%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV057^5 : 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 : n011.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 09:40:11 AM UTC 2026
% Result : Theorem 1.53s 1.37s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 351 ( 167 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 525 ( 113 ~; 90 |; 52 &; 252 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 140 ( 50 ^; 58 !; 32 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: ( a > a ) > a ).
thf(func_def_6,type,
sK2: a > ( a > a ) > a ).
thf(func_def_7,type,
sK3: ( a > a ) > a ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK6: a ).
thf(func_def_20,type,
sK7: a ).
thf(f196,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f145,f192,f195]) ).
thf(f195,plain,
~ spl4_12,
inference(avatar_contradiction_clause,[status(thm)],[f194]) ).
thf(f194,plain,
( $false
| ~ spl4_12 ),
inference(subsumption_resolution,[status(thm)],[f193,f24]) ).
thf(f24,plain,
( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a] : Y0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a] : Y0 ) ) )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a] : Y0 ) ) )
| ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a] : Y0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f21]) ).
thf(f21,plain,
! [X1: a > a] :
( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
| ( $true
= ( sK0 @ ( sK1 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: a > a] :
( ( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
& ! [X3: a] :
( ( ( sK1 @ X1 )
!= ( X1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( ( ( sK2 @ X3 @ X1 )
!= X3 )
& ( $true
= ( sK0 @ ( sK2 @ X3 @ X1 ) ) )
& ( ( X1 @ ( sK2 @ X3 @ X1 ) )
= ( sK1 @ X1 ) ) ) ) )
| ( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
& ( $true
!= ( sK0 @ ( X1 @ ( sK3 @ X1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o] :
! [X1: a > a] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= X2 )
| ( ( X0 @ X3 )
!= $true )
| ? [X4: a] :
( ( X3 != X4 )
& ( ( X0 @ X4 )
= $true )
& ( ( X1 @ X4 )
= X2 ) ) ) )
| ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X0 @ ( X1 @ X5 ) ) ) ) )
=> ! [X1: a > a] :
( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= X2 )
| ( $true
!= ( sK0 @ X3 ) )
| ? [X4: a] :
( ( X3 != X4 )
& ( $true
= ( sK0 @ X4 ) )
& ( ( X1 @ X4 )
= X2 ) ) ) )
| ? [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
& ( $true
!= ( sK0 @ ( X1 @ X5 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: a > a] :
( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= X2 )
| ( $true
!= ( sK0 @ X3 ) )
| ? [X4: a] :
( ( X3 != X4 )
& ( $true
= ( sK0 @ X4 ) )
& ( ( X1 @ X4 )
= X2 ) ) ) )
=> ( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
& ! [X3: a] :
( ( ( sK1 @ X1 )
!= ( X1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ? [X4: a] :
( ( X3 != X4 )
& ( $true
= ( sK0 @ X4 ) )
& ( ( X1 @ X4 )
= ( sK1 @ X1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X1: a > a,X3: a] :
( ? [X4: a] :
( ( X3 != X4 )
& ( $true
= ( sK0 @ X4 ) )
& ( ( X1 @ X4 )
= ( sK1 @ X1 ) ) )
=> ( ( ( sK2 @ X3 @ X1 )
!= X3 )
& ( $true
= ( sK0 @ ( sK2 @ X3 @ X1 ) ) )
& ( ( X1 @ ( sK2 @ X3 @ X1 ) )
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X1: a > a] :
( ? [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
& ( $true
!= ( sK0 @ ( X1 @ X5 ) ) ) )
=> ( ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
& ( $true
!= ( sK0 @ ( X1 @ ( sK3 @ X1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o] :
! [X1: a > a] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= X2 )
| ( ( X0 @ X3 )
!= $true )
| ? [X4: a] :
( ( X3 != X4 )
& ( ( X0 @ X4 )
= $true )
& ( ( X1 @ X4 )
= X2 ) ) ) )
| ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X0 @ ( X1 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o] :
! [X1: a > a] :
( ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ! [X4: a] :
( ( ( X1 @ X4 )
!= X3 )
| ( ( X0 @ X4 )
!= $true )
| ? [X5: a] :
( ( X4 != X5 )
& ( $true
= ( X0 @ X5 ) )
& ( ( X1 @ X5 )
= X3 ) ) ) )
| ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ ( X1 @ X2 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o] :
! [X1: a > a] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ ( X1 @ X2 ) )
!= $true ) )
| ? [X3: a] :
( ! [X4: a] :
( ? [X5: a] :
( ( X4 != X5 )
& ( ( X1 @ X5 )
= X3 )
& ( $true
= ( X0 @ X5 ) ) )
| ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
!= X3 ) )
& ( ( X0 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
? [X1: a > a] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X0 @ ( X1 @ X2 ) )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ? [X4: a] :
( ! [X5: a] :
( ( ( ( X1 @ X5 )
= X3 )
& ( $true
= ( X0 @ X5 ) ) )
=> ( X4 = X5 ) )
& ( ( X0 @ X4 )
= $true )
& ( ( X1 @ X4 )
= X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
? [X1: a > a] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X0 @ ( X1 @ X2 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ? [X4: a] :
( ( X0 @ X4 )
& ! [X5: a] :
( ( ( X0 @ X5 )
& ( ( X1 @ X5 )
= X3 ) )
=> ( X4 = X5 ) )
& ( ( X1 @ X4 )
= X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
? [X1: a > a] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X0 @ ( X1 @ X2 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ? [X2: a] :
( ( X0 @ X2 )
& ! [X4: a] :
( ( ( X0 @ X4 )
& ( ( X1 @ X4 )
= X3 ) )
=> ( X2 = X4 ) )
& ( ( X1 @ X2 )
= X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
? [X1: a > a] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X0 @ ( X1 @ X2 ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ? [X2: a] :
( ( X0 @ X2 )
& ! [X4: a] :
( ( ( X0 @ X4 )
& ( ( X1 @ X4 )
= X3 ) )
=> ( X2 = X4 ) )
& ( ( X1 @ X2 )
= X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3z6fzSVsnx/DTF2THF_18596.p',cEQP1_1A_pme) ).
thf(f20,plain,
! [X1: a > a] :
( ( $true
!= ( sK0 @ ( X1 @ ( sK3 @ X1 ) ) ) )
| ( $true
= ( sK0 @ ( sK1 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f193,plain,
( ( $true
!= ( sK0
@ ( sK1
@ ^ [Y0: a] : Y0 ) ) )
| ~ spl4_12 ),
inference(equality_resolution,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X0: a] :
( ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[status(thm)],[f143]) ).
thf(f143,definition,
( spl4_12
<=> ! [X0: a] :
( ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition]) ).
thf(f192,plain,
( spl4_12
| ~ spl4_11 ),
inference(avatar_split_clause,[status(thm)],[f191,f139,f143]) ).
thf(f139,definition,
( spl4_11
<=> ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition]) ).
thf(f191,plain,
( ! [X0: a] :
( ( $true
!= ( sK0 @ X0 ) )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 ) )
| ~ spl4_11 ),
inference(subsumption_resolution,[status(thm)],[f187,f141]) ).
thf(f141,plain,
( ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[status(thm)],[f139]) ).
thf(f187,plain,
( ! [X0: a] :
( ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) )
| ~ spl4_11 ),
inference(duplicate_literal_removal,[status(thm)],[f186]) ).
thf(f186,plain,
( ! [X0: a] :
( ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) )
| ~ spl4_11 ),
inference(beta_eta_normalization,[status(thm)],[f185]) ).
thf(f185,plain,
( ! [X0: a] :
( ( $true
!= ( sK0
@ ( ^ [Y0: a] : Y0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) ) )
| ~ spl4_11 ),
inference(duplicate_literal_removal,[status(thm)],[f183]) ).
thf(f183,plain,
( ! [X0: a] :
( ( $true
!= ( sK0
@ ( ^ [Y0: a] : Y0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 ) )
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f149,f14]) ).
thf(f14,plain,
! [X3: a,X1: a > a] :
( ( ( X1 @ ( sK2 @ X3 @ X1 ) )
= ( sK1 @ X1 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X1 )
!= ( X1 @ X3 ) )
| ( $true
!= ( sK0 @ ( X1 @ ( sK3 @ X1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f149,plain,
( ! [X0: a] :
( ( ( sK2 @ X0
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) ) )
| ~ spl4_11 ),
inference(beta_eta_normalization,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X0: a] :
( ( ( sK2 @ X0
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) )
| ( $true
!= ( sK0 @ X0 ) ) )
| ~ spl4_11 ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK2 @ X0
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) ) )
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f18,f141]) ).
thf(f18,plain,
! [X3: a,X1: a > a] :
( ( $true
!= ( sK0 @ ( X1 @ ( sK3 @ X1 ) ) ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X1 )
!= ( X1 @ X3 ) )
| ( ( sK2 @ X3 @ X1 )
!= X3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f145,plain,
( spl4_11
| spl4_12 ),
inference(avatar_split_clause,[status(thm)],[f131,f143,f139]) ).
thf(f131,plain,
! [X0: a] :
( ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f130]) ).
thf(f130,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 ) )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: a] :
( ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 ) )
| ( $true
!= ( sK0 @ X0 ) )
| ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) )
| ( $true
= ( sK0
@ ( sK3
@ ^ [Y0: a] : Y0 ) ) )
| ( ( ^ [Y0: a] : Y0
@ X0 )
!= ( sK1
@ ^ [Y0: a] : Y0 ) )
| ( ( sK1
@ ^ [Y0: a] : Y0 )
!= X0 ) ),
inference(superposition,[status(thm)],[f19,f15]) ).
thf(f15,plain,
! [X3: a,X1: a > a] :
( ( ( X1 @ ( sK2 @ X3 @ X1 ) )
= ( sK1 @ X1 ) )
| ( ( sK1 @ X1 )
!= ( X1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK0 @ ( sK3 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f19,plain,
! [X3: a,X1: a > a] :
( ( ( sK2 @ X3 @ X1 )
!= X3 )
| ( $true
= ( sK0 @ ( sK3 @ X1 ) ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X1 )
!= ( X1 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV057^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n011.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:39:17 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEV057^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Set Theory (Relations)
% 0.16/0.39 % Problem : TPS problem EQP1-1A
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0323 [Bro09]
% 0.16/0.39 % : EQP1-1A [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.39 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.39 % Number of connectives : 15 ( 0 ~; 0 |; 4 &; 8 @)
% 0.16/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 13 ( 13 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.39 % Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % : Polymorphic definitions expanded.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(cEQP1_1A_pme,conjecture,
% 0.16/0.39 ! [Xx: a > $o] :
% 0.16/0.39 ? [Xs: a > a] :
% 0.16/0.39 ( ! [Xx0: a] :
% 0.16/0.39 ( ( Xx @ Xx0 )
% 0.16/0.39 => ( Xx @ ( Xs @ Xx0 ) ) )
% 0.16/0.39 & ! [Xy: a] :
% 0.16/0.39 ( ( Xx @ Xy )
% 0.16/0.39 => ? [Xx0: a] :
% 0.16/0.39 ( ( Xx @ Xx0 )
% 0.16/0.39 & ( Xy
% 0.16/0.39 = ( Xs @ Xx0 ) )
% 0.16/0.39 & ! [Xz: a] :
% 0.16/0.39 ( ( ( Xx @ Xz )
% 0.16/0.39 & ( Xy
% 0.16/0.39 = ( Xs @ Xz ) ) )
% 0.16/0.39 => ( Xz = Xx0 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.53/1.30 ---- Embedded in THF ---
% 1.53/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.30 %%% Generated on Tue Feb 24 12:39:18 EST 2026
% 1.53/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.30 %%% Logic specification used:
% 1.53/1.30 %%% thf(spec, logic, $$dhol).
% 1.53/1.30
% 1.53/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3z6fzSVsnx/DTF2DTF18596.p
% See solution above
% 1.53/1.30 ------------------------
% 1.53/1.31 ---- Cleaned THF ---
% 1.53/1.31 thf(a_type,type,
% 1.53/1.31 a: $tType ).
% 1.53/1.31
% 1.53/1.31 thf(cEQP1_1A_pme,conjecture,
% 1.53/1.31 ! [Xx: a > $o] :
% 1.53/1.31 ? [Xs: a > a] :
% 1.53/1.31 ( ! [Xx0: a] :
% 1.53/1.31 ( ( Xx @ Xx0 )
% 1.53/1.31 => ( Xx @ ( Xs @ Xx0 ) ) )
% 1.53/1.31 & ! [Xy: a] :
% 1.53/1.31 ( ( Xx @ Xy )
% 1.53/1.31 => ? [Xx0: a] :
% 1.53/1.31 ( ( Xx @ Xx0 )
% 1.53/1.31 & ( Xy
% 1.53/1.31 = ( Xs @ Xx0 ) )
% 1.53/1.31 & ! [Xz: a] :
% 1.53/1.31 ( ( ( Xx @ Xz )
% 1.53/1.31 & ( Xy
% 1.53/1.31 = ( Xs @ Xz ) ) )
% 1.53/1.31 => ( Xz = Xx0 ) ) ) ) ) ).
% 1.53/1.31 ------------------------
% 1.53/1.33 % (18697)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_18596 for (3000ds/2Mi)
% 1.53/1.33 % (18699)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18596 for (3000ds/18Mi)
% 1.53/1.33 % (18695)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_18596 for (3000ds/27Mi)
% 1.53/1.33 % (18696)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18596 for (3000ds/2Mi)
% 1.53/1.33 % (18693)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18596 for (3000ds/183Mi)
% 1.53/1.33 % (18694)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_18596 for (3000ds/4Mi)
% 1.53/1.33 % (18698)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_18596 for (3000ds/275Mi)
% 1.53/1.33 % (18696)Instruction limit reached!
% 1.53/1.33 % (18696)------------------------------
% 1.53/1.33 % (18696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.33 % (18696)Termination reason: Unknown
% 1.53/1.33 % (18697)Instruction limit reached!
% 1.53/1.33 % (18697)------------------------------
% 1.53/1.33 % (18697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.33 % (18696)Termination phase: Saturation
% 1.53/1.33
% 1.53/1.33 % (18696)Memory used [KB]: 1023
% 1.53/1.33 % (18696)Time elapsed: 0.003 s
% 1.53/1.33 % (18696)Instructions burned: 2 (million)
% 1.53/1.33 % (18696)------------------------------
% 1.53/1.33 % (18696)------------------------------
% 1.53/1.33 % (18697)Termination reason: Unknown
% 1.53/1.33 % (18697)Termination phase: Saturation
% 1.53/1.33
% 1.53/1.33 % (18697)Memory used [KB]: 5373
% 1.53/1.33 % (18697)Time elapsed: 0.003 s
% 1.53/1.33 % (18697)Instructions burned: 2 (million)
% 1.53/1.33 % (18697)------------------------------
% 1.53/1.33 % (18697)------------------------------
% 1.53/1.34 % (18695)Refutation not found, incomplete strategy
% 1.53/1.34 % (18695)------------------------------
% 1.53/1.34 % (18695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (18694)Instruction limit reached!
% 1.53/1.34 % (18694)------------------------------
% 1.53/1.34 % (18694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (18694)Termination reason: Unknown
% 1.53/1.34 % (18694)Termination phase: Saturation
% 1.53/1.34
% 1.53/1.34 % (18694)Memory used [KB]: 5500
% 1.53/1.34 % (18694)Time elapsed: 0.005 s
% 1.53/1.34 % (18694)Instructions burned: 5 (million)
% 1.53/1.34 % (18694)------------------------------
% 1.53/1.34 % (18694)------------------------------
% 1.53/1.34 % (18695)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.34
% 1.53/1.34
% 1.53/1.34 % (18695)Memory used [KB]: 5500
% 1.53/1.34 % (18695)Time elapsed: 0.005 s
% 1.53/1.34 % (18695)Instructions burned: 3 (million)
% 1.53/1.34 % (18695)------------------------------
% 1.53/1.34 % (18695)------------------------------
% 1.53/1.34 % (18698)Refutation not found, incomplete strategy
% 1.53/1.34 % (18698)------------------------------
% 1.53/1.34 % (18698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (18698)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.34
% 1.53/1.34
% 1.53/1.34 % (18698)Memory used [KB]: 5500
% 1.53/1.34 % (18698)Time elapsed: 0.004 s
% 1.53/1.34 % (18698)Instructions burned: 3 (million)
% 1.53/1.34 % (18698)------------------------------
% 1.53/1.34 % (18698)------------------------------
% 1.53/1.34 % (18699)Instruction limit reached!
% 1.53/1.34 % (18699)------------------------------
% 1.53/1.34 % (18699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (18699)Termination reason: Unknown
% 1.53/1.34 % (18699)Termination phase: Saturation
% 1.53/1.34
% 1.53/1.34 % (18699)Memory used [KB]: 5628
% 1.53/1.34 % (18699)Time elapsed: 0.012 s
% 1.53/1.34 % (18699)Instructions burned: 18 (million)
% 1.53/1.34 % (18699)------------------------------
% 1.53/1.34 % (18699)------------------------------
% 1.53/1.35 % (18700)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18596 for (2999ds/3Mi)
% 1.53/1.35 % (18701)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_18596 for (2999ds/37Mi)
% 1.53/1.35 % (18700)Instruction limit reached!
% 1.53/1.35 % (18700)------------------------------
% 1.53/1.35 % (18700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (18700)Termination reason: Unknown
% 1.53/1.35 % (18702)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_18596 for (2999ds/15Mi)
% 1.53/1.35 % (18700)Termination phase: Saturation
% 1.53/1.35
% 1.53/1.35 % (18700)Memory used [KB]: 5500
% 1.53/1.35 % (18700)Time elapsed: 0.003 s
% 1.53/1.35 % (18700)Instructions burned: 3 (million)
% 1.53/1.35 % (18700)------------------------------
% 1.53/1.35 % (18700)------------------------------
% 1.53/1.35 % (18703)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_18596 for (2999ds/3Mi)
% 1.53/1.35 % (18704)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_18596 for (2999ds/1041Mi)
% 1.53/1.35 % (18703)Instruction limit reached!
% 1.53/1.35 % (18703)------------------------------
% 1.53/1.35 % (18703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (18703)Termination reason: Unknown
% 1.53/1.35 % (18703)Termination phase: Saturation
% 1.53/1.35
% 1.53/1.35 % (18703)Memory used [KB]: 5500
% 1.53/1.35 % (18703)Time elapsed: 0.004 s
% 1.53/1.35 % (18703)Instructions burned: 4 (million)
% 1.53/1.35 % (18703)------------------------------
% 1.53/1.35 % (18703)------------------------------
% 1.53/1.36 % (18705)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18596 for (2999ds/7Mi)
% 1.53/1.36 % (18702)Instruction limit reached!
% 1.53/1.36 % (18702)------------------------------
% 1.53/1.36 % (18702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (18702)Termination reason: Unknown
% 1.53/1.36 % (18702)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (18702)Memory used [KB]: 5500
% 1.53/1.36 % (18702)Time elapsed: 0.010 s
% 1.53/1.36 % (18702)Instructions burned: 16 (million)
% 1.53/1.36 % (18702)------------------------------
% 1.53/1.36 % (18702)------------------------------
% 1.53/1.36 % (18705)Instruction limit reached!
% 1.53/1.36 % (18705)------------------------------
% 1.53/1.36 % (18705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (18705)Termination reason: Unknown
% 1.53/1.36 % (18705)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (18705)Memory used [KB]: 1023
% 1.53/1.36 % (18705)Time elapsed: 0.006 s
% 1.53/1.36 % (18705)Instructions burned: 8 (million)
% 1.53/1.36 % (18705)------------------------------
% 1.53/1.36 % (18705)------------------------------
% 1.53/1.36 % (18693)First to succeed.
% 1.53/1.37 % (18693)Refutation found. Thanks to Tanya!
% 1.53/1.37 % SZS status Theorem for DTF2THF_18596
% 1.53/1.37 % SZS output start Proof for DTF2THF_18596
% 1.53/1.37 thf(type_def_5, type, a: $tType).
% 1.53/1.37 thf(func_def_0, type, a: $tType).
% 1.53/1.37 thf(func_def_4, type, sK0: a > $o).
% 1.53/1.37 thf(func_def_5, type, sK1: (a > a) > a).
% 1.53/1.37 thf(func_def_6, type, sK2: a > (a > a) > a).
% 1.53/1.37 thf(func_def_7, type, sK3: (a > a) > a).
% 1.53/1.37 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.53/1.37 thf(func_def_19, type, sK6: a).
% 1.53/1.37 thf(func_def_20, type, sK7: a).
% 1.53/1.37 thf(f196,plain,(
% 1.53/1.37 $false),
% 1.53/1.37 inference(avatar_sat_refutation,[status(thm)],[f145,f192,f195])).
% 1.53/1.37 thf(f195,plain,(
% 1.53/1.37 ~spl4_12),
% 1.53/1.37 inference(avatar_contradiction_clause,[status(thm)],[f194])).
% 1.53/1.37 thf(f194,plain,(
% 1.53/1.37 $false | ~spl4_12),
% 1.53/1.37 inference(subsumption_resolution,[status(thm)],[f193,f24])).
% 1.53/1.37 thf(f24,plain,(
% 1.53/1.37 ($true = (sK0 @ (sK1 @ (^[Y0 : a]: (Y0)))))),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.53/1.37 thf(f23,plain,(
% 1.53/1.37 ($true = (sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) | ($true != $true)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.53/1.37 thf(f22,plain,(
% 1.53/1.37 ($true = (sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) | ($true = (sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) | ($true != $true)),
% 1.53/1.37 inference(superposition,[status(thm)],[f20,f21])).
% 1.53/1.37 thf(f21,plain,(
% 1.53/1.37 ( ! [X1 : a > a] : (($true = (sK0 @ (sK3 @ X1))) | ($true = (sK0 @ (sK1 @ X1)))) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 thf(f13,plain,(
% 1.53/1.37 ! [X1 : a > a] : ((($true = (sK0 @ (sK1 @ X1))) & ! [X3 : a] : (((sK1 @ X1) != (X1 @ X3)) | ($true != (sK0 @ X3)) | (((sK2 @ X3 @ X1) != X3) & ($true = (sK0 @ (sK2 @ X3 @ X1))) & ((X1 @ (sK2 @ X3 @ X1)) = (sK1 @ X1))))) | (($true = (sK0 @ (sK3 @ X1))) & ($true != (sK0 @ (X1 @ (sK3 @ X1))))))),
% 1.53/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9])).
% 1.53/1.37 thf(f9,plain,(
% 1.53/1.37 ? [X0 : a > $o] : ! [X1 : a > a] : (? [X2 : a] : (((X0 @ X2) = $true) & ! [X3 : a] : (((X1 @ X3) != X2) | ((X0 @ X3) != $true) | ? [X4 : a] : ((X3 != X4) & ((X0 @ X4) = $true) & ((X1 @ X4) = X2)))) | ? [X5 : a] : (($true = (X0 @ X5)) & ($true != (X0 @ (X1 @ X5))))) => ! [X1 : a > a] : (? [X2 : a] : (($true = (sK0 @ X2)) & ! [X3 : a] : (((X1 @ X3) != X2) | ($true != (sK0 @ X3)) | ? [X4 : a] : ((X3 != X4) & ($true = (sK0 @ X4)) & ((X1 @ X4) = X2)))) | ? [X5 : a] : (($true = (sK0 @ X5)) & ($true != (sK0 @ (X1 @ X5)))))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f10,plain,(
% 1.53/1.37 ! [X1 : a > a] : (? [X2 : a] : (($true = (sK0 @ X2)) & ! [X3 : a] : (((X1 @ X3) != X2) | ($true != (sK0 @ X3)) | ? [X4 : a] : ((X3 != X4) & ($true = (sK0 @ X4)) & ((X1 @ X4) = X2)))) => (($true = (sK0 @ (sK1 @ X1))) & ! [X3 : a] : (((sK1 @ X1) != (X1 @ X3)) | ($true != (sK0 @ X3)) | ? [X4 : a] : ((X3 != X4) & ($true = (sK0 @ X4)) & ((X1 @ X4) = (sK1 @ X1))))))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f11,plain,(
% 1.53/1.37 ! [X1 : a > a,X3 : a] : (? [X4 : a] : ((X3 != X4) & ($true = (sK0 @ X4)) & ((X1 @ X4) = (sK1 @ X1))) => (((sK2 @ X3 @ X1) != X3) & ($true = (sK0 @ (sK2 @ X3 @ X1))) & ((X1 @ (sK2 @ X3 @ X1)) = (sK1 @ X1))))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f12,plain,(
% 1.53/1.37 ! [X1 : a > a] : (? [X5 : a] : (($true = (sK0 @ X5)) & ($true != (sK0 @ (X1 @ X5)))) => (($true = (sK0 @ (sK3 @ X1))) & ($true != (sK0 @ (X1 @ (sK3 @ X1))))))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f8,plain,(
% 1.53/1.37 ? [X0 : a > $o] : ! [X1 : a > a] : (? [X2 : a] : (((X0 @ X2) = $true) & ! [X3 : a] : (((X1 @ X3) != X2) | ((X0 @ X3) != $true) | ? [X4 : a] : ((X3 != X4) & ((X0 @ X4) = $true) & ((X1 @ X4) = X2)))) | ? [X5 : a] : (($true = (X0 @ X5)) & ($true != (X0 @ (X1 @ X5)))))),
% 1.53/1.37 inference(rectify,[status(thm)],[f7])).
% 1.53/1.37 thf(f7,plain,(
% 1.53/1.37 ? [X0 : a > $o] : ! [X1 : a > a] : (? [X3 : a] : (((X0 @ X3) = $true) & ! [X4 : a] : (((X1 @ X4) != X3) | ((X0 @ X4) != $true) | ? [X5 : a] : ((X4 != X5) & ($true = (X0 @ X5)) & ((X1 @ X5) = X3)))) | ? [X2 : a] : (((X0 @ X2) = $true) & ((X0 @ (X1 @ X2)) != $true)))),
% 1.53/1.37 inference(flattening,[status(thm)],[f6])).
% 1.53/1.37 thf(f6,plain,(
% 1.53/1.37 ? [X0 : a > $o] : ! [X1 : a > a] : (? [X2 : a] : (((X0 @ X2) = $true) & ((X0 @ (X1 @ X2)) != $true)) | ? [X3 : a] : (! [X4 : a] : (? [X5 : a] : ((X4 != X5) & (((X1 @ X5) = X3) & ($true = (X0 @ X5)))) | ((X0 @ X4) != $true) | ((X1 @ X4) != X3)) & ((X0 @ X3) = $true)))),
% 1.53/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.37 thf(f5,plain,(
% 1.53/1.37 ~! [X0 : a > $o] : ? [X1 : a > a] : (! [X2 : a] : (((X0 @ X2) = $true) => ((X0 @ (X1 @ X2)) = $true)) & ! [X3 : a] : (((X0 @ X3) = $true) => ? [X4 : a] : (! [X5 : a] : ((((X1 @ X5) = X3) & ($true = (X0 @ X5))) => (X4 = X5)) & ((X0 @ X4) = $true) & ((X1 @ X4) = X3))))),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.37 thf(f4,plain,(
% 1.53/1.37 ~! [X0 : a > $o] : ? [X1 : a > a] : (! [X2 : a] : ((X0 @ X2) => (X0 @ (X1 @ X2))) & ! [X3 : a] : ((X0 @ X3) => ? [X4 : a] : ((X0 @ X4) & ! [X5 : a] : (((X0 @ X5) & ((X1 @ X5) = X3)) => (X4 = X5)) & ((X1 @ X4) = X3))))),
% 1.53/1.37 inference(rectify,[status(thm)],[f2])).
% 1.53/1.37 thf(f2,negated_conjecture,(
% 1.53/1.37 ~! [X0 : a > $o] : ? [X1 : a > a] : (! [X2 : a] : ((X0 @ X2) => (X0 @ (X1 @ X2))) & ! [X3 : a] : ((X0 @ X3) => ? [X2 : a] : ((X0 @ X2) & ! [X4 : a] : (((X0 @ X4) & ((X1 @ X4) = X3)) => (X2 = X4)) & ((X1 @ X2) = X3))))),
% 1.53/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.37 thf(f1,conjecture,(
% 1.53/1.37 ! [X0 : a > $o] : ? [X1 : a > a] : (! [X2 : a] : ((X0 @ X2) => (X0 @ (X1 @ X2))) & ! [X3 : a] : ((X0 @ X3) => ? [X2 : a] : ((X0 @ X2) & ! [X4 : a] : (((X0 @ X4) & ((X1 @ X4) = X3)) => (X2 = X4)) & ((X1 @ X2) = X3))))),
% 1.53/1.37 file('/export/starexec/sandbox/tmp/tmp.3z6fzSVsnx/DTF2THF_18596.p',cEQP1_1A_pme)).
% 1.53/1.37 thf(f20,plain,(
% 1.53/1.37 ( ! [X1 : a > a] : (($true != (sK0 @ (X1 @ (sK3 @ X1)))) | ($true = (sK0 @ (sK1 @ X1)))) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 thf(f193,plain,(
% 1.53/1.37 ($true != (sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) | ~spl4_12),
% 1.53/1.37 inference(equality_resolution,[status(thm)],[f144])).
% 1.53/1.37 thf(f144,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0))) ) | ~spl4_12),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f143])).
% 1.53/1.37 thf(f143,definition,(
% 1.53/1.37 spl4_12 <=> ! [X0 : a] : (((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0)))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition])).
% 1.53/1.37 thf(f192,plain,(
% 1.53/1.37 spl4_12 | ~spl4_11),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f191,f139,f143])).
% 1.53/1.37 thf(f139,definition,(
% 1.53/1.37 spl4_11 <=> ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.53/1.37 thf(f191,plain,(
% 1.53/1.37 ( ! [X0 : a] : (($true != (sK0 @ X0)) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0)) ) | ~spl4_11),
% 1.53/1.37 inference(subsumption_resolution,[status(thm)],[f187,f141])).
% 1.53/1.37 thf(f141,plain,(
% 1.53/1.37 ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0))))) | ~spl4_11),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f139])).
% 1.53/1.37 thf(f187,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0)) | ($true != (sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) ) | ~spl4_11),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f186])).
% 1.53/1.37 thf(f186,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0)) | ($true != (sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) ) | ~spl4_11),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f185])).
% 1.53/1.37 thf(f185,plain,(
% 1.53/1.37 ( ! [X0 : a] : (($true != (sK0 @ ((^[Y0 : a]: (Y0)) @ (sK3 @ (^[Y0 : a]: (Y0)))))) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0)) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0))))) ) | ~spl4_11),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f183])).
% 1.53/1.37 thf(f183,plain,(
% 1.53/1.37 ( ! [X0 : a] : (($true != (sK0 @ ((^[Y0 : a]: (Y0)) @ (sK3 @ (^[Y0 : a]: (Y0)))))) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0)))) | ($true != (sK0 @ X0)) | ($true != (sK0 @ X0)) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0)) ) | ~spl4_11),
% 1.53/1.37 inference(superposition,[status(thm)],[f149,f14])).
% 1.53/1.37 thf(f14,plain,(
% 1.53/1.37 ( ! [X3 : a,X1 : a > a] : (((X1 @ (sK2 @ X3 @ X1)) = (sK1 @ X1)) | ($true != (sK0 @ X3)) | ((sK1 @ X1) != (X1 @ X3)) | ($true != (sK0 @ (X1 @ (sK3 @ X1))))) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 thf(f149,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK2 @ X0 @ (^[Y0 : a]: (Y0))) != X0) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0))) ) | ~spl4_11),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f148])).
% 1.53/1.37 thf(f148,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK2 @ X0 @ (^[Y0 : a]: (Y0))) != X0) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0)))) | ($true != (sK0 @ X0))) ) | ~spl4_11),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.53/1.37 thf(f146,plain,(
% 1.53/1.37 ( ! [X0 : a] : (($true != $true) | ((sK2 @ X0 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0)) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0))))) ) | ~spl4_11),
% 1.53/1.37 inference(superposition,[status(thm)],[f18,f141])).
% 1.53/1.37 thf(f18,plain,(
% 1.53/1.37 ( ! [X3 : a,X1 : a > a] : (($true != (sK0 @ (X1 @ (sK3 @ X1)))) | ($true != (sK0 @ X3)) | ((sK1 @ X1) != (X1 @ X3)) | ((sK2 @ X3 @ X1) != X3)) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 thf(f145,plain,(
% 1.53/1.37 spl4_11 | spl4_12),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f131,f143,f139])).
% 1.53/1.37 thf(f131,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true != (sK0 @ X0)) | ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) )),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f130])).
% 1.53/1.37 thf(f130,plain,(
% 1.53/1.37 ( ! [X0 : a] : (($true != (sK0 @ X0)) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0) | ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0))))) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0)) )),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f129])).
% 1.53/1.37 thf(f129,plain,(
% 1.53/1.37 ( ! [X0 : a] : (((sK1 @ (^[Y0 : a]: (Y0))) != X0) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0)))) | ($true != (sK0 @ X0)) | ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) )),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f121])).
% 1.53/1.37 thf(f121,plain,(
% 1.53/1.37 ( ! [X0 : a] : (($true != (sK0 @ X0)) | ($true != (sK0 @ X0)) | ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0))))) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0)))) | ($true = (sK0 @ (sK3 @ (^[Y0 : a]: (Y0))))) | (((^[Y0 : a]: (Y0)) @ X0) != (sK1 @ (^[Y0 : a]: (Y0)))) | ((sK1 @ (^[Y0 : a]: (Y0))) != X0)) )),
% 1.53/1.37 inference(superposition,[status(thm)],[f19,f15])).
% 1.53/1.37 thf(f15,plain,(
% 1.53/1.37 ( ! [X3 : a,X1 : a > a] : (((X1 @ (sK2 @ X3 @ X1)) = (sK1 @ X1)) | ((sK1 @ X1) != (X1 @ X3)) | ($true != (sK0 @ X3)) | ($true = (sK0 @ (sK3 @ X1)))) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 thf(f19,plain,(
% 1.53/1.37 ( ! [X3 : a,X1 : a > a] : (((sK2 @ X3 @ X1) != X3) | ($true = (sK0 @ (sK3 @ X1))) | ($true != (sK0 @ X3)) | ((sK1 @ X1) != (X1 @ X3))) )),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f13])).
% 1.53/1.37 % SZS output end Proof for DTF2THF_18596
% 1.53/1.37 % (18693)------------------------------
% 1.53/1.37 % (18693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (18693)Termination reason: Refutation
% 1.53/1.37
% 1.53/1.37 % (18693)Memory used [KB]: 5756
% 1.53/1.37 % (18693)Time elapsed: 0.035 s
% 1.53/1.37 % (18693)Instructions burned: 62 (million)
% 1.53/1.37 % (18693)------------------------------
% 1.53/1.37 % (18693)------------------------------
% 1.53/1.37 % (18692)Success in time 0.045 s
%------------------------------------------------------------------------------