%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV061^5 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:11 AM UTC 2026
% Result : Theorem 1.51s 1.24s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 182 ( 101 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 252 ( 47 ~; 39 |; 40 &; 110 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 48 !; 28 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_5,type,
sK0: a ).
thf(func_def_6,type,
sK1: b > a > $o ).
thf(func_def_7,type,
sK2: b > a > $o ).
thf(func_def_8,type,
sK3: b ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: b ).
thf(f36,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f29,f35]) ).
thf(f35,plain,
spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
| spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f33,f14]) ).
thf(f14,plain,
( ( sK1 @ sK5 @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( sK5 != sK3 )
| ( sK4 != sK0 ) )
& ( ( sK2 @ sK5 @ sK4 )
= $true )
& ( ( sK1 @ sK5 @ sK4 )
!= $true )
& ! [X6: b,X7: a] :
( ( ( sK1 @ X6 @ X7 )
= $true )
| ( ( sK3 = X6 )
& ( sK0 = X7 ) )
| ( ( sK2 @ X6 @ X7 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: b > a > $o,X2: b > a > $o,X3: b] :
( ? [X4: a,X5: b] :
( ( ( X3 != X5 )
| ( X0 != X4 ) )
& ( $true
= ( X2 @ X5 @ X4 ) )
& ( $true
!= ( X1 @ X5 @ X4 ) ) )
& ! [X6: b,X7: a] :
( ( $true
= ( X1 @ X6 @ X7 ) )
| ( ( X3 = X6 )
& ( X0 = X7 ) )
| ( ( X2 @ X6 @ X7 )
!= $true ) ) )
=> ( ? [X5: b,X4: a] :
( ( ( sK3 != X5 )
| ( sK0 != X4 ) )
& ( ( sK2 @ X5 @ X4 )
= $true )
& ( $true
!= ( sK1 @ X5 @ X4 ) ) )
& ! [X7: a,X6: b] :
( ( ( sK1 @ X6 @ X7 )
= $true )
| ( ( sK3 = X6 )
& ( sK0 = X7 ) )
| ( ( sK2 @ X6 @ X7 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: b,X4: a] :
( ( ( sK3 != X5 )
| ( sK0 != X4 ) )
& ( ( sK2 @ X5 @ X4 )
= $true )
& ( $true
!= ( sK1 @ X5 @ X4 ) ) )
=> ( ( ( sK5 != sK3 )
| ( sK4 != sK0 ) )
& ( ( sK2 @ sK5 @ sK4 )
= $true )
& ( ( sK1 @ sK5 @ sK4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: b > a > $o,X2: b > a > $o,X3: b] :
( ? [X4: a,X5: b] :
( ( ( X3 != X5 )
| ( X0 != X4 ) )
& ( $true
= ( X2 @ X5 @ X4 ) )
& ( $true
!= ( X1 @ X5 @ X4 ) ) )
& ! [X6: b,X7: a] :
( ( $true
= ( X1 @ X6 @ X7 ) )
| ( ( X3 = X6 )
& ( X0 = X7 ) )
| ( ( X2 @ X6 @ X7 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a,X1: b > a > $o,X0: b > a > $o,X3: b] :
( ? [X7: a,X6: b] :
( ( ( X3 != X6 )
| ( X2 != X7 ) )
& ( ( X0 @ X6 @ X7 )
= $true )
& ( $true
!= ( X1 @ X6 @ X7 ) ) )
& ! [X4: b,X5: a] :
( ( $true
= ( X1 @ X4 @ X5 ) )
| ( ( X3 = X4 )
& ( X2 = X5 ) )
| ( $true
!= ( X0 @ X4 @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: b > a > $o,X3: b,X1: b > a > $o,X2: a] :
( ? [X7: a,X6: b] :
( ( $true
!= ( X1 @ X6 @ X7 ) )
& ( ( X0 @ X6 @ X7 )
= $true )
& ( ( X3 != X6 )
| ( X2 != X7 ) ) )
& ! [X4: b,X5: a] :
( ( $true
= ( X1 @ X4 @ X5 ) )
| ( ( X3 = X4 )
& ( X2 = X5 ) )
| ( $true
!= ( X0 @ X4 @ X5 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: b > a > $o,X3: b,X1: b > a > $o,X2: a] :
( ! [X4: b,X5: a] :
( ( $true
= ( X0 @ X4 @ X5 ) )
=> ( ( $true
= ( X1 @ X4 @ X5 ) )
| ( ( X3 = X4 )
& ( X2 = X5 ) ) ) )
=> ! [X7: a,X6: b] :
( ( ( ( X0 @ X6 @ X7 )
= $true )
& ~ ( ( X3 = X6 )
& ( X2 = X7 ) ) )
=> ( $true
= ( X1 @ X6 @ X7 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > a > $o,X1: b > a > $o,X2: a,X3: b] :
( ! [X4: b,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( ( ( X2 = X5 )
& ( X3 = X4 ) )
| ( X1 @ X4 @ X5 ) ) )
=> ! [X6: b,X7: a] :
( ( ( X0 @ X6 @ X7 )
& ~ ( ( X2 = X7 )
& ( X3 = X6 ) ) )
=> ( X1 @ X6 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: b > a > $o,X2: b > a > $o,X1: a,X0: b] :
( ! [X4: b,X5: a] :
( ( X3 @ X4 @ X5 )
=> ( ( ( X1 = X5 )
& ( X0 = X4 ) )
| ( X2 @ X4 @ X5 ) ) )
=> ! [X6: b,X7: a] :
( ( ( X3 @ X6 @ X7 )
& ~ ( ( X1 = X7 )
& ( X0 = X6 ) ) )
=> ( X2 @ X6 @ X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: b > a > $o,X2: b > a > $o,X1: a,X0: b] :
( ! [X4: b,X5: a] :
( ( X3 @ X4 @ X5 )
=> ( ( ( X1 = X5 )
& ( X0 = X4 ) )
| ( X2 @ X4 @ X5 ) ) )
=> ! [X6: b,X7: a] :
( ( ( X3 @ X6 @ X7 )
& ~ ( ( X1 = X7 )
& ( X0 = X6 ) ) )
=> ( X2 @ X6 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0TJlJaunP9/DTF2THF_7083.p',cTHM176_pme) ).
thf(f33,plain,
( ( ( sK1 @ sK5 @ sK4 )
= $true )
| spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f32,f20]) ).
thf(f20,plain,
( ( sK5 != sK3 )
| spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl6_1
<=> ( sK5 = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f32,plain,
( ( sK5 = sK3 )
| ( ( sK1 @ sK5 @ sK4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( sK1 @ sK5 @ sK4 )
= $true )
| ( $true != $true )
| ( sK5 = sK3 ) ),
inference(superposition,[status(thm)],[f13,f15]) ).
thf(f15,plain,
( ( sK2 @ sK5 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
! [X6: b,X7: a] :
( ( ( sK2 @ X6 @ X7 )
!= $true )
| ( ( sK1 @ X6 @ X7 )
= $true )
| ( sK3 = X6 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f29,plain,
spl6_2,
inference(avatar_split_clause,[status(thm)],[f28,f22]) ).
thf(f22,definition,
( spl6_2
<=> ( sK4 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f28,plain,
sK4 = sK0,
inference(subsumption_resolution,[status(thm)],[f27,f14]) ).
thf(f27,plain,
( ( ( sK1 @ sK5 @ sK4 )
= $true )
| ( sK4 = sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK1 @ sK5 @ sK4 )
= $true )
| ( sK4 = sK0 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f15]) ).
thf(f12,plain,
! [X6: b,X7: a] :
( ( ( sK2 @ X6 @ X7 )
!= $true )
| ( sK0 = X7 )
| ( ( sK1 @ X6 @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f25,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f16,f22,f18]) ).
thf(f16,plain,
( ( sK5 != sK3 )
| ( sK4 != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV061^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:39:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEV061^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Set Theory (Relations)
% 0.30/0.45 % Problem : TPS problem THM176
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0331 [Bro09]
% 0.30/0.45 % : THM176 [TPS]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.30/0.45 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.45 % Number of connectives : 16 ( 1 ~; 1 |; 3 &; 8 @)
% 0.30/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 12 ( 12 avg)
% 0.30/0.45 % Number of types : 3 ( 2 usr)
% 0.30/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.45 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 % : Polymorphic definitions expanded.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(b_type,type,
% 0.30/0.45 b: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(a_type,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(cTHM176_pme,conjecture,
% 0.30/0.45 ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
% 0.30/0.45 ( ! [Xx_2: b,Xy_47: a] :
% 0.30/0.45 ( ( Xk @ Xx_2 @ Xy_47 )
% 0.30/0.45 => ( ( Xs @ Xx_2 @ Xy_47 )
% 0.30/0.45 | ( ( Xx_2 = Xx )
% 0.30/0.45 & ( Xy_47 = Xy ) ) ) )
% 0.30/0.45 => ! [Xx_3: b,Xy_48: a] :
% 0.30/0.45 ( ( ( Xk @ Xx_3 @ Xy_48 )
% 0.30/0.45 & ~ ( ( Xx_3 = Xx )
% 0.30/0.45 & ( Xy_48 = Xy ) ) )
% 0.30/0.45 => ( Xs @ Xx_3 @ Xy_48 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.51/1.22 ---- Embedded in THF ---
% 1.51/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.22 %%% Generated on Tue Feb 24 12:39:19 EST 2026
% 1.51/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.22 %%% Logic specification used:
% 1.51/1.22 %%% thf(spec, logic, $$dhol).
% 1.51/1.22
% 1.51/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.0TJlJaunP9/DTF2DTF7083.p
% See solution above
% 1.51/1.22 ------------------------
% 1.51/1.23 ---- Cleaned THF ---
% 1.51/1.23 thf(b_type,type,
% 1.51/1.23 b: $tType ).
% 1.51/1.23
% 1.51/1.23 thf(a_type,type,
% 1.51/1.23 a: $tType ).
% 1.51/1.23
% 1.51/1.23 thf(cTHM176_pme,conjecture,
% 1.51/1.23 ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
% 1.51/1.23 ( ! [Xx_2: b,Xy_47: a] :
% 1.51/1.23 ( ( Xk @ Xx_2 @ Xy_47 )
% 1.51/1.23 => ( ( Xs @ Xx_2 @ Xy_47 )
% 1.51/1.23 | ( ( Xx_2 = Xx )
% 1.51/1.23 & ( Xy_47 = Xy ) ) ) )
% 1.51/1.23 => ! [Xx_3: b,Xy_48: a] :
% 1.51/1.23 ( ( ( Xk @ Xx_3 @ Xy_48 )
% 1.51/1.23 & ~ ( ( Xx_3 = Xx )
% 1.51/1.23 & ( Xy_48 = Xy ) ) )
% 1.51/1.23 => ( Xs @ Xx_3 @ Xy_48 ) ) ) ).
% 1.51/1.23 ------------------------
% 1.51/1.24 % (7186)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7083 for (3000ds/18Mi)
% 1.51/1.24 % (7185)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_7083 for (3000ds/275Mi)
% 1.51/1.24 % (7186)First to succeed.
% 1.51/1.24 % (7185)Also succeeded, but the first one will report.
% 1.51/1.24 % (7186)Refutation found. Thanks to Tanya!
% 1.51/1.24 % SZS status Theorem for DTF2THF_7083
% 1.51/1.24 % SZS output start Proof for DTF2THF_7083
% 1.51/1.24 thf(type_def_5, type, b: $tType).
% 1.51/1.24 thf(type_def_6, type, a: $tType).
% 1.51/1.24 thf(func_def_0, type, b: $tType).
% 1.51/1.24 thf(func_def_1, type, a: $tType).
% 1.51/1.24 thf(func_def_5, type, sK0: a).
% 1.51/1.24 thf(func_def_6, type, sK1: b > a > $o).
% 1.51/1.24 thf(func_def_7, type, sK2: b > a > $o).
% 1.51/1.24 thf(func_def_8, type, sK3: b).
% 1.51/1.24 thf(func_def_9, type, sK4: a).
% 1.51/1.24 thf(func_def_10, type, sK5: b).
% 1.51/1.24 thf(f36,plain,(
% 1.51/1.24 $false),
% 1.51/1.24 inference(avatar_sat_refutation,[status(thm)],[f25,f29,f35])).
% 1.51/1.24 thf(f35,plain,(
% 1.51/1.24 spl6_1),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.51/1.24 thf(f34,plain,(
% 1.51/1.24 $false | spl6_1),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f33,f14])).
% 1.51/1.24 thf(f14,plain,(
% 1.51/1.24 ((sK1 @ sK5 @ sK4) != $true)),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.24 thf(f11,plain,(
% 1.51/1.24 (((sK5 != sK3) | (sK4 != sK0)) & ((sK2 @ sK5 @ sK4) = $true) & ((sK1 @ sK5 @ sK4) != $true)) & ! [X6 : b,X7 : a] : (((sK1 @ X6 @ X7) = $true) | ((sK3 = X6) & (sK0 = X7)) | ((sK2 @ X6 @ X7) != $true))),
% 1.51/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f10,f9])).
% 1.51/1.24 thf(f9,plain,(
% 1.51/1.24 ? [X0 : a,X1 : b > a > $o,X2 : b > a > $o,X3 : b] : (? [X4 : a,X5 : b] : (((X3 != X5) | (X0 != X4)) & ($true = (X2 @ X5 @ X4)) & ($true != (X1 @ X5 @ X4))) & ! [X6 : b,X7 : a] : (($true = (X1 @ X6 @ X7)) | ((X3 = X6) & (X0 = X7)) | ((X2 @ X6 @ X7) != $true))) => (? [X5 : b,X4 : a] : (((sK3 != X5) | (sK0 != X4)) & ((sK2 @ X5 @ X4) = $true) & ($true != (sK1 @ X5 @ X4))) & ! [X7 : a,X6 : b] : (((sK1 @ X6 @ X7) = $true) | ((sK3 = X6) & (sK0 = X7)) | ((sK2 @ X6 @ X7) != $true)))),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f10,plain,(
% 1.51/1.24 ? [X5 : b,X4 : a] : (((sK3 != X5) | (sK0 != X4)) & ((sK2 @ X5 @ X4) = $true) & ($true != (sK1 @ X5 @ X4))) => (((sK5 != sK3) | (sK4 != sK0)) & ((sK2 @ sK5 @ sK4) = $true) & ((sK1 @ sK5 @ sK4) != $true))),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f8,plain,(
% 1.51/1.24 ? [X0 : a,X1 : b > a > $o,X2 : b > a > $o,X3 : b] : (? [X4 : a,X5 : b] : (((X3 != X5) | (X0 != X4)) & ($true = (X2 @ X5 @ X4)) & ($true != (X1 @ X5 @ X4))) & ! [X6 : b,X7 : a] : (($true = (X1 @ X6 @ X7)) | ((X3 = X6) & (X0 = X7)) | ((X2 @ X6 @ X7) != $true)))),
% 1.51/1.24 inference(rectify,[status(thm)],[f7])).
% 1.51/1.24 thf(f7,plain,(
% 1.51/1.24 ? [X2 : a,X1 : b > a > $o,X0 : b > a > $o,X3 : b] : (? [X7 : a,X6 : b] : (((X3 != X6) | (X2 != X7)) & ((X0 @ X6 @ X7) = $true) & ($true != (X1 @ X6 @ X7))) & ! [X4 : b,X5 : a] : (($true = (X1 @ X4 @ X5)) | ((X3 = X4) & (X2 = X5)) | ($true != (X0 @ X4 @ X5))))),
% 1.51/1.24 inference(flattening,[status(thm)],[f6])).
% 1.51/1.24 thf(f6,plain,(
% 1.51/1.24 ? [X0 : b > a > $o,X3 : b,X1 : b > a > $o,X2 : a] : (? [X7 : a,X6 : b] : (($true != (X1 @ X6 @ X7)) & (((X0 @ X6 @ X7) = $true) & ((X3 != X6) | (X2 != X7)))) & ! [X4 : b,X5 : a] : ((($true = (X1 @ X4 @ X5)) | ((X3 = X4) & (X2 = X5))) | ($true != (X0 @ X4 @ X5))))),
% 1.51/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.24 thf(f5,plain,(
% 1.51/1.24 ~! [X0 : b > a > $o,X3 : b,X1 : b > a > $o,X2 : a] : (! [X4 : b,X5 : a] : (($true = (X0 @ X4 @ X5)) => (($true = (X1 @ X4 @ X5)) | ((X3 = X4) & (X2 = X5)))) => ! [X7 : a,X6 : b] : ((((X0 @ X6 @ X7) = $true) & ~((X3 = X6) & (X2 = X7))) => ($true = (X1 @ X6 @ X7))))),
% 1.51/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.24 thf(f4,plain,(
% 1.51/1.24 ~! [X0 : b > a > $o,X1 : b > a > $o,X2 : a,X3 : b] : (! [X4 : b,X5 : a] : ((X0 @ X4 @ X5) => (((X2 = X5) & (X3 = X4)) | (X1 @ X4 @ X5))) => ! [X6 : b,X7 : a] : (((X0 @ X6 @ X7) & ~((X2 = X7) & (X3 = X6))) => (X1 @ X6 @ X7)))),
% 1.51/1.24 inference(rectify,[status(thm)],[f2])).
% 1.51/1.24 thf(f2,negated_conjecture,(
% 1.51/1.24 ~! [X3 : b > a > $o,X2 : b > a > $o,X1 : a,X0 : b] : (! [X4 : b,X5 : a] : ((X3 @ X4 @ X5) => (((X1 = X5) & (X0 = X4)) | (X2 @ X4 @ X5))) => ! [X6 : b,X7 : a] : (((X3 @ X6 @ X7) & ~((X1 = X7) & (X0 = X6))) => (X2 @ X6 @ X7)))),
% 1.51/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.24 thf(f1,conjecture,(
% 1.51/1.24 ! [X3 : b > a > $o,X2 : b > a > $o,X1 : a,X0 : b] : (! [X4 : b,X5 : a] : ((X3 @ X4 @ X5) => (((X1 = X5) & (X0 = X4)) | (X2 @ X4 @ X5))) => ! [X6 : b,X7 : a] : (((X3 @ X6 @ X7) & ~((X1 = X7) & (X0 = X6))) => (X2 @ X6 @ X7)))),
% 1.51/1.24 file('/export/starexec/sandbox2/tmp/tmp.0TJlJaunP9/DTF2THF_7083.p',cTHM176_pme)).
% 1.51/1.24 thf(f33,plain,(
% 1.51/1.24 ((sK1 @ sK5 @ sK4) = $true) | spl6_1),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f32,f20])).
% 1.51/1.24 thf(f20,plain,(
% 1.51/1.24 (sK5 != sK3) | spl6_1),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.51/1.24 thf(f18,definition,(
% 1.51/1.24 spl6_1 <=> (sK5 = sK3)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.51/1.24 thf(f32,plain,(
% 1.51/1.24 (sK5 = sK3) | ((sK1 @ sK5 @ sK4) = $true)),
% 1.51/1.24 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.51/1.24 thf(f31,plain,(
% 1.51/1.24 ((sK1 @ sK5 @ sK4) = $true) | ($true != $true) | (sK5 = sK3)),
% 1.51/1.24 inference(superposition,[status(thm)],[f13,f15])).
% 1.51/1.24 thf(f15,plain,(
% 1.51/1.24 ((sK2 @ sK5 @ sK4) = $true)),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.24 thf(f13,plain,(
% 1.51/1.24 ( ! [X6 : b,X7 : a] : (((sK2 @ X6 @ X7) != $true) | ((sK1 @ X6 @ X7) = $true) | (sK3 = X6)) )),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.24 thf(f29,plain,(
% 1.51/1.24 spl6_2),
% 1.51/1.24 inference(avatar_split_clause,[status(thm)],[f28,f22])).
% 1.51/1.24 thf(f22,definition,(
% 1.51/1.24 spl6_2 <=> (sK4 = sK0)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.51/1.24 thf(f28,plain,(
% 1.51/1.24 (sK4 = sK0)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f27,f14])).
% 1.51/1.24 thf(f27,plain,(
% 1.51/1.24 ((sK1 @ sK5 @ sK4) = $true) | (sK4 = sK0)),
% 1.51/1.24 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.51/1.24 thf(f26,plain,(
% 1.51/1.24 ((sK1 @ sK5 @ sK4) = $true) | (sK4 = sK0) | ($true != $true)),
% 1.51/1.24 inference(superposition,[status(thm)],[f12,f15])).
% 1.51/1.24 thf(f12,plain,(
% 1.51/1.24 ( ! [X6 : b,X7 : a] : (((sK2 @ X6 @ X7) != $true) | (sK0 = X7) | ((sK1 @ X6 @ X7) = $true)) )),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.24 thf(f25,plain,(
% 1.51/1.24 ~spl6_1 | ~spl6_2),
% 1.51/1.24 inference(avatar_split_clause,[status(thm)],[f16,f22,f18])).
% 1.51/1.24 thf(f16,plain,(
% 1.51/1.24 (sK5 != sK3) | (sK4 != sK0)),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.24 % SZS output end Proof for DTF2THF_7083
% 1.51/1.24 % (7186)------------------------------
% 1.51/1.24 % (7186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (7186)Termination reason: Refutation
% 1.51/1.24
% 1.51/1.24 % (7186)Memory used [KB]: 5500
% 1.51/1.24 % (7186)Time elapsed: 0.003 s
% 1.51/1.24 % (7186)Instructions burned: 2 (million)
% 1.51/1.24 % (7186)------------------------------
% 1.51/1.24 % (7186)------------------------------
% 1.51/1.24 % (7179)Success in time 0.004 s
%------------------------------------------------------------------------------