%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO223^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 1.60s 1.32s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 517 ( 129 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 397 ( 82 ~; 84 |; 32 &; 181 @)
% ( 7 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 71 ( 2 ^; 56 !; 13 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cLIKE: $i > $i > $o ).
thf(func_def_2,type,
cUNIQUE: $i > $o ).
thf(func_def_11,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f298,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f53,f62,f127,f239,f255,f281]) ).
thf(f281,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[status(thm)],[f280]) ).
thf(f280,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f279]) ).
thf(f279,plain,
( ( $false = $true )
| ~ spl1_3 ),
inference(duplicate_literal_removal,[status(thm)],[f278]) ).
thf(f278,plain,
( ( $false = $true )
| ( $false = $true )
| ~ spl1_3 ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ( ( ^ [Y0: $i] : $false
@ cS )
= $true )
| ( ( ^ [Y0: $i] : $false
@ cJ )
= $true )
| ~ spl1_3 ),
inference(primitive_instantiation,[status(thm)],[f257]) ).
thf(f257,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cS )
= $true )
| ( ( X2 @ cJ )
= $true ) )
| ~ spl1_3 ),
inference(forward_demodulation,[status(thm)],[f33,f64]) ).
thf(f64,plain,
! [X0: $i] : ( cS = X0 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $i] :
( ( $true != $true )
| ( cS = X0 ) ),
inference(superposition,[status(thm)],[f16,f15]) ).
thf(f15,plain,
( ( cUNIQUE @ cS )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ! [X1: $i] : ( X0 = X1 )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cUNIQUE @ cS )
= $true )
& ! [X2: $i > $o] :
( ( ( ( ( X2 @ cJ )
!= $true )
| ! [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( cUNIQUE @ X3 )
!= $true ) ) )
& ( ( ( X2 @ cJ )
= $true )
| ( ( ( cLIKE @ cJ @ sK0 )
= $true )
& ( ( cUNIQUE @ sK0 )
= $true ) ) ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X4: $i] :
( ( ( cLIKE @ cJ @ X4 )
= $true )
& ( ( cUNIQUE @ X4 )
= $true ) )
=> ( ( ( cLIKE @ cJ @ sK0 )
= $true )
& ( ( cUNIQUE @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ! [X1: $i] : ( X0 = X1 )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cUNIQUE @ cS )
= $true )
& ! [X2: $i > $o] :
( ( ( ( ( X2 @ cJ )
!= $true )
| ! [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( cUNIQUE @ X3 )
!= $true ) ) )
& ( ( ( X2 @ cJ )
= $true )
| ? [X4: $i] :
( ( ( cLIKE @ cJ @ X4 )
= $true )
& ( ( cUNIQUE @ X4 )
= $true ) ) ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i] :
( ! [X1: $i] : ( X0 = X1 )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cUNIQUE @ cS )
= $true )
& ! [X2: $i > $o] :
( ( ( ( ( X2 @ cJ )
!= $true )
| ! [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( cUNIQUE @ X3 )
!= $true ) ) )
& ( ( ( X2 @ cJ )
= $true )
| ? [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cUNIQUE @ X3 )
= $true ) ) ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i] :
( ! [X1: $i] : ( X0 = X1 )
| ( ( cUNIQUE @ X0 )
!= $true ) )
& ( ( cUNIQUE @ cS )
= $true )
& ! [X2: $i > $o] :
( ( ? [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cUNIQUE @ X3 )
= $true ) )
<~> ( ( X2 @ cJ )
= $true ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i > $o] :
( ( ? [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cUNIQUE @ X3 )
= $true ) )
<~> ( ( X2 @ cJ )
= $true ) )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) )
& ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ! [X1: $i] : ( X0 = X1 )
| ( ( cUNIQUE @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cUNIQUE @ cS )
= $true )
& ! [X0: $i] :
( ( ( cUNIQUE @ X0 )
= $true )
=> ! [X1: $i] : ( X0 = X1 ) ) )
=> ? [X2: $i > $o] :
( ( ( ( X2 @ cJ )
= $true )
<=> ? [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
= $true )
& ( ( cUNIQUE @ X3 )
= $true ) ) )
& ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cUNIQUE @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] : ( X0 = X1 ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ? [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
& ( cUNIQUE @ X3 ) )
= ( X2 @ cJ ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cUNIQUE @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] : ( X0 = X1 ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ? [X0: $i] :
( ( ( cLIKE @ cJ @ X0 )
& ( cUNIQUE @ X0 ) )
= ( X2 @ cJ ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cUNIQUE @ cS )
& ! [X0: $i] :
( ( cUNIQUE @ X0 )
=> ! [X1: $i] : ( X0 = X1 ) ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ cP )
= ( cLIKE @ cP @ cS ) )
& ? [X0: $i] :
( ( ( cLIKE @ cJ @ X0 )
& ( cUNIQUE @ X0 ) )
= ( X2 @ cJ ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CqirdRYcGl/DTF2THF_30570.p',cLING2) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( cUNIQUE @ X0 )
!= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f33,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cJ )
= $true )
| ( ( X2 @ cP )
= $true ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl1_3
<=> ! [X2: $i > $o] :
( ( ( X2 @ cJ )
= $true )
| ( ( X2 @ cP )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f255,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f254]) ).
thf(f254,plain,
( $false
| ~ spl1_1
| spl1_2 ),
inference(subsumption_resolution,[status(thm)],[f176,f201]) ).
thf(f201,plain,
( ! [X0: $i] :
( ( cLIKE @ X0 @ cS )
= $true )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f194,f65]) ).
thf(f65,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f64,f64]) ).
thf(f194,plain,
( ( ( cLIKE @ cJ @ cS )
= $true )
| ~ spl1_1 ),
inference(forward_demodulation,[status(thm)],[f26,f64]) ).
thf(f26,plain,
( ( ( cLIKE @ cJ @ sK0 )
= $true )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl1_1
<=> ( ( cLIKE @ cJ @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f176,plain,
( ( ( cLIKE @ cS @ cS )
!= $true )
| spl1_2 ),
inference(forward_demodulation,[status(thm)],[f29,f64]) ).
thf(f29,plain,
( ( ( cLIKE @ cP @ cS )
!= $true )
| spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl1_2
<=> ( ( cLIKE @ cP @ cS )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f239,plain,
~ spl1_8,
inference(avatar_contradiction_clause,[status(thm)],[f238]) ).
thf(f238,plain,
( $false
| ~ spl1_8 ),
inference(subsumption_resolution,[status(thm)],[f217,f66]) ).
thf(f66,plain,
! [X0: $i] :
( ( cUNIQUE @ X0 )
= $true ),
inference(superposition,[status(thm)],[f15,f64]) ).
thf(f217,plain,
( ( ( cUNIQUE @ cJ )
!= $true )
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f209]) ).
thf(f209,plain,
( ( $false = $true )
| ( ( cUNIQUE @ cJ )
!= $true )
| ~ spl1_8 ),
inference(superposition,[status(thm)],[f173,f15]) ).
thf(f173,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cS )
= $false )
| ( ( X2 @ cJ )
!= $true ) )
| ~ spl1_8 ),
inference(forward_demodulation,[status(thm)],[f52,f64]) ).
thf(f52,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ cP )
= $false )
| ( ( X2 @ cJ )
!= $true ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl1_8
<=> ! [X2: $i > $o] :
( ( ( X2 @ cJ )
!= $true )
| ( ( X2 @ cP )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f127,plain,
( ~ spl1_2
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl1_2
| ~ spl1_7 ),
inference(subsumption_resolution,[status(thm)],[f116,f114]) ).
thf(f114,plain,
( ! [X0: $i,X1: $i] :
( ( cLIKE @ X0 @ X1 )
!= $true )
| ~ spl1_7 ),
inference(subsumption_resolution,[status(thm)],[f112,f66]) ).
thf(f112,plain,
( ! [X0: $i,X1: $i] :
( ( ( cLIKE @ X0 @ X1 )
!= $true )
| ( ( cUNIQUE @ X1 )
!= $true ) )
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f48,f65]) ).
thf(f48,plain,
( ! [X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( cUNIQUE @ X3 )
!= $true ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl1_7
<=> ! [X3: $i] :
( ( ( cUNIQUE @ X3 )
!= $true )
| ( ( cLIKE @ cJ @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f116,plain,
( ! [X0: $i,X1: $i] :
( ( cLIKE @ X0 @ X1 )
= $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f69,f65]) ).
thf(f69,plain,
( ! [X0: $i] :
( ( cLIKE @ cS @ X0 )
= $true )
| ~ spl1_2 ),
inference(forward_demodulation,[status(thm)],[f67,f64]) ).
thf(f67,plain,
( ! [X0: $i] :
( ( cLIKE @ cP @ X0 )
= $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f30,f64]) ).
thf(f30,plain,
( ( ( cLIKE @ cP @ cS )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f62,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(forward_demodulation,[status(thm)],[f30,f38]) ).
thf(f38,plain,
( ( ( cLIKE @ cP @ cS )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl1_4
<=> ( ( cLIKE @ cP @ cS )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f53,plain,
( spl1_7
| spl1_8
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f36,f51,f47]) ).
thf(f20,plain,
! [X2: $i > $o,X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( cLIKE @ cP @ cS )
= $false )
| ( ( cUNIQUE @ X3 )
!= $true )
| ( ( X2 @ cJ )
!= $true )
| ( ( X2 @ cP )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i > $o,X3: $i] :
( ( ( cLIKE @ cJ @ X3 )
!= $true )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( cUNIQUE @ X3 )
!= $true )
| ( ( X2 @ cJ )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f34,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f21,f32,f28,f24]) ).
thf(f21,plain,
! [X2: $i > $o] :
( ( ( X2 @ cJ )
= $true )
| ( ( cLIKE @ cJ @ sK0 )
= $true )
| ( ( cLIKE @ cP @ cS )
= $true )
| ( ( X2 @ cP )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: $i > $o] :
( ( ( cLIKE @ cJ @ sK0 )
= $true )
| ( ( X2 @ cJ )
= $true )
| ( ( X2 @ cP )
!= ( cLIKE @ cP @ cS ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO223^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n009.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:26:10 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO223^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem LING2
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0357 [Bro09]
% 0.30/0.46 % : LING2 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.30/0.46 % Number of atoms : 8 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 5 ( 8 avg)
% 0.30/0.46 % Number of connectives : 14 ( 0 ~; 0 |; 3 &; 9 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cJ,type,
% 0.30/0.46 cJ: $i ).
% 0.30/0.46
% 0.30/0.46 thf(cLIKE,type,
% 0.30/0.46 cLIKE: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cUNIQUE,type,
% 0.30/0.46 cUNIQUE: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cS,type,
% 0.30/0.46 cS: $i ).
% 0.30/0.46
% 0.30/0.46 thf(cP,type,
% 0.30/0.46 cP: $i ).
% 0.30/0.46
% 0.30/0.46 thf(cLING2,conjecture,
% 0.30/0.46 ( ( ! [X: $i] :
% 0.30/0.46 ( ( cUNIQUE @ X )
% 0.30/0.46 => ! [Z: $i] : ( X = Z ) )
% 0.30/0.46 & ( cUNIQUE @ cS ) )
% 0.30/0.46 => ? [Xan: $i > $o] :
% 0.30/0.46 ( ( ( Xan @ cP )
% 0.30/0.46 = ( cLIKE @ cP @ cS ) )
% 0.30/0.46 & ( ( Xan @ cJ )
% 0.30/0.46 = ( ? [X: $i] :
% 0.30/0.46 ( ( cUNIQUE @ X )
% 0.30/0.46 & ( cLIKE @ cJ @ X ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 14:26:11 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CqirdRYcGl/DTF2DTF30570.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.28 ---- Cleaned THF ---
% 1.44/1.29 thf(cJ,type,
% 1.44/1.29 cJ: $i ).
% 1.44/1.29
% 1.44/1.29 thf(cLIKE,type,
% 1.44/1.29 cLIKE: $i > $i > $o ).
% 1.44/1.29
% 1.44/1.29 thf(cUNIQUE,type,
% 1.44/1.29 cUNIQUE: $i > $o ).
% 1.44/1.29
% 1.44/1.29 thf(cS,type,
% 1.44/1.29 cS: $i ).
% 1.44/1.29
% 1.44/1.29 thf(cP,type,
% 1.44/1.29 cP: $i ).
% 1.44/1.29
% 1.44/1.29 thf(cLING2,conjecture,
% 1.44/1.29 ( ( ! [X: $i] :
% 1.44/1.29 ( ( cUNIQUE @ X )
% 1.44/1.29 => ! [Z: $i] : ( X = Z ) )
% 1.44/1.29 & ( cUNIQUE @ cS ) )
% 1.44/1.29 => ? [Xan: $i > $o] :
% 1.44/1.29 ( ( ( Xan @ cP )
% 1.44/1.29 = ( cLIKE @ cP @ cS ) )
% 1.44/1.29 & ( ( Xan @ cJ )
% 1.44/1.29 = ( ? [X: $i] :
% 1.44/1.29 ( ( cUNIQUE @ X )
% 1.44/1.29 & ( cLIKE @ cJ @ X ) ) ) ) ) ) ).
% 1.44/1.29 ------------------------
% 1.60/1.30 % (30843)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_30570 for (3000ds/4Mi)
% 1.60/1.30 % (30843)Instruction limit reached!
% 1.60/1.30 % (30843)------------------------------
% 1.60/1.30 % (30843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (30843)Termination reason: Unknown
% 1.60/1.30 % (30843)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (30843)Memory used [KB]: 5500
% 1.60/1.30 % (30843)Time elapsed: 0.003 s
% 1.60/1.30 % (30843)Instructions burned: 4 (million)
% 1.60/1.30 % (30843)------------------------------
% 1.60/1.30 % (30843)------------------------------
% 1.60/1.31 % (30842)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30570 for (3000ds/183Mi)
% 1.60/1.31 % (30845)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30570 for (3000ds/2Mi)
% 1.60/1.31 % (30844)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_30570 for (3000ds/27Mi)
% 1.60/1.31 % (30846)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_30570 for (3000ds/2Mi)
% 1.60/1.31 % (30848)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30570 for (3000ds/18Mi)
% 1.60/1.31 % (30847)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_30570 for (3000ds/275Mi)
% 1.60/1.31 % (30846)Instruction limit reached!
% 1.60/1.31 % (30846)------------------------------
% 1.60/1.31 % (30846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (30846)Termination reason: Unknown
% 1.60/1.31 % (30846)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (30846)Memory used [KB]: 895
% 1.60/1.31 % (30846)Time elapsed: 0.003 s
% 1.60/1.31 % (30846)Instructions burned: 2 (million)
% 1.60/1.31 % (30846)------------------------------
% 1.60/1.31 % (30846)------------------------------
% 1.60/1.31 % (30845)Instruction limit reached!
% 1.60/1.31 % (30845)------------------------------
% 1.60/1.31 % (30845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (30845)Termination reason: Unknown
% 1.60/1.31 % (30845)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (30845)Memory used [KB]: 5500
% 1.60/1.31 % (30845)Time elapsed: 0.004 s
% 1.60/1.31 % (30845)Instructions burned: 3 (million)
% 1.60/1.31 % (30845)------------------------------
% 1.60/1.31 % (30845)------------------------------
% 1.60/1.31 % (30849)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30570 for (2999ds/3Mi)
% 1.60/1.31 % (30849)Instruction limit reached!
% 1.60/1.31 % (30849)------------------------------
% 1.60/1.31 % (30849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (30849)Termination reason: Unknown
% 1.60/1.31 % (30849)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (30849)Memory used [KB]: 5500
% 1.60/1.31 % (30849)Time elapsed: 0.002 s
% 1.60/1.31 % (30849)Instructions burned: 3 (million)
% 1.60/1.31 % (30849)------------------------------
% 1.60/1.31 % (30849)------------------------------
% 1.60/1.32 % (30848)Instruction limit reached!
% 1.60/1.32 % (30848)------------------------------
% 1.60/1.32 % (30848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (30848)Termination reason: Unknown
% 1.60/1.32 % (30848)Termination phase: Saturation
% 1.60/1.32
% 1.60/1.32 % (30848)Memory used [KB]: 5628
% 1.60/1.32 % (30848)Time elapsed: 0.015 s
% 1.60/1.32 % (30848)Instructions burned: 18 (million)
% 1.60/1.32 % (30848)------------------------------
% 1.60/1.32 % (30848)------------------------------
% 1.60/1.32 % (30852)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_30570 for (2999ds/3Mi)
% 1.60/1.32 % (30847)First to succeed.
% 1.60/1.32 % (30842)Also succeeded, but the first one will report.
% 1.60/1.32 % (30852)Instruction limit reached!
% 1.60/1.32 % (30852)------------------------------
% 1.60/1.32 % (30852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (30852)Termination reason: Unknown
% 1.60/1.32 % (30852)Termination phase: Saturation
% 1.60/1.32
% 1.60/1.32 % (30852)Memory used [KB]: 5500
% 1.60/1.32 % (30852)Time elapsed: 0.003 s
% 1.60/1.32 % (30852)Instructions burned: 5 (million)
% 1.60/1.32 % (30852)------------------------------
% 1.60/1.32 % (30852)------------------------------
% 1.60/1.32 % (30844)Also succeeded, but the first one will report.
% 1.60/1.32 % (30847)Refutation found. Thanks to Tanya!
% 1.60/1.32 % SZS status Theorem for DTF2THF_30570
% 1.60/1.32 % SZS output start Proof for DTF2THF_30570
% 1.60/1.32 thf(func_def_1, type, cLIKE: $i > $i > $o).
% 1.60/1.32 thf(func_def_2, type, cUNIQUE: $i > $o).
% 1.60/1.32 thf(func_def_11, type, ph2: !>[X0: $tType]:(X0)).
% 1.60/1.32 thf(f298,plain,(
% 1.60/1.32 $false),
% 1.60/1.32 inference(avatar_sat_refutation,[status(thm)],[f34,f53,f62,f127,f239,f255,f281])).
% 1.60/1.32 thf(f281,plain,(
% 1.60/1.32 ~spl1_3),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f280])).
% 1.60/1.32 thf(f280,plain,(
% 1.60/1.32 $false | ~spl1_3),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f279])).
% 1.60/1.32 thf(f279,plain,(
% 1.60/1.32 ($false = $true) | ~spl1_3),
% 1.60/1.32 inference(duplicate_literal_removal,[status(thm)],[f278])).
% 1.60/1.32 thf(f278,plain,(
% 1.60/1.32 ($false = $true) | ($false = $true) | ~spl1_3),
% 1.60/1.32 inference(beta_eta_normalization,[status(thm)],[f268])).
% 1.60/1.32 thf(f268,plain,(
% 1.60/1.32 (((^[Y0 : $i]: ($false)) @ cS) = $true) | (((^[Y0 : $i]: ($false)) @ cJ) = $true) | ~spl1_3),
% 1.60/1.32 inference(primitive_instantiation,[status(thm)],[f257])).
% 1.60/1.32 thf(f257,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o] : (((X2 @ cS) = $true) | ((X2 @ cJ) = $true)) ) | ~spl1_3),
% 1.60/1.32 inference(forward_demodulation,[status(thm)],[f33,f64])).
% 1.60/1.32 thf(f64,plain,(
% 1.60/1.32 ( ! [X0 : $i] : ((cS = X0)) )),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.60/1.32 thf(f63,plain,(
% 1.60/1.32 ( ! [X0 : $i] : (($true != $true) | (cS = X0)) )),
% 1.60/1.32 inference(superposition,[status(thm)],[f16,f15])).
% 1.60/1.32 thf(f15,plain,(
% 1.60/1.32 ((cUNIQUE @ cS) = $true)),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f11,plain,(
% 1.60/1.32 ! [X0 : $i] : (! [X1 : $i] : (X0 = X1) | ((cUNIQUE @ X0) != $true)) & ((cUNIQUE @ cS) = $true) & ! [X2 : $i > $o] : (((((X2 @ cJ) != $true) | ! [X3 : $i] : (((cLIKE @ cJ @ X3) != $true) | ((cUNIQUE @ X3) != $true))) & (((X2 @ cJ) = $true) | (((cLIKE @ cJ @ sK0) = $true) & ((cUNIQUE @ sK0) = $true)))) | ((X2 @ cP) != (cLIKE @ cP @ cS)))),
% 1.60/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.60/1.32 thf(f10,plain,(
% 1.60/1.32 ? [X4 : $i] : (((cLIKE @ cJ @ X4) = $true) & ((cUNIQUE @ X4) = $true)) => (((cLIKE @ cJ @ sK0) = $true) & ((cUNIQUE @ sK0) = $true))),
% 1.60/1.32 introduced(definition,[],[choice_axiom])).
% 1.60/1.32 thf(f9,plain,(
% 1.60/1.32 ! [X0 : $i] : (! [X1 : $i] : (X0 = X1) | ((cUNIQUE @ X0) != $true)) & ((cUNIQUE @ cS) = $true) & ! [X2 : $i > $o] : (((((X2 @ cJ) != $true) | ! [X3 : $i] : (((cLIKE @ cJ @ X3) != $true) | ((cUNIQUE @ X3) != $true))) & (((X2 @ cJ) = $true) | ? [X4 : $i] : (((cLIKE @ cJ @ X4) = $true) & ((cUNIQUE @ X4) = $true)))) | ((X2 @ cP) != (cLIKE @ cP @ cS)))),
% 1.60/1.32 inference(rectify,[status(thm)],[f8])).
% 1.60/1.32 thf(f8,plain,(
% 1.60/1.32 ! [X0 : $i] : (! [X1 : $i] : (X0 = X1) | ((cUNIQUE @ X0) != $true)) & ((cUNIQUE @ cS) = $true) & ! [X2 : $i > $o] : (((((X2 @ cJ) != $true) | ! [X3 : $i] : (((cLIKE @ cJ @ X3) != $true) | ((cUNIQUE @ X3) != $true))) & (((X2 @ cJ) = $true) | ? [X3 : $i] : (((cLIKE @ cJ @ X3) = $true) & ((cUNIQUE @ X3) = $true)))) | ((X2 @ cP) != (cLIKE @ cP @ cS)))),
% 1.60/1.32 inference(nnf_transformation,[status(thm)],[f7])).
% 1.60/1.32 thf(f7,plain,(
% 1.60/1.32 ! [X0 : $i] : (! [X1 : $i] : (X0 = X1) | ((cUNIQUE @ X0) != $true)) & ((cUNIQUE @ cS) = $true) & ! [X2 : $i > $o] : ((? [X3 : $i] : (((cLIKE @ cJ @ X3) = $true) & ((cUNIQUE @ X3) = $true)) <~> ((X2 @ cJ) = $true)) | ((X2 @ cP) != (cLIKE @ cP @ cS)))),
% 1.60/1.32 inference(flattening,[status(thm)],[f6])).
% 1.60/1.32 thf(f6,plain,(
% 1.60/1.32 ! [X2 : $i > $o] : ((? [X3 : $i] : (((cLIKE @ cJ @ X3) = $true) & ((cUNIQUE @ X3) = $true)) <~> ((X2 @ cJ) = $true)) | ((X2 @ cP) != (cLIKE @ cP @ cS))) & (((cUNIQUE @ cS) = $true) & ! [X0 : $i] : (! [X1 : $i] : (X0 = X1) | ((cUNIQUE @ X0) != $true)))),
% 1.60/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.60/1.32 thf(f5,plain,(
% 1.60/1.32 ~((((cUNIQUE @ cS) = $true) & ! [X0 : $i] : (((cUNIQUE @ X0) = $true) => ! [X1 : $i] : (X0 = X1))) => ? [X2 : $i > $o] : ((((X2 @ cJ) = $true) <=> ? [X3 : $i] : (((cLIKE @ cJ @ X3) = $true) & ((cUNIQUE @ X3) = $true))) & ((X2 @ cP) = (cLIKE @ cP @ cS))))),
% 1.60/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.32 thf(f4,plain,(
% 1.60/1.32 ~(((cUNIQUE @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (X0 = X1))) => ? [X2 : $i > $o] : (((X2 @ cP) = (cLIKE @ cP @ cS)) & (? [X3 : $i] : ((cLIKE @ cJ @ X3) & (cUNIQUE @ X3)) = (X2 @ cJ))))),
% 1.60/1.32 inference(rectify,[status(thm)],[f2])).
% 1.60/1.32 thf(f2,negated_conjecture,(
% 1.60/1.32 ~(((cUNIQUE @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (X0 = X1))) => ? [X2 : $i > $o] : (((X2 @ cP) = (cLIKE @ cP @ cS)) & (? [X0 : $i] : ((cLIKE @ cJ @ X0) & (cUNIQUE @ X0)) = (X2 @ cJ))))),
% 1.60/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.32 thf(f1,conjecture,(
% 1.60/1.32 ((cUNIQUE @ cS) & ! [X0 : $i] : ((cUNIQUE @ X0) => ! [X1 : $i] : (X0 = X1))) => ? [X2 : $i > $o] : (((X2 @ cP) = (cLIKE @ cP @ cS)) & (? [X0 : $i] : ((cLIKE @ cJ @ X0) & (cUNIQUE @ X0)) = (X2 @ cJ)))),
% 1.60/1.32 file('/export/starexec/sandbox2/tmp/tmp.CqirdRYcGl/DTF2THF_30570.p',cLING2)).
% 1.60/1.32 thf(f16,plain,(
% 1.60/1.32 ( ! [X0 : $i,X1 : $i] : (((cUNIQUE @ X0) != $true) | (X0 = X1)) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f33,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o] : (((X2 @ cJ) = $true) | ((X2 @ cP) = $true)) ) | ~spl1_3),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.60/1.32 thf(f32,definition,(
% 1.60/1.32 spl1_3 <=> ! [X2 : $i > $o] : (((X2 @ cJ) = $true) | ((X2 @ cP) = $true))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.60/1.32 thf(f255,plain,(
% 1.60/1.32 ~spl1_1 | spl1_2),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f254])).
% 1.60/1.32 thf(f254,plain,(
% 1.60/1.32 $false | (~spl1_1 | spl1_2)),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f176,f201])).
% 1.60/1.32 thf(f201,plain,(
% 1.60/1.32 ( ! [X0 : $i] : (((cLIKE @ X0 @ cS) = $true)) ) | ~spl1_1),
% 1.60/1.32 inference(superposition,[status(thm)],[f194,f65])).
% 1.60/1.32 thf(f65,plain,(
% 1.60/1.32 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.60/1.32 inference(superposition,[status(thm)],[f64,f64])).
% 1.60/1.32 thf(f194,plain,(
% 1.60/1.32 ((cLIKE @ cJ @ cS) = $true) | ~spl1_1),
% 1.60/1.32 inference(forward_demodulation,[status(thm)],[f26,f64])).
% 1.60/1.32 thf(f26,plain,(
% 1.60/1.32 ((cLIKE @ cJ @ sK0) = $true) | ~spl1_1),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.60/1.32 thf(f24,definition,(
% 1.60/1.32 spl1_1 <=> ((cLIKE @ cJ @ sK0) = $true)),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.60/1.32 thf(f176,plain,(
% 1.60/1.32 ((cLIKE @ cS @ cS) != $true) | spl1_2),
% 1.60/1.32 inference(forward_demodulation,[status(thm)],[f29,f64])).
% 1.60/1.32 thf(f29,plain,(
% 1.60/1.32 ((cLIKE @ cP @ cS) != $true) | spl1_2),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.60/1.32 thf(f28,definition,(
% 1.60/1.32 spl1_2 <=> ((cLIKE @ cP @ cS) = $true)),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.60/1.32 thf(f239,plain,(
% 1.60/1.32 ~spl1_8),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f238])).
% 1.60/1.32 thf(f238,plain,(
% 1.60/1.32 $false | ~spl1_8),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f217,f66])).
% 1.60/1.32 thf(f66,plain,(
% 1.60/1.32 ( ! [X0 : $i] : (((cUNIQUE @ X0) = $true)) )),
% 1.60/1.32 inference(superposition,[status(thm)],[f15,f64])).
% 1.60/1.32 thf(f217,plain,(
% 1.60/1.32 ((cUNIQUE @ cJ) != $true) | ~spl1_8),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f209])).
% 1.60/1.32 thf(f209,plain,(
% 1.60/1.32 ($false = $true) | ((cUNIQUE @ cJ) != $true) | ~spl1_8),
% 1.60/1.32 inference(superposition,[status(thm)],[f173,f15])).
% 1.60/1.32 thf(f173,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o] : (((X2 @ cS) = $false) | ((X2 @ cJ) != $true)) ) | ~spl1_8),
% 1.60/1.32 inference(forward_demodulation,[status(thm)],[f52,f64])).
% 1.60/1.32 thf(f52,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o] : (((X2 @ cP) = $false) | ((X2 @ cJ) != $true)) ) | ~spl1_8),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.60/1.32 thf(f51,definition,(
% 1.60/1.32 spl1_8 <=> ! [X2 : $i > $o] : (((X2 @ cJ) != $true) | ((X2 @ cP) = $false))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.60/1.32 thf(f127,plain,(
% 1.60/1.32 ~spl1_2 | ~spl1_7),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.60/1.32 thf(f126,plain,(
% 1.60/1.32 $false | (~spl1_2 | ~spl1_7)),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f116,f114])).
% 1.60/1.32 thf(f114,plain,(
% 1.60/1.32 ( ! [X0 : $i,X1 : $i] : (((cLIKE @ X0 @ X1) != $true)) ) | ~spl1_7),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f112,f66])).
% 1.60/1.32 thf(f112,plain,(
% 1.60/1.32 ( ! [X0 : $i,X1 : $i] : (((cLIKE @ X0 @ X1) != $true) | ((cUNIQUE @ X1) != $true)) ) | ~spl1_7),
% 1.60/1.32 inference(superposition,[status(thm)],[f48,f65])).
% 1.60/1.32 thf(f48,plain,(
% 1.60/1.32 ( ! [X3 : $i] : (((cLIKE @ cJ @ X3) != $true) | ((cUNIQUE @ X3) != $true)) ) | ~spl1_7),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.60/1.32 thf(f47,definition,(
% 1.60/1.32 spl1_7 <=> ! [X3 : $i] : (((cUNIQUE @ X3) != $true) | ((cLIKE @ cJ @ X3) != $true))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.60/1.32 thf(f116,plain,(
% 1.60/1.32 ( ! [X0 : $i,X1 : $i] : (((cLIKE @ X0 @ X1) = $true)) ) | ~spl1_2),
% 1.60/1.32 inference(superposition,[status(thm)],[f69,f65])).
% 1.60/1.32 thf(f69,plain,(
% 1.60/1.32 ( ! [X0 : $i] : (((cLIKE @ cS @ X0) = $true)) ) | ~spl1_2),
% 1.60/1.32 inference(forward_demodulation,[status(thm)],[f67,f64])).
% 1.60/1.32 thf(f67,plain,(
% 1.60/1.32 ( ! [X0 : $i] : (((cLIKE @ cP @ X0) = $true)) ) | ~spl1_2),
% 1.60/1.32 inference(superposition,[status(thm)],[f30,f64])).
% 1.60/1.32 thf(f30,plain,(
% 1.60/1.32 ((cLIKE @ cP @ cS) = $true) | ~spl1_2),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.60/1.32 thf(f62,plain,(
% 1.60/1.32 ~spl1_2 | ~spl1_4),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f61])).
% 1.60/1.32 thf(f61,plain,(
% 1.60/1.32 $false | (~spl1_2 | ~spl1_4)),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.60/1.32 thf(f60,plain,(
% 1.60/1.32 ($false = $true) | (~spl1_2 | ~spl1_4)),
% 1.60/1.32 inference(forward_demodulation,[status(thm)],[f30,f38])).
% 1.60/1.32 thf(f38,plain,(
% 1.60/1.32 ((cLIKE @ cP @ cS) = $false) | ~spl1_4),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.60/1.32 thf(f36,definition,(
% 1.60/1.32 spl1_4 <=> ((cLIKE @ cP @ cS) = $false)),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.60/1.32 thf(f53,plain,(
% 1.60/1.32 spl1_7 | spl1_8 | spl1_4),
% 1.60/1.32 inference(avatar_split_clause,[status(thm)],[f20,f36,f51,f47])).
% 1.60/1.32 thf(f20,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o,X3 : $i] : (((cLIKE @ cJ @ X3) != $true) | ((cLIKE @ cP @ cS) = $false) | ((cUNIQUE @ X3) != $true) | ((X2 @ cJ) != $true) | ((X2 @ cP) = $false)) )),
% 1.60/1.32 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.60/1.32 thf(f14,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o,X3 : $i] : (((cLIKE @ cJ @ X3) != $true) | ((X2 @ cP) != (cLIKE @ cP @ cS)) | ((cUNIQUE @ X3) != $true) | ((X2 @ cJ) != $true)) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 thf(f34,plain,(
% 1.60/1.32 spl1_1 | spl1_2 | spl1_3),
% 1.60/1.32 inference(avatar_split_clause,[status(thm)],[f21,f32,f28,f24])).
% 1.60/1.32 thf(f21,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o] : (((X2 @ cJ) = $true) | ((cLIKE @ cJ @ sK0) = $true) | ((cLIKE @ cP @ cS) = $true) | ((X2 @ cP) = $true)) )),
% 1.60/1.32 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.60/1.32 thf(f13,plain,(
% 1.60/1.32 ( ! [X2 : $i > $o] : (((cLIKE @ cJ @ sK0) = $true) | ((X2 @ cJ) = $true) | ((X2 @ cP) != (cLIKE @ cP @ cS))) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.32 % SZS output end Proof for DTF2THF_30570
% 1.60/1.32 % (30847)------------------------------
% 1.60/1.32 % (30847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (30847)Termination reason: Refutation
% 1.60/1.32
% 1.60/1.32 % (30847)Memory used [KB]: 5628
% 1.60/1.32 % (30847)Time elapsed: 0.016 s
% 1.60/1.32 % (30847)Instructions burned: 18 (million)
% 1.60/1.32 % (30847)------------------------------
% 1.60/1.32 % (30847)------------------------------
% 1.60/1.32 % (30841)Success in time 0.031 s
%------------------------------------------------------------------------------