1.65/1.48 % (6249)------------------------------
% 1.65/1.48 % (6249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (6249)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.48
% 1.65/1.48
% 1.65/1.48 % (6249)Memory used [KB]: 5373
% 1.65/1.48 % (6249)Time elapsed: 0.003 s
% 1.65/1.48 % (6249)Instructions burned: 1 (million)
% 1.65/1.48 % (6249)------------------------------
% 1.65/1.48 % (6249)------------------------------
% 1.65/1.49 % (6247)Instruction limit reached!
% 1.65/1.49 % (6247)------------------------------
% 1.65/1.49 % (6247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (6247)Termination reason: Unknown
% 1.65/1.49 % (6247)Termination phase: Property scanning
% 1.65/1.49
% 1.65/1.49 % (6247)Memory used [KB]: 895
% 1.65/1.49 % (6247)Time elapsed: 0.002 s
% 1.65/1.49 % (6247)Instructions burned: 2 (million)
% 1.65/1.49 % (6247)------------------------------
% 1.65/1.49 % (6247)------------------------------
% 1.65/1.49 % (6246)Refutation not found, incomplete strategy
% 1.65/1.49 % (6246)------------------------------
% 1.65/1.49 % (6246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (6246)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.49
% 1.65/1.49
% 1.65/1.49 % (6246)Memory used [KB]: 5500
% 1.65/1.49 % (6246)Time elapsed: 0.004 s
% 1.65/1.49 % (6246)Instructions burned: 2 (million)
% 1.65/1.49 % (6246)------------------------------
% 1.65/1.49 % (6246)------------------------------
% 1.65/1.49 % (6245)Instruction limit reached!
% 1.65/1.49 % (6245)------------------------------
% 1.65/1.49 % (6245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (6245)Termination reason: Unknown
% 1.65/1.49 % (6245)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (6245)Memory used [KB]: 5500
% 1.65/1.49 % (6245)Time elapsed: 0.004 s
% 1.65/1.49 % (6245)Instructions burned: 5 (million)
% 1.65/1.49 % (6245)------------------------------
% 1.65/1.49 % (6245)------------------------------
% 1.65/1.49 % (6250)Instruction limit reached!
% 1.65/1.49 % (6250)------------------------------
% 1.65/1.49 % (6250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (6250)Termination reason: Unknown
% 1.65/1.49 % (6250)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (6250)Memory used [KB]: 5628
% 1.65/1.49 % (6250)Time elapsed: 0.012 s
% 1.65/1.49 % (6250)Instructions burned: 18 (million)
% 1.65/1.49 % (6250)------------------------------
% 1.65/1.49 % (6250)------------------------------
% 1.78/1.50 % (6253)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_6147 for (2999ds/15Mi)
% 1.78/1.50 % (6251)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/3Mi)
% 1.78/1.50 % (6254)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_6147 for (2999ds/3Mi)
% 1.78/1.50 % (6252)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_6147 for (2999ds/37Mi)
% 1.78/1.50 % (6253)Refutation not found, incomplete strategy
% 1.78/1.50 % (6253)------------------------------
% 1.78/1.50 % (6253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6253)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.50
% 1.78/1.50
% 1.78/1.50 % (6253)Memory used [KB]: 5500
% 1.78/1.50 % (6253)Time elapsed: 0.003 s
% 1.78/1.50 % (6253)Instructions burned: 2 (million)
% 1.78/1.50 % (6253)------------------------------
% 1.78/1.50 % (6253)------------------------------
% 1.78/1.50 % (6254)Instruction limit reached!
% 1.78/1.50 % (6254)------------------------------
% 1.78/1.50 % (6254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6254)Termination reason: Unknown
% 1.78/1.50 % (6254)Termination phase: Saturation
% 1.78/1.50
% 1.78/1.50 % (6254)Memory used [KB]: 5500
% 1.78/1.50 % (6254)Time elapsed: 0.003 s
% 1.78/1.50 % (6254)Instructions burned: 3 (million)
% 1.78/1.50 % (6254)------------------------------
% 1.78/1.50 % (6254)------------------------------
% 1.78/1.50 % (6251)Instruction limit reached!
% 1.78/1.50 % (6251)------------------------------
% 1.78/1.50 % (6251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (6251)Termination reason: Unknown
% 1.78/1.50 % (6251)Termination phase: Saturation
% 1.78/1.50
% 1.78/1.50 % (6251)Memory used [KB]: 5500
% 1.78/1.50 % (6251)Time elapsed: 0.005 s
% 1.78/1.50 % (6251)Instructions burned: 4 (million)
% 1.78/1.50 % (6251)------------------------------
% 1.78/1.50 % (6251)------------------------------
% 1.78/1.50 % (6255)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_6147 for (2999ds/1041Mi)
% 1.78/1.51 % (6256)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/7Mi)
% 1.78/1.52 % (6256)Instruction limit reached!
% 1.78/1.52 % (6256)------------------------------
% 1.78/1.52 % (6256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.52 % (6256)Termination reason: Unknown
% 1.78/1.52 % (6256)Termination phase: Saturation
% 1.78/1.52
% 1.78/1.52 % (6256)Memory used [KB]: 1023
% 1.78/1.52 % (6256)Time elapsed: 0.007 s
% 1.78/1.52 % (6256)Instructions burned: 8 (million)
% 1.78/1.52 % (6256)------------------------------
% 1.78/1.52 % (6256)------------------------------
% 1.78/1.52 % (6258)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_6147 for (2999ds/3Mi)
% 1.78/1.52 % (6259)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_6147 for (2999ds/3Mi)
% 1.78/1.52 % (6257)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/16Mi)
% 1.78/1.52 % (6259)Instruction limit reached!
% 1.78/1.52 % (6259)------------------------------
% 1.78/1.52 % (6259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.52 % (6259)Termination reason: Unknown
% 1.78/1.52 % (6259)Termination phase: Saturation
% 1.78/1.52
% 1.78/1.52 % (6259)Memory used [KB]: 1023
% 1.78/1.52 % (6259)Time elapsed: 0.003 s
% 1.78/1.52 % (6259)Instructions burned: 3 (million)
% 1.78/1.52 % (6252)Instruction limit reached!
% 1.78/1.52 % (6252)------------------------------
% 1.78/1.52 % (6252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.52 % (6252)Termination reason: Unknown
% 1.78/1.52 % (6252)Termination phase: Saturation
% 1.78/1.52
% 1.78/1.52 % (6252)Memory used [KB]: 5628
% 1.78/1.52 % (6252)Time elapsed: 0.021 s
% 1.78/1.52 % (6252)Instructions burned: 37 (million)
% 1.78/1.52 % (6252)------------------------------
% 1.78/1.52 % (6252)------------------------------
% 1.78/1.52 % (6259)------------------------------
% 1.78/1.52 % (6259)------------------------------
% 1.78/1.52 % (6258)Instruction limit reached!
% 1.78/1.52 % (6258)------------------------------
% 1.78/1.52 % (6258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.52 % (6258)Termination reason: Unknown
% 1.78/1.52 % (6258)Termination phase: Saturation
% 1.78/1.52
% 1.78/1.52 % (6258)Memory used [KB]: 5500
% 1.78/1.52 % (6258)Time elapsed: 0.004 s
% 1.78/1.52 % (6258)Instructions burned: 4 (million)
% 1.78/1.52 % (6258)------------------------------
% 1.78/1.52 % (6258)------------------------------
% 1.78/1.53 % (6257)Instruction limit reached!
% 1.78/1.53 % (6257)------------------------------
% 1.78/1.53 % (6257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.53 % (6257)Termination reason: Unknown
% 1.78/1.53 % (6257)Termination phase: Saturation
% 1.78/1.53
% 1.78/1.53 % (6257)Memory used [KB]: 5628
% 1.78/1.53 % (6257)Time elapsed: 0.011 s
% 1.78/1.53 % (6257)Instructions burned: 16 (million)
% 1.78/1.53 % (6257)------------------------------
% 1.78/1.53 % (6257)------------------------------
% 1.78/1.53 % (6260)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/7Mi)
% 1.78/1.54 % (6262)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/4Mi)
% 1.78/1.54 % (6263)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/18Mi)
% 1.78/1.54 % (6260)Instruction limit reached!
% 1.78/1.54 % (6260)------------------------------
% 1.78/1.54 % (6260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.54 % (6261)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/3Mi)
% 1.78/1.54 % (6260)Termination reason: Unknown
% 1.78/1.54 % (6260)Termination phase: Saturation
% 1.78/1.54
% 1.78/1.54 % (6260)Memory used [KB]: 5500
% 1.78/1.54 % (6260)Time elapsed: 0.007 s
% 1.78/1.54 % (6260)Instructions burned: 8 (million)
% 1.78/1.54 % (6260)------------------------------
% 1.78/1.54 % (6260)------------------------------
% 1.78/1.54 % (6261)Instruction limit reached!
% 1.78/1.54 % (6261)------------------------------
% 1.78/1.54 % (6261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.54 % (6261)Termination reason: Unknown
% 1.78/1.54 % (6261)Termination phase: Saturation
% 1.78/1.54
% 1.78/1.54 % (6261)Memory used [KB]: 5500
% 1.78/1.54 % (6261)Time elapsed: 0.003 s
% 1.78/1.54 % (6261)Instructions burned: 3 (million)
% 1.78/1.54 % (6261)------------------------------
% 1.78/1.54 % (6261)------------------------------
% 1.78/1.54 % (6263)Refutation not found, incomplete strategy
% 1.78/1.54 % (6263)------------------------------
% 1.78/1.54 % (6263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.54 % (6263)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.54
% 1.78/1.54
% 1.78/1.54 % (6263)Memory used [KB]: 5500
% 1.78/1.54 % (6263)Time elapsed: 0.003 s
% 1.78/1.54 % (6263)Instructions burned: 3 (million)
% 1.78/1.54 % (6263)------------------------------
% 1.78/1.54 % (6263)------------------------------
% 1.78/1.54 % (6262)Instruction limit reached!
% 1.78/1.54 % (6262)------------------------------
% 1.78/1.54 % (6262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.54 % (6262)Termination reason: Unknown
% 1.78/1.54 % (6262)Termination phase: Saturation
% 1.78/1.54
% 1.78/1.54 % (6262)Memory used [KB]: 5500
% 1.78/1.54 % (6262)Time elapsed: 0.005 s
% 1.78/1.54 % (6262)Instructions burned: 5 (million)
% 1.78/1.54 % (6262)------------------------------
% 1.78/1.54 % (6262)------------------------------
% 1.78/1.55 % (6264)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/710Mi)
% 1.78/1.56 % (6265)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/6Mi)
% 1.78/1.56 % (6267)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_6147 for (2999ds/21Mi)
% 1.78/1.56 % (6268)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/5Mi)
% 1.78/1.56 % (6266)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_6147 for (2999ds/902Mi)
% 1.78/1.56 % (6266)Refutation not found, incomplete strategy
% 1.78/1.56 % (6266)------------------------------
% 1.78/1.56 % (6266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.56 % (6266)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.56
% 1.78/1.56
% 1.78/1.56 % (6266)Memory used [KB]: 5500
% 1.78/1.56 % (6266)Time elapsed: 0.003 s
% 1.78/1.56 % (6266)Instructions burned: 2 (million)
% 1.78/1.56 % (6266)------------------------------
% 1.78/1.56 % (6266)------------------------------
% 1.78/1.56 % (6265)Instruction limit reached!
% 1.78/1.56 % (6265)------------------------------
% 1.78/1.56 % (6265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.56 % (6265)Termination reason: Unknown
% 1.78/1.56 % (6265)Termination phase: Saturation
% 1.78/1.56
% 1.78/1.56 % (6265)Memory used [KB]: 5500
% 1.78/1.56 % (6265)Time elapsed: 0.006 s
% 1.78/1.56 % (6265)Instructions burned: 6 (million)
% 1.78/1.56 % (6265)------------------------------
% 1.78/1.56 % (6265)------------------------------
% 1.78/1.56 % (6268)Instruction limit reached!
% 1.78/1.56 % (6268)------------------------------
% 1.78/1.56 % (6268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.56 % (6268)Termination reason: Unknown
% 1.78/1.56 % (6268)Termination phase: Saturation
% 1.78/1.56
% 1.78/1.56 % (6268)Memory used [KB]: 5500
% 1.78/1.56 % (6268)Time elapsed: 0.005 s
% 1.78/1.56 % (6268)Instructions burned: 6 (million)
% 1.78/1.56 % (6268)------------------------------
% 1.78/1.56 % (6268)------------------------------
% 1.78/1.57 % (6267)Instruction limit reached!
% 1.78/1.57 % (6267)------------------------------
% 1.78/1.57 % (6267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.57 % (6267)Termination reason: Unknown
% 1.78/1.57 % (6267)Termination phase: Saturation
% 1.78/1.57
% 1.78/1.57 % (6267)Memory used [KB]: 5628
% 1.78/1.57 % (6267)Time elapsed: 0.013 s
% 1.78/1.57 % (6267)Instructions burned: 21 (million)
% 1.78/1.57 % (6267)------------------------------
% 1.78/1.57 % (6267)------------------------------
% 1.78/1.58 % (6271)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_6147 for (2999ds/779Mi)
% 1.78/1.58 % (6270)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6147 for (2999ds/377Mi)
% 1.78/1.58 % (6269)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_6147 for (2999ds/6Mi)
% 1.78/1.58 % (6269)Refutation not found, incomplete strategy
% 1.78/1.58 % (6269)------------------------------
% 1.78/1.58 % (6269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.58 % (6269)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.58
% 1.78/1.58
% 1.78/1.58 % (6269)Memory used [KB]: 5500
% 1.78/1.58 % (6269)Time elapsed: 0.004 s
% 1.78/1.58 % (6269)Instructions burned: 2 (million)
% 1.78/1.58 % (6269)------------------------------
% 1.78/1.58 % (6269)------------------------------
% 1.78/1.58 % (6271)Refutation not found, incomplete strategy
% 1.78/1.58 % (6271)------------------------------
% 1.78/1.58 % (6271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.58 % (6271)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.58
% 1.78/1.58
% 1.78/1.58 % (6271)Memory used [KB]: 5500
% 1.78/1.58 % (6271)Time elapsed: 0.007 s
% 1.78/1.58 % (6271)Instructions burned: 7 (million)
% 1.78/1.58 % (6271)------------------------------
% 1.78/1.58 % (6271)------------------------------
% 1.78/1.58 % (6244)Instruction limit reached!
% 1.78/1.58 % (6244)------------------------------
% 1.78/1.58 % (6244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.58 % (6244)Termination reason: Unknown
% 1.78/1.58 % (6244)Termination phase: Saturation
% 1.78/1.58
% 1.78/1.58 % (6244)Memory used [KB]: 6140
% 1.78/1.58 % (6244)Time elapsed: 0.101 s
% 1.78/1.58 % (6244)Instructions burned: 183 (million)
% 1.78/1.58 % (6244)------------------------------
% 1.78/1.58 % (6244)------------------------------
% 1.78/1.59 % (6272)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_6147 for (2999ds/19Mi)
% 1.78/1.59 % (6272)Refutation not found, incomplete strategy
% 1.78/1.59 % (6272)------------------------------
% 1.78/1.59 % (6272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.59 % (6272)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.59
% 1.78/1.59
% 1.78/1.59 % (6272)Memory used [KB]: 5500
% 1.78/1.59 % (6272)Time elapsed: 0.003 s
% 1.78/1.59 % (6272)Instructions burned: 2 (million)
% 1.78/1.59 % (6272)------------------------------
% 1.78/1.59 % (6272)------------------------------
% 1.78/1.60 % (6273)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/879Mi)
% 1.78/1.60 % (6274)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/17Mi)
% 1.78/1.60 % (6275)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/3Mi)
% 1.78/1.60 % (6275)Instruction limit reached!
% 1.78/1.60 % (6275)------------------------------
% 1.78/1.60 % (6275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.60 % (6275)Termination reason: Unknown
% 1.78/1.60 % (6275)Termination phase: Saturation
% 1.78/1.60
% 1.78/1.60 % (6275)Memory used [KB]: 1023
% 1.78/1.60 % (6275)Time elapsed: 0.003 s
% 1.78/1.60 % (6275)Instructions burned: 3 (million)
% 1.78/1.60 % (6275)------------------------------
% 1.78/1.60 % (6275)------------------------------
% 1.78/1.60 % (6276)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/30Mi)
% 1.78/1.61 % (6274)Instruction limit reached!
% 1.78/1.61 % (6274)------------------------------
% 1.78/1.61 % (6274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.61 % (6274)Termination reason: Unknown
% 1.78/1.61 % (6274)Termination phase: Saturation
% 1.78/1.61
% 1.78/1.61 % (6274)Memory used [KB]: 5628
% 1.78/1.61 % (6274)Time elapsed: 0.011 s
% 1.78/1.61 % (6274)Instructions burned: 17 (million)
% 1.78/1.61 % (6274)------------------------------
% 1.78/1.61 % (6274)------------------------------
% 1.78/1.62 % (6276)Instruction limit reached!
% 1.78/1.62 % (6276)------------------------------
% 1.78/1.62 % (6276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.62 % (6276)Termination reason: Unknown
% 1.78/1.62 % (6276)Termination phase: Saturation
% 1.78/1.62
% 1.78/1.62 % (6276)Memory used [KB]: 5628
% 1.78/1.62 % (6276)Time elapsed: 0.018 s
% 1.78/1.62 % (6276)Instructions burned: 31 (million)
% 1.78/1.62 % (6276)------------------------------
% 1.78/1.62 % (6276)------------------------------
% 1.78/1.62 % (6277)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/127Mi)
% 1.78/1.63 % (6278)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/100Mi)
% 1.78/1.64 % (6278)First to succeed.
% 1.78/1.64 % (6279)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_6147 for (2998ds/3Mi)
% 1.78/1.64 % (6278)Refutation found. Thanks to Tanya!
% 1.78/1.64 % SZS status Theorem for DTF2THF_6147
% 1.78/1.64 % SZS output start Proof for DTF2THF_6147
% 1.78/1.64 thf(type_def_5, type, lst: $tType).
% 1.78/1.64 thf(type_def_7, type, a: $tType).
% 1.78/1.64 thf(func_def_0, type, lst: $tType).
% 1.78/1.64 thf(func_def_1, type, a: $tType).
% 1.78/1.64 thf(func_def_2, type, ap: lst > lst > lst).
% 1.78/1.64 thf(func_def_3, type, cns: a > lst > lst).
% 1.78/1.64 thf(func_def_4, type, nl: lst).
% 1.78/1.64 thf(func_def_5, type, xs: lst).
% 1.78/1.64 thf(func_def_16, type, sK0: lst).
% 1.78/1.64 thf(func_def_17, type, sK1: lst).
% 1.78/1.64 thf(func_def_19, type, sK3: a).
% 1.78/1.64 thf(func_def_20, type, sK4: lst).
% 1.78/1.64 thf(func_def_21, type, sK5: (lst > $o) > a).
% 1.78/1.64 thf(func_def_22, type, sK6: (lst > $o) > lst).
% 1.78/1.64 thf(func_def_23, type, sK7: a).
% 1.78/1.64 thf(func_def_24, type, sK8: lst).
% 1.78/1.64 thf(func_def_25, type, sK9: a).
% 1.78/1.64 thf(func_def_26, type, sK10: lst).
% 1.78/1.64 thf(func_def_27, type, sK11: a).
% 1.78/1.64 thf(func_def_28, type, sK12: lst).
% 1.78/1.64 thf(func_def_29, type, ph13: !>[X0: $tType]:(X0)).
% 1.78/1.64 thf(f194,plain,(
% 1.78/1.64 $false),
% 1.78/1.64 inference(avatar_sat_refutation,[status(thm)],[f122,f131,f175,f183,f191])).
% 1.78/1.64 thf(f191,plain,(
% 1.78/1.64 ~spl2_11),
% 1.78/1.64 inference(avatar_contradiction_clause,[status(thm)],[f190])).
% 1.78/1.64 thf(f190,plain,(
% 1.78/1.64 $false | ~spl2_11),
% 1.78/1.64 inference(trivial_inequality_removal,[status(thm)],[f189])).
% 1.78/1.64 thf(f189,plain,(
% 1.78/1.64 ((ap @ xs @ (ap @ sK1 @ sK0)) != (ap @ xs @ (ap @ sK1 @ sK0))) | ~spl2_11),
% 1.78/1.64 inference(superposition,[status(thm)],[f18,f126])).
% 1.78/1.64 thf(f126,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0)))) ) | ~spl2_11),
% 1.78/1.64 inference(avatar_component_clause,[status(thm)],[f125])).
% 1.78/1.64 thf(f125,definition,(
% 1.78/1.64 spl2_11 <=> ! [X0 : lst] : ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0)))),
% 1.78/1.64 introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition])).
% 1.78/1.64 thf(f18,plain,(
% 1.78/1.64 ((ap @ xs @ (ap @ sK1 @ sK0)) != (ap @ (ap @ xs @ sK1) @ sK0))),
% 1.78/1.64 inference(cnf_transformation,[status(thm)],[f16])).
% 1.78/1.64 thf(f16,plain,(
% 1.78/1.64 ((ap @ xs @ (ap @ sK1 @ sK0)) != (ap @ (ap @ xs @ sK1) @ sK0))),
% 1.78/1.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15])).
% 1.78/1.64 thf(f15,plain,(
% 1.78/1.64 ? [X0 : lst,X1 : lst] : ((ap @ (ap @ xs @ X1) @ X0) != (ap @ xs @ (ap @ X1 @ X0))) => ((ap @ xs @ (ap @ sK1 @ sK0)) != (ap @ (ap @ xs @ sK1) @ sK0))),
% 1.78/1.64 introduced(definition,[],[choice_axiom])).
% 1.78/1.64 thf(f14,plain,(
% 1.78/1.64 ? [X0 : lst,X1 : lst] : ((ap @ (ap @ xs @ X1) @ X0) != (ap @ xs @ (ap @ X1 @ X0)))),
% 1.78/1.64 inference(ennf_transformation,[status(thm)],[f13])).
% 1.78/1.64 thf(f13,plain,(
% 1.78/1.64 ~! [X0 : lst,X1 : lst] : ((ap @ (ap @ xs @ X1) @ X0) = (ap @ xs @ (ap @ X1 @ X0)))),
% 1.78/1.64 inference(rectify,[status(thm)],[f5])).
% 1.78/1.64 thf(f5,negated_conjecture,(
% 1.78/1.64 ~! [X8 : lst,X7 : lst] : ((ap @ xs @ (ap @ X7 @ X8)) = (ap @ (ap @ xs @ X7) @ X8))),
% 1.78/1.64 inference(negated_conjecture,[status(cth)],[f4])).
% 1.78/1.64 thf(f4,conjecture,(
% 1.78/1.64 ! [X8 : lst,X7 : lst] : ((ap @ xs @ (ap @ X7 @ X8)) = (ap @ (ap @ xs @ X7) @ X8))),
% 1.78/1.64 file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',conj_0)).
% 1.78/1.64 thf(f183,plain,(
% 1.78/1.64 ~spl2_9 | spl2_12),
% 1.78/1.64 inference(avatar_contradiction_clause,[status(thm)],[f182])).
% 1.78/1.64 thf(f182,plain,(
% 1.78/1.64 $false | (~spl2_9 | spl2_12)),
% 1.78/1.64 inference(trivial_inequality_removal,[status(thm)],[f181])).
% 1.78/1.64 thf(f181,plain,(
% 1.78/1.64 ((cns @ sK9 @ (ap @ sK10 @ (ap @ sK1 @ sK0))) != (cns @ sK9 @ (ap @ sK10 @ (ap @ sK1 @ sK0)))) | (~spl2_9 | spl2_12)),
% 1.78/1.64 inference(forward_demodulation,[status(thm)],[f180,f117])).
% 1.78/1.64 thf(f117,plain,(
% 1.78/1.64 ((ap @ sK10 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ sK10 @ sK1) @ sK0)) | ~spl2_9),
% 1.78/1.64 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.78/1.64 thf(f115,definition,(
% 1.78/1.64 spl2_9 <=> ((ap @ sK10 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ sK10 @ sK1) @ sK0))),
% 1.78/1.64 introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition])).
% 1.78/1.64 thf(f180,plain,(
% 1.78/1.64 ((cns @ sK9 @ (ap @ (ap @ sK10 @ sK1) @ sK0)) != (cns @ sK9 @ (ap @ sK10 @ (ap @ sK1 @ sK0)))) | spl2_12),
% 1.78/1.64 inference(superposition,[status(thm)],[f178,f168])).
% 1.78/1.64 thf(f168,plain,(
% 1.78/1.64 ( ! [X2 : a,X3 : lst,X1 : lst] : (((ap @ (cns @ X2 @ X3) @ X1) = (cns @ X2 @ (ap @ X3 @ X1)))) )),
% 1.78/1.64 inference(equality_proxy_clausification,[status(thm)],[f167])).
% 1.78/1.64 thf(f167,plain,(
% 1.78/1.64 ( ! [X2 : a,X3 : lst,X1 : lst] : ((((ap @ (cns @ X2 @ X3) @ X1) = (cns @ X2 @ (ap @ X3 @ X1))) = $true)) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f166])).
% 1.78/1.64 thf(f166,plain,(
% 1.78/1.64 ( ! [X2 : a,X3 : lst,X1 : lst] : ((((^[Y0 : lst]: ((ap @ (cns @ X2 @ Y0) @ X1) = (cns @ X2 @ (ap @ Y0 @ X1)))) @ X3) = $true)) )),
% 1.78/1.64 inference(pi_clausification,[status(thm)],[f165])).
% 1.78/1.64 thf(f165,plain,(
% 1.78/1.64 ( ! [X2 : a,X1 : lst] : (((!! @ lst @ (^[Y0 : lst]: ((ap @ (cns @ X2 @ Y0) @ X1) = (cns @ X2 @ (ap @ Y0 @ X1))))) = $true)) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f164])).
% 1.78/1.64 thf(f164,plain,(
% 1.78/1.64 ( ! [X2 : a,X1 : lst] : (($true = ((^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: ((ap @ (cns @ Y0 @ Y1) @ X1) = (cns @ Y0 @ (ap @ Y1 @ X1)))))) @ X2))) )),
% 1.78/1.64 inference(pi_clausification,[status(thm)],[f163])).
% 1.78/1.64 thf(f163,plain,(
% 1.78/1.64 ( ! [X1 : lst] : (((!! @ a @ (^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: ((ap @ (cns @ Y0 @ Y1) @ X1) = (cns @ Y0 @ (ap @ Y1 @ X1))))))) = $true)) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f162])).
% 1.78/1.64 thf(f162,plain,(
% 1.78/1.64 ( ! [X1 : lst] : (($true = ((^[Y0 : lst]: (!! @ a @ (^[Y1 : a]: (!! @ lst @ (^[Y2 : lst]: ((ap @ (cns @ Y1 @ Y2) @ Y0) = (cns @ Y1 @ (ap @ Y2 @ Y0)))))))) @ X1))) )),
% 1.78/1.64 inference(pi_clausification,[status(thm)],[f20])).
% 1.78/1.64 thf(f20,plain,(
% 1.78/1.64 ((!! @ lst @ (^[Y0 : lst]: (!! @ a @ (^[Y1 : a]: (!! @ lst @ (^[Y2 : lst]: ((ap @ (cns @ Y1 @ Y2) @ Y0) = (cns @ Y1 @ (ap @ Y2 @ Y0))))))))) = $true)),
% 1.78/1.64 inference(cnf_transformation,[status(thm)],[f8])).
% 1.78/1.64 thf(f8,plain,(
% 1.78/1.64 ((!! @ lst @ (^[Y0 : lst]: (!! @ a @ (^[Y1 : a]: (!! @ lst @ (^[Y2 : lst]: ((ap @ (cns @ Y1 @ Y2) @ Y0) = (cns @ Y1 @ (ap @ Y2 @ Y0))))))))) = $true)),
% 1.78/1.64 inference(fool_elimination,[status(thm)],[f7])).
% 1.78/1.64 thf(f7,plain,(
% 1.78/1.64 ! [X0 : lst,X1 : a,X2 : lst] : ((ap @ (cns @ X1 @ X0) @ X2) = (cns @ X1 @ (ap @ X0 @ X2)))),
% 1.78/1.64 inference(rectify,[status(thm)],[f2])).
% 1.78/1.64 thf(f2,axiom,(
% 1.78/1.64 ! [X5 : lst,X6 : a,X4 : lst] : ((ap @ (cns @ X6 @ X5) @ X4) = (cns @ X6 @ (ap @ X5 @ X4)))),
% 1.78/1.64 file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',fact_1p_Osimps_I2_J)).
% 1.78/1.64 thf(f178,plain,(
% 1.78/1.64 ((cns @ sK9 @ (ap @ sK10 @ (ap @ sK1 @ sK0))) != (ap @ (cns @ sK9 @ (ap @ sK10 @ sK1)) @ sK0)) | spl2_12),
% 1.78/1.64 inference(forward_demodulation,[status(thm)],[f177,f168])).
% 1.78/1.64 thf(f177,plain,(
% 1.78/1.64 ((cns @ sK9 @ (ap @ sK10 @ (ap @ sK1 @ sK0))) != (ap @ (ap @ (cns @ sK9 @ sK10) @ sK1) @ sK0)) | spl2_12),
% 1.78/1.64 inference(forward_demodulation,[status(thm)],[f130,f168])).
% 1.78/1.64 thf(f130,plain,(
% 1.78/1.64 ((ap @ (ap @ (cns @ sK9 @ sK10) @ sK1) @ sK0) != (ap @ (cns @ sK9 @ sK10) @ (ap @ sK1 @ sK0))) | spl2_12),
% 1.78/1.64 inference(avatar_component_clause,[status(thm)],[f128])).
% 1.78/1.64 thf(f128,definition,(
% 1.78/1.64 spl2_12 <=> ((ap @ (ap @ (cns @ sK9 @ sK10) @ sK1) @ sK0) = (ap @ (cns @ sK9 @ sK10) @ (ap @ sK1 @ sK0)))),
% 1.78/1.64 introduced(definition,[new_symbols(naming,[spl2_12])],[avatar_definition])).
% 1.78/1.64 thf(f175,plain,(
% 1.78/1.64 spl2_10),
% 1.78/1.64 inference(avatar_contradiction_clause,[status(thm)],[f174])).
% 1.78/1.64 thf(f174,plain,(
% 1.78/1.64 $false | spl2_10),
% 1.78/1.64 inference(subsumption_resolution,[status(thm)],[f173,f171])).
% 1.78/1.64 thf(f171,plain,(
% 1.78/1.64 ( ! [X1 : lst] : (((ap @ nl @ X1) = X1)) )),
% 1.78/1.64 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 1.78/1.64 thf(f170,plain,(
% 1.78/1.64 ( ! [X1 : lst] : ((((ap @ nl @ X1) = X1) = $true)) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f169])).
% 1.78/1.64 thf(f169,plain,(
% 1.78/1.64 ( ! [X1 : lst] : ((((^[Y0 : lst]: ((ap @ nl @ Y0) = Y0)) @ X1) = $true)) )),
% 1.78/1.64 inference(pi_clausification,[status(thm)],[f19])).
% 1.78/1.64 thf(f19,plain,(
% 1.78/1.64 ((!! @ lst @ (^[Y0 : lst]: ((ap @ nl @ Y0) = Y0))) = $true)),
% 1.78/1.64 inference(cnf_transformation,[status(thm)],[f10])).
% 1.78/1.64 thf(f10,plain,(
% 1.78/1.64 ((!! @ lst @ (^[Y0 : lst]: ((ap @ nl @ Y0) = Y0))) = $true)),
% 1.78/1.64 inference(fool_elimination,[status(thm)],[f9])).
% 1.78/1.64 thf(f9,plain,(
% 1.78/1.64 ! [X0 : lst] : ((ap @ nl @ X0) = X0)),
% 1.78/1.64 inference(rectify,[status(thm)],[f3])).
% 1.78/1.64 thf(f3,axiom,(
% 1.78/1.64 ! [X4 : lst] : ((ap @ nl @ X4) = X4)),
% 1.78/1.64 file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',fact_2p_Osimps_I1_J)).
% 1.78/1.64 thf(f173,plain,(
% 1.78/1.64 ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ sK1 @ sK0)) | spl2_10),
% 1.78/1.64 inference(forward_demodulation,[status(thm)],[f121,f171])).
% 1.78/1.64 thf(f121,plain,(
% 1.78/1.64 ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | spl2_10),
% 1.78/1.64 inference(avatar_component_clause,[status(thm)],[f119])).
% 1.78/1.64 thf(f119,definition,(
% 1.78/1.64 spl2_10 <=> ((ap @ nl @ (ap @ sK1 @ sK0)) = (ap @ (ap @ nl @ sK1) @ sK0))),
% 1.78/1.64 introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition])).
% 1.78/1.64 thf(f131,plain,(
% 1.78/1.64 spl2_11 | ~spl2_12 | ~spl2_10),
% 1.78/1.64 inference(avatar_split_clause,[status(thm)],[f123,f119,f128,f125])).
% 1.78/1.64 thf(f123,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ (ap @ (cns @ sK9 @ sK10) @ sK1) @ sK0) != (ap @ (cns @ sK9 @ sK10) @ (ap @ sK1 @ sK0))) | ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0)))) )),
% 1.78/1.64 inference(equality_proxy_clausification,[status(thm)],[f110])).
% 1.78/1.64 thf(f110,plain,(
% 1.78/1.64 ( ! [X0 : lst] : ((((ap @ (cns @ sK9 @ sK10) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ sK9 @ sK10) @ sK1) @ sK0)) = $false) | ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0))) | ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0))) )),
% 1.78/1.64 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.78/1.64 thf(f109,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0))) | ($false = (((ap @ sK10 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ sK10 @ sK1) @ sK0)) => ((ap @ (cns @ sK9 @ sK10) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ sK9 @ sK10) @ sK1) @ sK0)))) | ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0))) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.78/1.64 thf(f108,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (($false = ((^[Y0 : lst]: (((ap @ Y0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y0 @ sK1) @ sK0)) => ((ap @ (cns @ sK9 @ Y0) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ sK9 @ Y0) @ sK1) @ sK0)))) @ sK10)) | ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0)))) )),
% 1.78/1.64 inference(sigma_clausification,[status(thm)],[f107])).
% 1.78/1.64 thf(f107,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0))) | ((!! @ lst @ (^[Y0 : lst]: (((ap @ Y0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y0 @ sK1) @ sK0)) => ((ap @ (cns @ sK9 @ Y0) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ sK9 @ Y0) @ sK1) @ sK0))))) = $false)) )),
% 1.78/1.64 inference(equality_proxy_clausification,[status(thm)],[f106])).
% 1.78/1.64 thf(f106,plain,(
% 1.78/1.64 ( ! [X0 : lst] : ((((ap @ X0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ X0 @ sK1) @ sK0)) = $true) | ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ((!! @ lst @ (^[Y0 : lst]: (((ap @ Y0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y0 @ sK1) @ sK0)) => ((ap @ (cns @ sK9 @ Y0) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ sK9 @ Y0) @ sK1) @ sK0))))) = $false)) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.78/1.64 thf(f105,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ($false = ((^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: (((ap @ Y1 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y1 @ sK1) @ sK0)) => ((ap @ (cns @ Y0 @ Y1) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ Y0 @ Y1) @ sK1) @ sK0)))))) @ sK9)) | (((ap @ X0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ X0 @ sK1) @ sK0)) = $true)) )),
% 1.78/1.64 inference(sigma_clausification,[status(thm)],[f104])).
% 1.78/1.64 thf(f104,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (($false = (!! @ a @ (^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: (((ap @ Y1 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y1 @ sK1) @ sK0)) => ((ap @ (cns @ Y0 @ Y1) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ Y0 @ Y1) @ sK1) @ sK0)))))))) | ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | (((ap @ X0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ X0 @ sK1) @ sK0)) = $true)) )),
% 1.78/1.64 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.78/1.64 thf(f103,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ($true = ((!! @ a @ (^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: (((ap @ Y1 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y1 @ sK1) @ sK0)) => ((ap @ (cns @ Y0 @ Y1) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ Y0 @ Y1) @ sK1) @ sK0))))))) => ((ap @ X0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ X0 @ sK1) @ sK0))))) )),
% 1.78/1.64 inference(equality_proxy_clausification,[status(thm)],[f102])).
% 1.78/1.64 thf(f102,plain,(
% 1.78/1.64 ( ! [X0 : lst] : ((((ap @ nl @ (ap @ sK1 @ sK0)) = (ap @ (ap @ nl @ sK1) @ sK0)) = $false) | ($true = ((!! @ a @ (^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: (((ap @ Y1 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y1 @ sK1) @ sK0)) => ((ap @ (cns @ Y0 @ Y1) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ Y0 @ Y1) @ sK1) @ sK0))))))) => ((ap @ X0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ X0 @ sK1) @ sK0))))) )),
% 1.78/1.64 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.78/1.64 thf(f29,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (($true = (((ap @ nl @ (ap @ sK1 @ sK0)) = (ap @ (ap @ nl @ sK1) @ sK0)) => ((!! @ a @ (^[Y0 : a]: (!! @ lst @ (^[Y1 : lst]: (((ap @ Y1 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y1 @ sK1) @ sK0)) => ((ap @ (cns @ Y0 @ Y1) @ (ap @ sK1 @ sK0)) = (ap @ (ap @ (cns @ Y0 @ Y1) @ sK1) @ sK0))))))) => ((ap @ X0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ X0 @ sK1) @ sK0)))))) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.78/1.64 thf(f25,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (($true = ((^[Y0 : lst > $o]: ((Y0 @ nl) => ((!! @ a @ (^[Y1 : a]: (!! @ lst @ (^[Y2 : lst]: ((Y0 @ Y2) => (Y0 @ (cns @ Y1 @ Y2))))))) => (Y0 @ X0)))) @ (^[Y0 : lst]: ((ap @ Y0 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ Y0 @ sK1) @ sK0)))))) )),
% 1.78/1.64 inference(heuristic_instantiation,[status(thm)],[f22])).
% 1.78/1.64 thf(f22,plain,(
% 1.78/1.64 ( ! [X1 : lst] : (((!! @ (lst > $o) @ (^[Y0 : lst > $o]: ((Y0 @ nl) => ((!! @ a @ (^[Y1 : a]: (!! @ lst @ (^[Y2 : lst]: ((Y0 @ Y2) => (Y0 @ (cns @ Y1 @ Y2))))))) => (Y0 @ X1))))) = $true)) )),
% 1.78/1.64 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.78/1.64 thf(f21,plain,(
% 1.78/1.64 ( ! [X1 : lst] : ((((^[Y0 : lst]: (!! @ (lst > $o) @ (^[Y1 : lst > $o]: ((Y1 @ nl) => ((!! @ a @ (^[Y2 : a]: (!! @ lst @ (^[Y3 : lst]: ((Y1 @ Y3) => (Y1 @ (cns @ Y2 @ Y3))))))) => (Y1 @ Y0)))))) @ X1) = $true)) )),
% 1.78/1.64 inference(pi_clausification,[status(thm)],[f17])).
% 1.78/1.64 thf(f17,plain,(
% 1.78/1.64 ((!! @ lst @ (^[Y0 : lst]: (!! @ (lst > $o) @ (^[Y1 : lst > $o]: ((Y1 @ nl) => ((!! @ a @ (^[Y2 : a]: (!! @ lst @ (^[Y3 : lst]: ((Y1 @ Y3) => (Y1 @ (cns @ Y2 @ Y3))))))) => (Y1 @ Y0))))))) = $true)),
% 1.78/1.64 inference(cnf_transformation,[status(thm)],[f12])).
% 1.78/1.64 thf(f12,plain,(
% 1.78/1.64 ((!! @ lst @ (^[Y0 : lst]: (!! @ (lst > $o) @ (^[Y1 : lst > $o]: ((Y1 @ nl) => ((!! @ a @ (^[Y2 : a]: (!! @ lst @ (^[Y3 : lst]: ((Y1 @ Y3) => (Y1 @ (cns @ Y2 @ Y3))))))) => (Y1 @ Y0))))))) = $true)),
% 1.78/1.64 inference(fool_elimination,[status(thm)],[f11])).
% 1.78/1.64 thf(f11,plain,(
% 1.78/1.64 ! [X0 : lst > $o,X1 : lst] : ((X0 @ nl) => (! [X2 : lst,X3 : a] : ((X0 @ X2) => (X0 @ (cns @ X3 @ X2))) => (X0 @ X1)))),
% 1.78/1.64 inference(rectify,[status(thm)],[f1])).
% 1.78/1.64 thf(f1,axiom,(
% 1.78/1.64 ! [X1 : lst > $o,X0 : lst] : ((X1 @ nl) => (! [X3 : lst,X2 : a] : ((X1 @ X3) => (X1 @ (cns @ X2 @ X3))) => (X1 @ X0)))),
% 1.78/1.64 file('/export/starexec/sandbox/tmp/tmp.OpHlIVglg3/DTF2THF_6147.p',fact_0_lst_Oinduct)).
% 1.78/1.64 thf(f122,plain,(
% 1.78/1.64 spl2_9 | ~spl2_10),
% 1.78/1.64 inference(avatar_split_clause,[status(thm)],[f113,f119,f115])).
% 1.78/1.64 thf(f113,plain,(
% 1.78/1.64 ((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ((ap @ sK10 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ sK10 @ sK1) @ sK0))),
% 1.78/1.64 inference(condensation,[status(thm)],[f112])).
% 1.78/1.64 thf(f112,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ((ap @ sK10 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ sK10 @ sK1) @ sK0)) | ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0)))) )),
% 1.78/1.64 inference(equality_proxy_clausification,[status(thm)],[f111])).
% 1.78/1.64 thf(f111,plain,(
% 1.78/1.64 ( ! [X0 : lst] : (((ap @ nl @ (ap @ sK1 @ sK0)) != (ap @ (ap @ nl @ sK1) @ sK0)) | ($true = ((ap @ sK10 @ (ap @ sK1 @ sK0)) = (ap @ (ap @ sK10 @ sK1) @ sK0))) | ((ap @ (ap @ X0 @ sK1) @ sK0) = (ap @ X0 @ (ap @ sK1 @ sK0)))) )),
% 1.78/1.64 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.78/1.64 % SZS output end Proof for DTF2THF_6147
% 1.78/1.64 % (6278)------------------------------
% 1.78/1.64 % (6278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.64 % (6278)Termination reason: Refutation
% 1.78/1.64
% 1.78/1.64 % (6278)Memory used [KB]: 5628
% 1.78/1.64 % (6278)Time elapsed: 0.015 s
% 1.78/1.64 % (6278)Instructions burned: 19 (million)
% 1.78/1.64 % (6278)------------------------------
% 1.78/1.64 % (6278)------------------------------
% 1.78/1.64 % (6243)Success in time 0.16 s
%------------------------------------------------------------------------------