%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO224^5 : 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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:42 AM UTC 2026
% Result : Theorem 1.65s 1.48s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 99 ( 6 unt; 0 typ; 11 def)
% Number of atoms : 1112 ( 266 equ; 0 cnn)
% Maximal formula atoms : 18 ( 11 avg)
% Number of connectives : 868 ( 196 ~; 232 |; 76 &; 337 @)
% ( 12 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 17 con; 0-2 aty)
% Number of variables : 75 ( 4 ^; 58 !; 13 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cLIKE: $i > $i > $o ).
thf(func_def_2,type,
cWRH: $i > $o ).
thf(func_def_3,type,
cW: $i > $o ).
thf(func_def_4,type,
cUNIQUE: $i > $o ).
thf(func_def_13,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f292,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f50,f55,f56,f61,f62,f67,f68,f75,f79,f82,f109,f195,f245,f271,f287]) ).
thf(f287,plain,
~ spl1_11,
inference(avatar_contradiction_clause,[status(thm)],[f286]) ).
thf(f286,plain,
( $false
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f285]) ).
thf(f285,plain,
( ( $false = $true )
| ( $true != $true )
| ~ spl1_11 ),
inference(beta_eta_normalization,[status(thm)],[f279]) ).
thf(f279,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ cP ) )
| ( ( ^ [Y0: $i] : $true
@ cJ )
!= $true )
| ~ spl1_11 ),
inference(primitive_instantiation,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X0: $i > $o] :
( ( $false
= ( X0 @ cP ) )
| ( ( X0 @ cJ )
!= $true ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl1_11
<=> ! [X0: $i > $o] :
( ( $false
= ( X0 @ cP ) )
| ( ( X0 @ cJ )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f271,plain,
( ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f270]) ).
thf(f270,plain,
( $false
| ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10 ),
inference(trivial_inequality_removal,[status(thm)],[f267]) ).
thf(f267,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10 ),
inference(superposition,[status(thm)],[f233,f265]) ).
thf(f265,plain,
( ( $false
= ( cLIKE @ cJ @ cS ) )
| ~ spl1_4
| ~ spl1_10 ),
inference(superposition,[status(thm)],[f46,f246]) ).
thf(f246,plain,
( ( cP = cJ )
| ~ spl1_10 ),
inference(leibniz_equality_elimination,[status(thm)],[f74]) ).
thf(f74,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ cP )
= $true )
| ( ( X0 @ cJ )
!= $true ) )
| ~ spl1_10 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl1_10
<=> ! [X0: $i > $o] :
( ( ( X0 @ cP )
= $true )
| ( ( X0 @ cJ )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition]) ).
thf(f46,plain,
( ( ( cLIKE @ cP @ cS )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl1_4
<=> ( ( cLIKE @ cP @ cS )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f233,plain,
( ( ( cLIKE @ cJ @ cS )
= $true )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_8 ),
inference(superposition,[status(thm)],[f66,f226]) ).
thf(f226,plain,
( ( cS = sK0 )
| ~ spl1_2
| ~ spl1_6 ),
inference(subsumption_resolution,[status(thm)],[f225,f37]) ).
thf(f37,plain,
( ( ( cWRH @ sK0 )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl1_2
<=> ( ( cWRH @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f225,plain,
( ( cS = sK0 )
| ( ( cWRH @ sK0 )
!= $true )
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f224]) ).
thf(f224,plain,
( ( cS = sK0 )
| ( $true != $true )
| ( ( cWRH @ sK0 )
!= $true )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f84,f54]) ).
thf(f54,plain,
( ( ( cW @ sK0 )
= $true )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl1_6
<=> ( ( cW @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f84,plain,
! [X0: $i] :
( ( ( cW @ X0 )
!= $true )
| ( cS = X0 )
| ( ( cWRH @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: $i] :
( ( ( cW @ X0 )
!= $true )
| ( cS = X0 )
| ( ( cWRH @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f20]) ).
thf(f20,plain,
( ( cUNIQUE @ cS )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i > $o] :
( ( ( ( ( X0 @ cJ )
!= $true )
| ! [X1: $i] :
( ( ( cW @ X1 )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true )
| ( ( cLIKE @ cJ @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true ) ) )
& ( ( ( X0 @ cJ )
= $true )
| ( ( ( cW @ sK0 )
= $true )
& ( ( cUNIQUE @ sK0 )
= $true )
& ( ( cLIKE @ cJ @ sK0 )
= $true )
& ( ( cWRH @ sK0 )
= $true ) ) ) )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) ) )
& ( ( cWRH @ cS )
= $true )
& ( ( cW @ cS )
= $true )
& ! [X3: $i] :
( ( $true
!= ( cUNIQUE @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( cW @ X4 ) )
| ( ( cWRH @ X4 )
!= $true )
| ( X3 = X4 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( ( cW @ X2 )
= $true )
& ( ( cUNIQUE @ X2 )
= $true )
& ( ( cLIKE @ cJ @ X2 )
= $true )
& ( ( cWRH @ X2 )
= $true ) )
=> ( ( ( cW @ sK0 )
= $true )
& ( ( cUNIQUE @ sK0 )
= $true )
& ( ( cLIKE @ cJ @ sK0 )
= $true )
& ( ( cWRH @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i > $o] :
( ( ( ( ( X0 @ cJ )
!= $true )
| ! [X1: $i] :
( ( ( cW @ X1 )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true )
| ( ( cLIKE @ cJ @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true ) ) )
& ( ( ( X0 @ cJ )
= $true )
| ? [X2: $i] :
( ( ( cW @ X2 )
= $true )
& ( ( cUNIQUE @ X2 )
= $true )
& ( ( cLIKE @ cJ @ X2 )
= $true )
& ( ( cWRH @ X2 )
= $true ) ) ) )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) ) )
& ( ( cWRH @ cS )
= $true )
& ( ( cW @ cS )
= $true )
& ! [X3: $i] :
( ( $true
!= ( cUNIQUE @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( cW @ X4 ) )
| ( ( cWRH @ X4 )
!= $true )
| ( X3 = X4 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X2: $i > $o] :
( ( ( ( ( X2 @ cJ )
!= $true )
| ! [X3: $i] :
( ( ( cW @ X3 )
!= $true )
| ( $true
!= ( cUNIQUE @ X3 ) )
| ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( cWRH @ X3 )
!= $true ) ) )
& ( ( ( X2 @ cJ )
= $true )
| ? [X3: $i] :
( ( ( cW @ X3 )
= $true )
& ( $true
= ( cUNIQUE @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cWRH @ X3 )
= $true ) ) ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) )
& ( ( cWRH @ cS )
= $true )
& ( ( cW @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true )
| ( X0 = X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cUNIQUE @ cS )
= $true )
& ! [X2: $i > $o] :
( ( ? [X3: $i] :
( ( ( cW @ X3 )
= $true )
& ( $true
= ( cUNIQUE @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cWRH @ X3 )
= $true ) )
<~> ( ( X2 @ cJ )
= $true ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) )
& ( ( cWRH @ cS )
= $true )
& ( ( cW @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true )
| ( X0 = X1 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i > $o] :
( ( ? [X3: $i] :
( ( ( cW @ X3 )
= $true )
& ( $true
= ( cUNIQUE @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cWRH @ X3 )
= $true ) )
<~> ( ( X2 @ cJ )
= $true ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) )
& ( ( cUNIQUE @ cS )
= $true )
& ( ( cW @ cS )
= $true )
& ! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true ) )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cWRH @ cS )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cUNIQUE @ cS )
= $true )
& ( ( cW @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( ( cW @ X1 )
= $true )
& ( ( cWRH @ X1 )
= $true ) )
=> ( X0 = X1 ) ) )
& ( ( cWRH @ cS )
= $true ) )
=> ? [X2: $i > $o] :
( ( ( ( X2 @ cJ )
= $true )
<=> ? [X3: $i] :
( ( ( cW @ X3 )
= $true )
& ( $true
= ( cUNIQUE @ X3 ) )
& ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cWRH @ X3 )
= $true ) ) )
& ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cW @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] :
( ( ( cWRH @ X1 )
& ( cW @ X1 ) )
=> ( X0 = X1 ) ) )
& ( cWRH @ cS )
& ( cUNIQUE @ cS ) )
=> ? [X2: $i > $o] :
( ? [X3: $i] :
( ( ( cWRH @ X3 )
& ( cLIKE @ cJ @ X3 )
& ( cW @ X3 )
& ( cUNIQUE @ X3 ) )
= ( X2 @ cJ ) )
& ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cW @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] :
( ( ( cWRH @ X1 )
& ( cW @ X1 ) )
=> ( X0 = X1 ) ) )
& ( cWRH @ cS )
& ( cUNIQUE @ cS ) )
=> ? [X2: $i > $o] :
( ? [X0: $i] :
( ( ( cWRH @ X0 )
& ( cLIKE @ cJ @ X0 )
& ( cW @ X0 )
& ( cUNIQUE @ X0 ) )
= ( X2 @ cJ ) )
& ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cW @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] :
( ( ( cWRH @ X1 )
& ( cW @ X1 ) )
=> ( X0 = X1 ) ) )
& ( cWRH @ cS )
& ( cUNIQUE @ cS ) )
=> ? [X2: $i > $o] :
( ? [X0: $i] :
( ( ( cWRH @ X0 )
& ( cLIKE @ cJ @ X0 )
& ( cW @ X0 )
& ( cUNIQUE @ X0 ) )
= ( X2 @ cJ ) )
& ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.POE620fLAG/DTF2THF_19261.p',cLING1) ).
thf(f12,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( cUNIQUE @ X3 ) )
| ( $true
!= ( cW @ X4 ) )
| ( X3 = X4 )
| ( ( cWRH @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f66,plain,
( ( ( cLIKE @ cJ @ sK0 )
= $true )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl1_8
<=> ( ( cLIKE @ cJ @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f245,plain,
( ~ spl1_2
| ~ spl1_6
| ~ spl1_7
| ~ spl1_8
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f244]) ).
thf(f244,plain,
( $false
| ~ spl1_2
| ~ spl1_6
| ~ spl1_7
| ~ spl1_8
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f243,f60]) ).
thf(f60,plain,
( ( ( cUNIQUE @ sK0 )
= $true )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl1_7
<=> ( ( cUNIQUE @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f243,plain,
( ( ( cUNIQUE @ sK0 )
!= $true )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f242,f37]) ).
thf(f242,plain,
( ( ( cWRH @ sK0 )
!= $true )
| ( ( cUNIQUE @ sK0 )
!= $true )
| ~ spl1_6
| ~ spl1_8
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f236,f54]) ).
thf(f236,plain,
( ( ( cW @ sK0 )
!= $true )
| ( ( cUNIQUE @ sK0 )
!= $true )
| ( ( cWRH @ sK0 )
!= $true )
| ~ spl1_8
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( cW @ sK0 )
!= $true )
| ( ( cWRH @ sK0 )
!= $true )
| ( ( cUNIQUE @ sK0 )
!= $true )
| ( $true != $true )
| ~ spl1_8
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f71,f66]) ).
thf(f71,plain,
( ! [X1: $i] :
( ( ( cLIKE @ cJ @ X1 )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl1_9
<=> ! [X1: $i] :
( ( ( cWRH @ X1 )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true )
| ( ( cLIKE @ cJ @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f195,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f194]) ).
thf(f194,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f193]) ).
thf(f193,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(duplicate_literal_removal,[status(thm)],[f192]) ).
thf(f192,plain,
( ( $false = $true )
| ( $false = $true )
| ~ spl1_1 ),
inference(beta_eta_normalization,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( ^ [Y0: $i] : $false
@ cP )
= $true )
| ( ( ^ [Y0: $i] : $false
@ cJ )
= $true )
| ~ spl1_1 ),
inference(primitive_instantiation,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ cP )
= $true )
| ( ( X0 @ cJ )
= $true ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl1_1
<=> ! [X0: $i > $o] :
( ( ( X0 @ cP )
= $true )
| ( ( X0 @ cJ )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f109,plain,
( ~ spl1_3
| ~ spl1_5
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f107,f13]) ).
thf(f13,plain,
( ( cW @ cS )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f107,plain,
( ( ( cW @ cS )
!= $true )
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f106,f14]) ).
thf(f14,plain,
( ( cWRH @ cS )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f106,plain,
( ( ( cWRH @ cS )
!= $true )
| ( ( cW @ cS )
!= $true )
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f105,f20]) ).
thf(f105,plain,
( ( ( cUNIQUE @ cS )
!= $true )
| ( ( cWRH @ cS )
!= $true )
| ( ( cW @ cS )
!= $true )
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ( cW @ cS )
!= $true )
| ( ( cUNIQUE @ cS )
!= $true )
| ( ( cWRH @ cS )
!= $true )
| ( $true != $true )
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f71,f99]) ).
thf(f99,plain,
( ( ( cLIKE @ cJ @ cS )
= $true )
| ~ spl1_3
| ~ spl1_5 ),
inference(superposition,[status(thm)],[f41,f87]) ).
thf(f87,plain,
( ( cP = cJ )
| ~ spl1_5 ),
inference(leibniz_equality_elimination,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X0: $i > $o] :
( ( $false
= ( X0 @ cP ) )
| ( ( X0 @ cJ )
= $true ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl1_5
<=> ! [X0: $i > $o] :
( ( ( X0 @ cJ )
= $true )
| ( $false
= ( X0 @ cP ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f41,plain,
( ( ( cLIKE @ cP @ cS )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl1_3
<=> ( ( cLIKE @ cP @ cS )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f82,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false = $true )
| ~ spl1_3
| ~ spl1_4 ),
inference(forward_demodulation,[status(thm)],[f41,f46]) ).
thf(f79,plain,
( spl1_11
| spl1_9
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f22,f44,f70,f77]) ).
thf(f22,plain,
! [X0: $i > $o,X1: $i] :
( ( ( cWRH @ X1 )
!= $true )
| ( ( cLIKE @ cJ @ X1 )
!= $true )
| ( $false
= ( X0 @ cP ) )
| ( ( X0 @ cJ )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( ( cLIKE @ cP @ cS )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i > $o,X1: $i] :
( ( ( cUNIQUE @ X1 )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( ( cWRH @ X1 )
!= $true )
| ( ( X0 @ cJ )
!= $true )
| ( ( cLIKE @ cJ @ X1 )
!= $true )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f75,plain,
( spl1_3
| spl1_9
| spl1_10 ),
inference(avatar_split_clause,[status(thm)],[f21,f73,f70,f39]) ).
thf(f21,plain,
! [X0: $i > $o,X1: $i] :
( ( ( cWRH @ X1 )
!= $true )
| ( ( cLIKE @ cJ @ X1 )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true )
| ( ( cW @ X1 )
!= $true )
| ( ( X0 @ cP )
= $true )
| ( ( X0 @ cJ )
!= $true )
| ( ( cLIKE @ cP @ cS )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f68,plain,
( spl1_5
| spl1_4
| spl1_8 ),
inference(avatar_split_clause,[status(thm)],[f24,f64,f44,f48]) ).
thf(f24,plain,
! [X0: $i > $o] :
( ( $false
= ( X0 @ cP ) )
| ( ( cLIKE @ cJ @ sK0 )
= $true )
| ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $o] :
( ( ( cLIKE @ cJ @ sK0 )
= $true )
| ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f67,plain,
( spl1_3
| spl1_8
| spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f23,f32,f64,f39]) ).
thf(f23,plain,
! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
= $true )
| ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cJ @ sK0 )
= $true )
| ( ( X0 @ cP )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f62,plain,
( spl1_4
| spl1_7
| spl1_5 ),
inference(avatar_split_clause,[status(thm)],[f26,f48,f58,f44]) ).
thf(f26,plain,
! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
= $false )
| ( ( X0 @ cJ )
= $true )
| ( ( cUNIQUE @ sK0 )
= $true )
| ( $false
= ( X0 @ cP ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i > $o] :
( ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( ( cUNIQUE @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f61,plain,
( spl1_1
| spl1_7
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f25,f39,f58,f32]) ).
thf(f25,plain,
! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
= $true )
| ( ( X0 @ cP )
= $true )
| ( ( cUNIQUE @ sK0 )
= $true )
| ( ( X0 @ cJ )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f56,plain,
( spl1_6
| spl1_5
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f28,f44,f48,f52]) ).
thf(f28,plain,
! [X0: $i > $o] :
( ( $false
= ( X0 @ cP ) )
| ( ( cW @ sK0 )
= $true )
| ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $o] :
( ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) )
| ( ( cW @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f55,plain,
( spl1_6
| spl1_3
| spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f27,f32,f39,f52]) ).
thf(f27,plain,
! [X0: $i > $o] :
( ( ( X0 @ cP )
= $true )
| ( ( cW @ sK0 )
= $true )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( ( X0 @ cJ )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f50,plain,
( spl1_4
| spl1_2
| spl1_5 ),
inference(avatar_split_clause,[status(thm)],[f30,f48,f35,f44]) ).
thf(f30,plain,
! [X0: $i > $o] :
( ( ( cLIKE @ cP @ cS )
= $false )
| ( ( X0 @ cJ )
= $true )
| ( $false
= ( X0 @ cP ) )
| ( ( cWRH @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i > $o] :
( ( ( cWRH @ sK0 )
= $true )
| ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
!= ( X0 @ cP ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f42,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f39,f35,f32]) ).
thf(f29,plain,
! [X0: $i > $o] :
( ( ( cWRH @ sK0 )
= $true )
| ( ( X0 @ cP )
= $true )
| ( ( X0 @ cJ )
= $true )
| ( ( cLIKE @ cP @ cS )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO224^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n031.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 14:27:18 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SYO224^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.48 % Domain : Syntactic
% 0.20/0.48 % Problem : TPS problem LING1
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_0499 [Bro09]
% 0.20/0.48 % : LING1 [TPS]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 0.33 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 8 ( 0 unt; 7 typ; 0 def)
% 0.20/0.48 % Number of atoms : 14 ( 3 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 9 ( 14 avg)
% 0.20/0.48 % Number of connectives : 26 ( 0 ~; 0 |; 8 &; 15 @)
% 0.20/0.48 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 9 ( 9 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(cJ,type,
% 0.20/0.48 cJ: $i ).
% 0.20/0.48
% 0.20/0.48 thf(cLIKE,type,
% 0.20/0.48 cLIKE: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cWRH,type,
% 0.20/0.48 cWRH: $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cW,type,
% 0.20/0.48 cW: $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cUNIQUE,type,
% 0.20/0.48 cUNIQUE: $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cS,type,
% 0.20/0.48 cS: $i ).
% 0.20/0.48
% 0.20/0.48 thf(cP,type,
% 0.20/0.48 cP: $i ).
% 0.20/0.48
% 0.20/0.48 thf(cLING1,conjecture,
% 0.20/0.48 ( ( ! [X: $i] :
% 0.20/0.48 ( ( cUNIQUE @ X )
% 0.20/0.48 => ! [Z: $i] :
% 0.20/0.48 ( ( ( cWRH @ Z )
% 0.20/0.48 & ( cW @ Z ) )
% 0.20/0.48 => ( X = Z ) ) )
% 0.20/0.48 & ( cUNIQUE @ cS )
% 0.20/0.48 & ( cW @ cS )
% 0.20/0.48 & ( cWRH @ cS ) )
% 0.20/0.48 => ? [Xan: $i > $o] :
% 0.20/0.48 ( ( ( Xan @ cP )
% 0.20/0.48 = ( cLIKE @ cP @ cS ) )
% 0.20/0.48 & ( ( Xan @ cJ )
% 0.20/0.48 = ( ? [X: $i] :
% 0.20/0.48 ( ( cUNIQUE @ X )
% 0.20/0.48 & ( cW @ X )
% 0.20/0.48 & ( cWRH @ X )
% 0.20/0.48 & ( cLIKE @ cJ @ X ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.65/1.44 ---- Embedded in THF ---
% 1.65/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.44 %%% Generated on Tue Feb 24 14:27:19 EST 2026
% 1.65/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.44 %%% Logic specification used:
% 1.65/1.44 %%% thf(spec, logic, $$dhol).
% 1.65/1.44
% 1.65/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.POE620fLAG/DTF2DTF19261.p
% See solution above
% 1.65/1.44 ------------------------
% 1.65/1.45 ---- Cleaned THF ---
% 1.65/1.45 thf(cJ,type,
% 1.65/1.45 cJ: $i ).
% 1.65/1.45
% 1.65/1.45 thf(cLIKE,type,
% 1.65/1.45 cLIKE: $i > $i > $o ).
% 1.65/1.45
% 1.65/1.45 thf(cWRH,type,
% 1.65/1.45 cWRH: $i > $o ).
% 1.65/1.45
% 1.65/1.45 thf(cW,type,
% 1.65/1.45 cW: $i > $o ).
% 1.65/1.45
% 1.65/1.45 thf(cUNIQUE,type,
% 1.65/1.45 cUNIQUE: $i > $o ).
% 1.65/1.45
% 1.65/1.45 thf(cS,type,
% 1.65/1.45 cS: $i ).
% 1.65/1.45
% 1.65/1.45 thf(cP,type,
% 1.65/1.45 cP: $i ).
% 1.65/1.45
% 1.65/1.45 thf(cLING1,conjecture,
% 1.65/1.45 ( ( ! [X: $i] :
% 1.65/1.45 ( ( cUNIQUE @ X )
% 1.65/1.45 => ! [Z: $i] :
% 1.65/1.45 ( ( ( cWRH @ Z )
% 1.65/1.45 & ( cW @ Z ) )
% 1.65/1.45 => ( X = Z ) ) )
% 1.65/1.45 & ( cUNIQUE @ cS )
% 1.65/1.45 & ( cW @ cS )
% 1.65/1.45 & ( cWRH @ cS ) )
% 1.65/1.45 => ? [Xan: $i > $o] :
% 1.65/1.45 ( ( ( Xan @ cP )
% 1.65/1.45 = ( cLIKE @ cP @ cS ) )
% 1.65/1.45 & ( ( Xan @ cJ )
% 1.65/1.45 = ( ? [X: $i] :
% 1.65/1.45 ( ( cUNIQUE @ X )
% 1.65/1.45 & ( cW @ X )
% 1.65/1.45 & ( cWRH @ X )
% 1.65/1.45 & ( cLIKE @ cJ @ X ) ) ) ) ) ) ).
% 1.65/1.45 ------------------------
% 1.65/1.47 % (19358)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19261 for (3000ds/183Mi)
% 1.65/1.47 % (19360)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_19261 for (3000ds/27Mi)
% 1.65/1.47 % (19359)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_19261 for (3000ds/4Mi)
% 1.65/1.47 % (19362)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_19261 for (3000ds/2Mi)
% 1.65/1.47 % (19363)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_19261 for (3000ds/275Mi)
% 1.65/1.47 % (19364)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19261 for (3000ds/18Mi)
% 1.65/1.47 % (19361)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19261 for (3000ds/2Mi)
% 1.65/1.47 % (19361)Instruction limit reached!
% 1.65/1.47 % (19361)------------------------------
% 1.65/1.47 % (19361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (19361)Termination reason: Unknown
% 1.65/1.47 % (19361)Termination phase: Saturation
% 1.65/1.47 % (19362)Instruction limit reached!
% 1.65/1.47 % (19362)------------------------------
% 1.65/1.47 % (19362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (19362)Termination reason: Unknown
% 1.65/1.47 % (19362)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (19362)Memory used [KB]: 5500
% 1.65/1.47 % (19362)Time elapsed: 0.003 s
% 1.65/1.47 % (19362)Instructions burned: 2 (million)
% 1.65/1.47 % (19362)------------------------------
% 1.65/1.47 % (19362)------------------------------
% 1.65/1.47
% 1.65/1.47 % (19361)Memory used [KB]: 5500
% 1.65/1.47 % (19361)Time elapsed: 0.003 s
% 1.65/1.47 % (19361)Instructions burned: 2 (million)
% 1.65/1.47 % (19361)------------------------------
% 1.65/1.47 % (19361)------------------------------
% 1.65/1.47 % (19359)Instruction limit reached!
% 1.65/1.47 % (19359)------------------------------
% 1.65/1.47 % (19359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (19359)Termination reason: Unknown
% 1.65/1.47 % (19359)Termination phase: Saturation
% 1.65/1.47
% 1.65/1.47 % (19359)Memory used [KB]: 5500
% 1.65/1.47 % (19359)Time elapsed: 0.005 s
% 1.65/1.47 % (19359)Instructions burned: 5 (million)
% 1.65/1.47 % (19359)------------------------------
% 1.65/1.47 % (19359)------------------------------
% 1.65/1.47 % (19360)Refutation not found, incomplete strategy
% 1.65/1.47 % (19360)------------------------------
% 1.65/1.47 % (19360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.47 % (19360)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.47
% 1.65/1.47
% 1.65/1.47 % (19360)Memory used [KB]: 5500
% 1.65/1.47 % (19360)Time elapsed: 0.005 s
% 1.65/1.47 % (19360)Instructions burned: 5 (million)
% 1.65/1.47 % (19360)------------------------------
% 1.65/1.47 % (19360)------------------------------
% 1.65/1.48 % (19364)Instruction limit reached!
% 1.65/1.48 % (19364)------------------------------
% 1.65/1.48 % (19364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (19364)Termination reason: Unknown
% 1.65/1.48 % (19364)Termination phase: Saturation
% 1.65/1.48
% 1.65/1.48 % (19364)Memory used [KB]: 5628
% 1.65/1.48 % (19364)Time elapsed: 0.012 s
% 1.65/1.48 % (19364)Instructions burned: 18 (million)
% 1.65/1.48 % (19364)------------------------------
% 1.65/1.48 % (19364)------------------------------
% 1.65/1.48 % (19363)First to succeed.
% 1.65/1.48 % (19363)Refutation found. Thanks to Tanya!
% 1.65/1.48 % SZS status Theorem for DTF2THF_19261
% 1.65/1.48 % SZS output start Proof for DTF2THF_19261
% 1.65/1.48 thf(func_def_1, type, cLIKE: $i > $i > $o).
% 1.65/1.48 thf(func_def_2, type, cWRH: $i > $o).
% 1.65/1.48 thf(func_def_3, type, cW: $i > $o).
% 1.65/1.48 thf(func_def_4, type, cUNIQUE: $i > $o).
% 1.65/1.48 thf(func_def_13, type, ph2: !>[X0: $tType]:(X0)).
% 1.65/1.48 thf(f292,plain,(
% 1.65/1.48 $false),
% 1.65/1.48 inference(avatar_sat_refutation,[status(thm)],[f42,f50,f55,f56,f61,f62,f67,f68,f75,f79,f82,f109,f195,f245,f271,f287])).
% 1.65/1.48 thf(f287,plain,(
% 1.65/1.48 ~spl1_11),
% 1.65/1.48 inference(avatar_contradiction_clause,[status(thm)],[f286])).
% 1.65/1.48 thf(f286,plain,(
% 1.65/1.48 $false | ~spl1_11),
% 1.65/1.48 inference(trivial_inequality_removal,[status(thm)],[f285])).
% 1.65/1.48 thf(f285,plain,(
% 1.65/1.48 ($false = $true) | ($true != $true) | ~spl1_11),
% 1.65/1.48 inference(beta_eta_normalization,[status(thm)],[f279])).
% 1.65/1.48 thf(f279,plain,(
% 1.65/1.48 ($false = ((^[Y0 : $i]: ($true)) @ cP)) | (((^[Y0 : $i]: ($true)) @ cJ) != $true) | ~spl1_11),
% 1.65/1.48 inference(primitive_instantiation,[status(thm)],[f78])).
% 1.65/1.48 thf(f78,plain,(
% 1.65/1.48 ( ! [X0 : $i > $o] : (($false = (X0 @ cP)) | ((X0 @ cJ) != $true)) ) | ~spl1_11),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.65/1.48 thf(f77,definition,(
% 1.65/1.48 spl1_11 <=> ! [X0 : $i > $o] : (($false = (X0 @ cP)) | ((X0 @ cJ) != $true))),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.65/1.48 thf(f271,plain,(
% 1.65/1.48 ~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_8 | ~spl1_10),
% 1.65/1.48 inference(avatar_contradiction_clause,[status(thm)],[f270])).
% 1.65/1.48 thf(f270,plain,(
% 1.65/1.48 $false | (~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_8 | ~spl1_10)),
% 1.65/1.48 inference(trivial_inequality_removal,[status(thm)],[f267])).
% 1.65/1.48 thf(f267,plain,(
% 1.65/1.48 ($false = $true) | (~spl1_2 | ~spl1_4 | ~spl1_6 | ~spl1_8 | ~spl1_10)),
% 1.65/1.48 inference(superposition,[status(thm)],[f233,f265])).
% 1.65/1.48 thf(f265,plain,(
% 1.65/1.48 ($false = (cLIKE @ cJ @ cS)) | (~spl1_4 | ~spl1_10)),
% 1.65/1.48 inference(superposition,[status(thm)],[f46,f246])).
% 1.65/1.48 thf(f246,plain,(
% 1.65/1.48 (cP = cJ) | ~spl1_10),
% 1.65/1.48 inference(leibniz_equality_elimination,[status(thm)],[f74])).
% 1.65/1.48 thf(f74,plain,(
% 1.65/1.48 ( ! [X0 : $i > $o] : (((X0 @ cP) = $true) | ((X0 @ cJ) != $true)) ) | ~spl1_10),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.65/1.48 thf(f73,definition,(
% 1.65/1.48 spl1_10 <=> ! [X0 : $i > $o] : (((X0 @ cP) = $true) | ((X0 @ cJ) != $true))),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 1.65/1.48 thf(f46,plain,(
% 1.65/1.48 ((cLIKE @ cP @ cS) = $false) | ~spl1_4),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.65/1.48 thf(f44,definition,(
% 1.65/1.48 spl1_4 <=> ((cLIKE @ cP @ cS) = $false)),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.65/1.48 thf(f233,plain,(
% 1.65/1.48 ((cLIKE @ cJ @ cS) = $true) | (~spl1_2 | ~spl1_6 | ~spl1_8)),
% 1.65/1.48 inference(superposition,[status(thm)],[f66,f226])).
% 1.65/1.48 thf(f226,plain,(
% 1.65/1.48 (cS = sK0) | (~spl1_2 | ~spl1_6)),
% 1.65/1.48 inference(subsumption_resolution,[status(thm)],[f225,f37])).
% 1.65/1.48 thf(f37,plain,(
% 1.65/1.48 ((cWRH @ sK0) = $true) | ~spl1_2),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.65/1.48 thf(f35,definition,(
% 1.65/1.48 spl1_2 <=> ((cWRH @ sK0) = $true)),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.65/1.48 thf(f225,plain,(
% 1.65/1.48 (cS = sK0) | ((cWRH @ sK0) != $true) | ~spl1_6),
% 1.65/1.48 inference(trivial_inequality_removal,[status(thm)],[f224])).
% 1.65/1.48 thf(f224,plain,(
% 1.65/1.48 (cS = sK0) | ($true != $true) | ((cWRH @ sK0) != $true) | ~spl1_6),
% 1.65/1.48 inference(superposition,[status(thm)],[f84,f54])).
% 1.65/1.48 thf(f54,plain,(
% 1.65/1.48 ((cW @ sK0) = $true) | ~spl1_6),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.65/1.48 thf(f52,definition,(
% 1.65/1.48 spl1_6 <=> ((cW @ sK0) = $true)),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.65/1.48 thf(f84,plain,(
% 1.65/1.48 ( ! [X0 : $i] : (((cW @ X0) != $true) | (cS = X0) | ((cWRH @ X0) != $true)) )),
% 1.65/1.48 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.65/1.48 thf(f83,plain,(
% 1.65/1.48 ( ! [X0 : $i] : (((cW @ X0) != $true) | (cS = X0) | ((cWRH @ X0) != $true) | ($true != $true)) )),
% 1.65/1.48 inference(superposition,[status(thm)],[f12,f20])).
% 1.65/1.48 thf(f20,plain,(
% 1.65/1.48 ((cUNIQUE @ cS) = $true)),
% 1.65/1.48 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.48 thf(f11,plain,(
% 1.65/1.48 ((cUNIQUE @ cS) = $true) & ! [X0 : $i > $o] : (((((X0 @ cJ) != $true) | ! [X1 : $i] : (((cW @ X1) != $true) | ((cUNIQUE @ X1) != $true) | ((cLIKE @ cJ @ X1) != $true) | ((cWRH @ X1) != $true))) & (((X0 @ cJ) = $true) | (((cW @ sK0) = $true) & ((cUNIQUE @ sK0) = $true) & ((cLIKE @ cJ @ sK0) = $true) & ((cWRH @ sK0) = $true)))) | ((cLIKE @ cP @ cS) != (X0 @ cP))) & ((cWRH @ cS) = $true) & ((cW @ cS) = $true) & ! [X3 : $i] : (($true != (cUNIQUE @ X3)) | ! [X4 : $i] : (($true != (cW @ X4)) | ((cWRH @ X4) != $true) | (X3 = X4)))),
% 1.65/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.65/1.48 thf(f10,plain,(
% 1.65/1.48 ? [X2 : $i] : (((cW @ X2) = $true) & ((cUNIQUE @ X2) = $true) & ((cLIKE @ cJ @ X2) = $true) & ((cWRH @ X2) = $true)) => (((cW @ sK0) = $true) & ((cUNIQUE @ sK0) = $true) & ((cLIKE @ cJ @ sK0) = $true) & ((cWRH @ sK0) = $true))),
% 1.65/1.48 introduced(definition,[],[choice_axiom])).
% 1.65/1.48 thf(f9,plain,(
% 1.65/1.48 ((cUNIQUE @ cS) = $true) & ! [X0 : $i > $o] : (((((X0 @ cJ) != $true) | ! [X1 : $i] : (((cW @ X1) != $true) | ((cUNIQUE @ X1) != $true) | ((cLIKE @ cJ @ X1) != $true) | ((cWRH @ X1) != $true))) & (((X0 @ cJ) = $true) | ? [X2 : $i] : (((cW @ X2) = $true) & ((cUNIQUE @ X2) = $true) & ((cLIKE @ cJ @ X2) = $true) & ((cWRH @ X2) = $true)))) | ((cLIKE @ cP @ cS) != (X0 @ cP))) & ((cWRH @ cS) = $true) & ((cW @ cS) = $true) & ! [X3 : $i] : (($true != (cUNIQUE @ X3)) | ! [X4 : $i] : (($true != (cW @ X4)) | ((cWRH @ X4) != $true) | (X3 = X4)))),
% 1.65/1.48 inference(rectify,[status(thm)],[f8])).
% 1.65/1.48 thf(f8,plain,(
% 1.65/1.48 ((cUNIQUE @ cS) = $true) & ! [X2 : $i > $o] : (((((X2 @ cJ) != $true) | ! [X3 : $i] : (((cW @ X3) != $true) | ($true != (cUNIQUE @ X3)) | ((cLIKE @ cJ @ X3) != $true) | ((cWRH @ X3) != $true))) & (((X2 @ cJ) = $true) | ? [X3 : $i] : (((cW @ X3) = $true) & ($true = (cUNIQUE @ X3)) & ((cLIKE @ cJ @ X3) = $true) & ((cWRH @ X3) = $true)))) | ((X2 @ cP) != (cLIKE @ cP @ cS))) & ((cWRH @ cS) = $true) & ((cW @ cS) = $true) & ! [X0 : $i] : (((cUNIQUE @ X0) != $true) | ! [X1 : $i] : (((cW @ X1) != $true) | ((cWRH @ X1) != $true) | (X0 = X1)))),
% 1.65/1.48 inference(nnf_transformation,[status(thm)],[f7])).
% 1.65/1.48 thf(f7,plain,(
% 1.65/1.48 ((cUNIQUE @ cS) = $true) & ! [X2 : $i > $o] : ((? [X3 : $i] : (((cW @ X3) = $true) & ($true = (cUNIQUE @ X3)) & ((cLIKE @ cJ @ X3) = $true) & ((cWRH @ X3) = $true)) <~> ((X2 @ cJ) = $true)) | ((X2 @ cP) != (cLIKE @ cP @ cS))) & ((cWRH @ cS) = $true) & ((cW @ cS) = $true) & ! [X0 : $i] : (((cUNIQUE @ X0) != $true) | ! [X1 : $i] : (((cW @ X1) != $true) | ((cWRH @ X1) != $true) | (X0 = X1)))),
% 1.65/1.48 inference(flattening,[status(thm)],[f6])).
% 1.65/1.48 thf(f6,plain,(
% 1.65/1.48 ! [X2 : $i > $o] : ((? [X3 : $i] : (((cW @ X3) = $true) & ($true = (cUNIQUE @ X3)) & ((cLIKE @ cJ @ X3) = $true) & ((cWRH @ X3) = $true)) <~> ((X2 @ cJ) = $true)) | ((X2 @ cP) != (cLIKE @ cP @ cS))) & (((cUNIQUE @ cS) = $true) & ((cW @ cS) = $true) & ! [X0 : $i] : (! [X1 : $i] : ((X0 = X1) | (((cW @ X1) != $true) | ((cWRH @ X1) != $true))) | ((cUNIQUE @ X0) != $true)) & ((cWRH @ cS) = $true))),
% 1.65/1.48 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.48 thf(f5,plain,(
% 1.65/1.48 ~((((cUNIQUE @ cS) = $true) & ((cW @ cS) = $true) & ! [X0 : $i] : (((cUNIQUE @ X0) = $true) => ! [X1 : $i] : ((((cW @ X1) = $true) & ((cWRH @ X1) = $true)) => (X0 = X1))) & ((cWRH @ cS) = $true)) => ? [X2 : $i > $o] : ((((X2 @ cJ) = $true) <=> ? [X3 : $i] : (((cW @ X3) = $true) & ($true = (cUNIQUE @ X3)) & ((cLIKE @ cJ @ X3) = $true) & ((cWRH @ X3) = $true))) & ((X2 @ cP) = (cLIKE @ cP @ cS))))),
% 1.65/1.48 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.48 thf(f4,plain,(
% 1.65/1.48 ~(((cW @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (((cWRH @ X1) & (cW @ X1)) => (X0 = X1))) & (cWRH @ cS) & (cUNIQUE @ cS)) => ? [X2 : $i > $o] : ((? [X3 : $i] : ((cWRH @ X3) & (cLIKE @ cJ @ X3) & (cW @ X3) & (cUNIQUE @ X3)) = (X2 @ cJ)) & ((X2 @ cP) = (cLIKE @ cP @ cS))))),
% 1.65/1.48 inference(rectify,[status(thm)],[f2])).
% 1.65/1.48 thf(f2,negated_conjecture,(
% 1.65/1.48 ~(((cW @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (((cWRH @ X1) & (cW @ X1)) => (X0 = X1))) & (cWRH @ cS) & (cUNIQUE @ cS)) => ? [X2 : $i > $o] : ((? [X0 : $i] : ((cWRH @ X0) & (cLIKE @ cJ @ X0) & (cW @ X0) & (cUNIQUE @ X0)) = (X2 @ cJ)) & ((X2 @ cP) = (cLIKE @ cP @ cS))))),
% 1.65/1.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.48 thf(f1,conjecture,(
% 1.65/1.48 ((cW @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (((cWRH @ X1) & (cW @ X1)) => (X0 = X1))) & (cWRH @ cS) & (cUNIQUE @ cS)) => ? [X2 : $i > $o] : ((? [X0 : $i] : ((cWRH @ X0) & (cLIKE @ cJ @ X0) & (cW @ X0) & (cUNIQUE @ X0)) = (X2 @ cJ)) & ((X2 @ cP) = (cLIKE @ cP @ cS)))),
% 1.65/1.48 file('/export/starexec/sandbox/tmp/tmp.POE620fLAG/DTF2THF_19261.p',cLING1)).
% 1.65/1.48 thf(f12,plain,(
% 1.65/1.48 ( ! [X3 : $i,X4 : $i] : (($true != (cUNIQUE @ X3)) | ($true != (cW @ X4)) | (X3 = X4) | ((cWRH @ X4) != $true)) )),
% 1.65/1.48 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.48 thf(f66,plain,(
% 1.65/1.48 ((cLIKE @ cJ @ sK0) = $true) | ~spl1_8),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.65/1.48 thf(f64,definition,(
% 1.65/1.48 spl1_8 <=> ((cLIKE @ cJ @ sK0) = $true)),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.65/1.48 thf(f245,plain,(
% 1.65/1.48 ~spl1_2 | ~spl1_6 | ~spl1_7 | ~spl1_8 | ~spl1_9),
% 1.65/1.48 inference(avatar_contradiction_clause,[status(thm)],[f244])).
% 1.65/1.48 thf(f244,plain,(
% 1.65/1.48 $false | (~spl1_2 | ~spl1_6 | ~spl1_7 | ~spl1_8 | ~spl1_9)),
% 1.65/1.48 inference(subsumption_resolution,[status(thm)],[f243,f60])).
% 1.65/1.48 thf(f60,plain,(
% 1.65/1.48 ((cUNIQUE @ sK0) = $true) | ~spl1_7),
% 1.65/1.48 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.65/1.48 thf(f58,definition,(
% 1.65/1.48 spl1_7 <=> ((cUNIQUE @ sK0) = $true)),
% 1.65/1.48 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.65/1.48 thf(f243,plain,(
% 1.65/1.48 ((cUNIQUE @ sK0) != $true) | (~spl1_2 | ~spl1_6 | ~spl1_8 | ~spl1_9)),
% 1.65/1.48 inference(subsumption_resolution,[status(thm)],[f242,f37])).
% 1.65/1.48 thf(f242,plain,(
% 1.65/1.48 ((cWRH @ sK0) != $true) | ((cUNIQUE @ sK0) != $true) | (~spl1_6 | ~spl1_8 | ~spl1_9)),
% 1.65/1.48 inference(subsumption_resolution,[status(thm)],[f236,f54])).
% 1.65/1.48 thf(f236,plain,(
% 1.65/1.48 ((cW @ sK0) != $true) | ((cUNIQUE @ sK0) != $true) | ((cWRH @ sK0) != $true) | (~spl1_8 | ~spl1_9)),
% 1.65/1.48 inference(trivial_inequality_removal,[status(thm)],[f235])).
% 1.65/1.48 thf(f235,plain,(
% 1.65/1.48 ((cW @ sK0) != $true) | ((cWRH @ sK0) != $true) | ((cUNIQUE @ sK0) != $true) | ($true != $true) | (~spl1_8 | ~spl1_9)),
% 1.65/1.49 inference(superposition,[status(thm)],[f71,f66])).
% 1.65/1.49 thf(f71,plain,(
% 1.65/1.49 ( ! [X1 : $i] : (((cLIKE @ cJ @ X1) != $true) | ((cW @ X1) != $true) | ((cWRH @ X1) != $true) | ((cUNIQUE @ X1) != $true)) ) | ~spl1_9),
% 1.65/1.49 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.65/1.49 thf(f70,definition,(
% 1.65/1.49 spl1_9 <=> ! [X1 : $i] : (((cWRH @ X1) != $true) | ((cW @ X1) != $true) | ((cUNIQUE @ X1) != $true) | ((cLIKE @ cJ @ X1) != $true))),
% 1.65/1.49 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.65/1.49 thf(f195,plain,(
% 1.65/1.49 ~spl1_1),
% 1.65/1.49 inference(avatar_contradiction_clause,[status(thm)],[f194])).
% 1.65/1.49 thf(f194,plain,(
% 1.65/1.49 $false | ~spl1_1),
% 1.65/1.49 inference(trivial_inequality_removal,[status(thm)],[f193])).
% 1.65/1.49 thf(f193,plain,(
% 1.65/1.49 ($false = $true) | ~spl1_1),
% 1.65/1.49 inference(duplicate_literal_removal,[status(thm)],[f192])).
% 1.65/1.49 thf(f192,plain,(
% 1.65/1.49 ($false = $true) | ($false = $true) | ~spl1_1),
% 1.65/1.49 inference(beta_eta_normalization,[status(thm)],[f188])).
% 1.65/1.49 thf(f188,plain,(
% 1.65/1.49 (((^[Y0 : $i]: ($false)) @ cP) = $true) | (((^[Y0 : $i]: ($false)) @ cJ) = $true) | ~spl1_1),
% 1.65/1.49 inference(primitive_instantiation,[status(thm)],[f33])).
% 1.65/1.49 thf(f33,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((X0 @ cP) = $true) | ((X0 @ cJ) = $true)) ) | ~spl1_1),
% 1.65/1.49 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.65/1.49 thf(f32,definition,(
% 1.65/1.49 spl1_1 <=> ! [X0 : $i > $o] : (((X0 @ cP) = $true) | ((X0 @ cJ) = $true))),
% 1.65/1.49 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.65/1.49 thf(f109,plain,(
% 1.65/1.49 ~spl1_3 | ~spl1_5 | ~spl1_9),
% 1.65/1.49 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.65/1.49 thf(f108,plain,(
% 1.65/1.49 $false | (~spl1_3 | ~spl1_5 | ~spl1_9)),
% 1.65/1.49 inference(subsumption_resolution,[status(thm)],[f107,f13])).
% 1.65/1.49 thf(f13,plain,(
% 1.65/1.49 ((cW @ cS) = $true)),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f107,plain,(
% 1.65/1.49 ((cW @ cS) != $true) | (~spl1_3 | ~spl1_5 | ~spl1_9)),
% 1.65/1.49 inference(subsumption_resolution,[status(thm)],[f106,f14])).
% 1.65/1.49 thf(f14,plain,(
% 1.65/1.49 ((cWRH @ cS) = $true)),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f106,plain,(
% 1.65/1.49 ((cWRH @ cS) != $true) | ((cW @ cS) != $true) | (~spl1_3 | ~spl1_5 | ~spl1_9)),
% 1.65/1.49 inference(subsumption_resolution,[status(thm)],[f105,f20])).
% 1.65/1.49 thf(f105,plain,(
% 1.65/1.49 ((cUNIQUE @ cS) != $true) | ((cWRH @ cS) != $true) | ((cW @ cS) != $true) | (~spl1_3 | ~spl1_5 | ~spl1_9)),
% 1.65/1.49 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.65/1.49 thf(f104,plain,(
% 1.65/1.49 ((cW @ cS) != $true) | ((cUNIQUE @ cS) != $true) | ((cWRH @ cS) != $true) | ($true != $true) | (~spl1_3 | ~spl1_5 | ~spl1_9)),
% 1.65/1.49 inference(superposition,[status(thm)],[f71,f99])).
% 1.65/1.49 thf(f99,plain,(
% 1.65/1.49 ((cLIKE @ cJ @ cS) = $true) | (~spl1_3 | ~spl1_5)),
% 1.65/1.49 inference(superposition,[status(thm)],[f41,f87])).
% 1.65/1.49 thf(f87,plain,(
% 1.65/1.49 (cP = cJ) | ~spl1_5),
% 1.65/1.49 inference(leibniz_equality_elimination,[status(thm)],[f49])).
% 1.65/1.49 thf(f49,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (($false = (X0 @ cP)) | ((X0 @ cJ) = $true)) ) | ~spl1_5),
% 1.65/1.49 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.65/1.49 thf(f48,definition,(
% 1.65/1.49 spl1_5 <=> ! [X0 : $i > $o] : (((X0 @ cJ) = $true) | ($false = (X0 @ cP)))),
% 1.65/1.49 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.65/1.49 thf(f41,plain,(
% 1.65/1.49 ((cLIKE @ cP @ cS) = $true) | ~spl1_3),
% 1.65/1.49 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.65/1.49 thf(f39,definition,(
% 1.65/1.49 spl1_3 <=> ((cLIKE @ cP @ cS) = $true)),
% 1.65/1.49 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.65/1.49 thf(f82,plain,(
% 1.65/1.49 ~spl1_3 | ~spl1_4),
% 1.65/1.49 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.65/1.49 thf(f81,plain,(
% 1.65/1.49 $false | (~spl1_3 | ~spl1_4)),
% 1.65/1.49 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.65/1.49 thf(f80,plain,(
% 1.65/1.49 ($false = $true) | (~spl1_3 | ~spl1_4)),
% 1.65/1.49 inference(forward_demodulation,[status(thm)],[f41,f46])).
% 1.65/1.49 thf(f79,plain,(
% 1.65/1.49 spl1_11 | spl1_9 | spl1_4),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f22,f44,f70,f77])).
% 1.65/1.49 thf(f22,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o,X1 : $i] : (((cWRH @ X1) != $true) | ((cLIKE @ cJ @ X1) != $true) | ($false = (X0 @ cP)) | ((X0 @ cJ) != $true) | ((cUNIQUE @ X1) != $true) | ((cW @ X1) != $true) | ((cLIKE @ cP @ cS) = $false)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.65/1.49 thf(f19,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o,X1 : $i] : (((cUNIQUE @ X1) != $true) | ((cW @ X1) != $true) | ((cWRH @ X1) != $true) | ((X0 @ cJ) != $true) | ((cLIKE @ cJ @ X1) != $true) | ((cLIKE @ cP @ cS) != (X0 @ cP))) )),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f75,plain,(
% 1.65/1.49 spl1_3 | spl1_9 | spl1_10),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f21,f73,f70,f39])).
% 1.65/1.49 thf(f21,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o,X1 : $i] : (((cWRH @ X1) != $true) | ((cLIKE @ cJ @ X1) != $true) | ((cUNIQUE @ X1) != $true) | ((cW @ X1) != $true) | ((X0 @ cP) = $true) | ((X0 @ cJ) != $true) | ((cLIKE @ cP @ cS) = $true)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.65/1.49 thf(f68,plain,(
% 1.65/1.49 spl1_5 | spl1_4 | spl1_8),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f24,f64,f44,f48])).
% 1.65/1.49 thf(f24,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (($false = (X0 @ cP)) | ((cLIKE @ cJ @ sK0) = $true) | ((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) = $false)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.65/1.49 thf(f16,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cLIKE @ cJ @ sK0) = $true) | ((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) != (X0 @ cP))) )),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f67,plain,(
% 1.65/1.49 spl1_3 | spl1_8 | spl1_1),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f23,f32,f64,f39])).
% 1.65/1.49 thf(f23,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cLIKE @ cP @ cS) = $true) | ((X0 @ cJ) = $true) | ((cLIKE @ cJ @ sK0) = $true) | ((X0 @ cP) = $true)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.65/1.49 thf(f62,plain,(
% 1.65/1.49 spl1_4 | spl1_7 | spl1_5),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f26,f48,f58,f44])).
% 1.65/1.49 thf(f26,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cLIKE @ cP @ cS) = $false) | ((X0 @ cJ) = $true) | ((cUNIQUE @ sK0) = $true) | ($false = (X0 @ cP))) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.65/1.49 thf(f17,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) != (X0 @ cP)) | ((cUNIQUE @ sK0) = $true)) )),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f61,plain,(
% 1.65/1.49 spl1_1 | spl1_7 | spl1_3),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f25,f39,f58,f32])).
% 1.65/1.49 thf(f25,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cLIKE @ cP @ cS) = $true) | ((X0 @ cP) = $true) | ((cUNIQUE @ sK0) = $true) | ((X0 @ cJ) = $true)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.65/1.49 thf(f56,plain,(
% 1.65/1.49 spl1_6 | spl1_5 | spl1_4),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f28,f44,f48,f52])).
% 1.65/1.49 thf(f28,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (($false = (X0 @ cP)) | ((cW @ sK0) = $true) | ((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) = $false)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.65/1.49 thf(f18,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) != (X0 @ cP)) | ((cW @ sK0) = $true)) )),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f55,plain,(
% 1.65/1.49 spl1_6 | spl1_3 | spl1_1),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f27,f32,f39,f52])).
% 1.65/1.49 thf(f27,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((X0 @ cP) = $true) | ((cW @ sK0) = $true) | ((cLIKE @ cP @ cS) = $true) | ((X0 @ cJ) = $true)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.65/1.49 thf(f50,plain,(
% 1.65/1.49 spl1_4 | spl1_2 | spl1_5),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f30,f48,f35,f44])).
% 1.65/1.49 thf(f30,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cLIKE @ cP @ cS) = $false) | ((X0 @ cJ) = $true) | ($false = (X0 @ cP)) | ((cWRH @ sK0) = $true)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.65/1.49 thf(f15,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cWRH @ sK0) = $true) | ((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) != (X0 @ cP))) )),
% 1.65/1.49 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.49 thf(f42,plain,(
% 1.65/1.49 spl1_1 | spl1_2 | spl1_3),
% 1.65/1.49 inference(avatar_split_clause,[status(thm)],[f29,f39,f35,f32])).
% 1.65/1.49 thf(f29,plain,(
% 1.65/1.49 ( ! [X0 : $i > $o] : (((cWRH @ sK0) = $true) | ((X0 @ cP) = $true) | ((X0 @ cJ) = $true) | ((cLIKE @ cP @ cS) = $true)) )),
% 1.65/1.49 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.65/1.49 % SZS output end Proof for DTF2THF_19261
% 1.65/1.49 % (19363)------------------------------
% 1.65/1.49 % (19363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (19363)Termination reason: Refutation
% 1.65/1.49
% 1.65/1.49 % (19363)Memory used [KB]: 5628
% 1.65/1.49 % (19363)Time elapsed: 0.015 s
% 1.65/1.49 % (19363)Instructions burned: 19 (million)
% 1.65/1.49 % (19363)------------------------------
% 1.65/1.49 % (19363)------------------------------
% 1.65/1.49 % (19357)Success in time 0.028 s
%------------------------------------------------------------------------------