%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO217^5 : 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 : n020.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 09:53:41 AM UTC 2026
% Result : Theorem 1.58s 1.20s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 149 ( 44 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 171 ( 35 ~; 31 |; 5 &; 88 @)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 32 !; 6 ?; 38 :)
% 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: b > a > $o ).
thf(func_def_6,type,
sK1: b > a > $o ).
thf(func_def_8,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
sK4: b ).
thf(func_def_10,type,
sK5: a ).
thf(f69,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f35,f41,f47,f54,f66]) ).
thf(f66,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f61,f24]) ).
thf(f24,plain,
( ( ( sK1 @ sK4 @ sK5 )
!= $true )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl2_2
<=> ( ( sK1 @ sK4 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f61,plain,
( ( ( sK1 @ sK4 @ sK5 )
= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( sK1 @ sK4 @ sK5 )
= $true )
| ( $false = $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f13,f21]) ).
thf(f21,plain,
( ( ( sK0 @ sK4 @ sK5 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl2_1
<=> ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f13,plain,
! [X2: b,X3: a] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK1 @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
! [X2: b,X3: a] :
( ( sK0 @ X2 @ X3 )
= ( sK1 @ X2 @ X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK1 != sK0 )
& ! [X2: b,X3: a] :
( ( sK0 @ X2 @ X3 )
= ( sK1 @ X2 @ X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: b > a > $o,X1: b > a > $o] :
( ( X0 != X1 )
& ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ) )
=> ( ( sK1 != sK0 )
& ! [X3: a,X2: b] :
( ( sK0 @ X2 @ X3 )
= ( sK1 @ X2 @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: b > a > $o,X1: b > a > $o] :
( ( X0 != X1 )
& ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: b > a > $o,X0: b > a > $o] :
( ( X0 != X1 )
& ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: b > a > $o,X1: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > a > $o,X1: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
<=> ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: b > a > $o,X1: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
<=> ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: b > a > $o,X1: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X0 @ X2 @ X3 )
<=> ( X1 @ X2 @ X3 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.q6kx8vptmx/DTF2THF_30615.p',cTHM174) ).
thf(f54,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f34,f25]) ).
thf(f25,plain,
( ( ( sK1 @ sK4 @ sK5 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f34,plain,
( ( ( sK1 @ sK4 @ sK5 )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl2_4
<=> ( ( sK1 @ sK4 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f47,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f46]) ).
thf(f46,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f21,f30]) ).
thf(f30,plain,
( ( $false
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl2_3
<=> ( $false
= ( sK0 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f41,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f23,f19]) ).
thf(f38,plain,
( ( ( sK0 @ sK4 @ sK5 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( sK0 @ sK4 @ sK5 )
= $true )
| ( $false = $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f12,f25]) ).
thf(f12,plain,
! [X2: b,X3: a] :
( ( $false
= ( sK1 @ X2 @ X3 ) )
| ( ( sK0 @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f35,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f17,f32,f28]) ).
thf(f17,plain,
( ( ( sK1 @ sK4 @ sK5 )
= $false )
| ( $false
= ( sK0 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK1 @ sK4 @ sK5 )
!= ( sK0 @ sK4 @ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sK0 @ sK4 )
!= ( sK1 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f11]) ).
thf(f11,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f26,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f16,f23,f19]) ).
thf(f16,plain,
( ( ( sK1 @ sK4 @ sK5 )
= $true )
| ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO217^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:26:12 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SYO217^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44 % Domain : Syntactic
% 0.18/0.44 % Problem : TPS problem THM174
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English : Principle of extensionality for binary relations.
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : tps_0105 [Bro09]
% 0.18/0.44 % : THM174 [TPS]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 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, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.18/0.44 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.18/0.44 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.44 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.18/0.44 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.44 % Number of types : 3 ( 2 usr)
% 0.18/0.44 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.44 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(b_type,type,
% 0.18/0.44 b: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(a_type,type,
% 0.18/0.44 a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(cTHM174,conjecture,
% 0.18/0.44 ! [Xr: b > a > $o,Xs: b > a > $o] :
% 0.18/0.44 ( ! [Xx: b,Xy: a] :
% 0.18/0.44 ( ( Xr @ Xx @ Xy )
% 0.18/0.44 <=> ( Xs @ Xx @ Xy ) )
% 0.18/0.44 => ( Xr = Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.48/1.17 ---- Embedded in THF ---
% 1.48/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.18 %%% Generated on Tue Feb 24 14:26:13 EST 2026
% 1.48/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.18 %%% Logic specification used:
% 1.48/1.18 %%% thf(spec, logic, $$dhol).
% 1.48/1.18
% 1.48/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.q6kx8vptmx/DTF2DTF30615.p
% See solution above
% 1.48/1.18 ------------------------
% 1.48/1.19 ---- Cleaned THF ---
% 1.48/1.19 thf(b_type,type,
% 1.48/1.19 b: $tType ).
% 1.48/1.19
% 1.48/1.19 thf(a_type,type,
% 1.48/1.19 a: $tType ).
% 1.48/1.19
% 1.48/1.19 thf(cTHM174,conjecture,
% 1.48/1.19 ! [Xr: b > a > $o,Xs: b > a > $o] :
% 1.48/1.19 ( ! [Xx: b,Xy: a] :
% 1.48/1.19 ( ( Xr @ Xx @ Xy )
% 1.48/1.19 <=> ( Xs @ Xx @ Xy ) )
% 1.48/1.19 => ( Xr = Xs ) ) ).
% 1.48/1.19 ------------------------
% 1.58/1.20 % (30803)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30615 for (2999ds/183Mi)
% 1.58/1.20 % (30805)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_30615 for (2999ds/27Mi)
% 1.58/1.20 % (30803)First to succeed.
% 1.58/1.20 % (30803)Refutation found. Thanks to Tanya!
% 1.58/1.20 % SZS status Theorem for DTF2THF_30615
% 1.58/1.20 % SZS output start Proof for DTF2THF_30615
% 1.58/1.20 thf(type_def_5, type, b: $tType).
% 1.58/1.20 thf(type_def_6, type, a: $tType).
% 1.58/1.20 thf(func_def_0, type, b: $tType).
% 1.58/1.20 thf(func_def_1, type, a: $tType).
% 1.58/1.20 thf(func_def_5, type, sK0: b > a > $o).
% 1.58/1.20 thf(func_def_6, type, sK1: b > a > $o).
% 1.58/1.20 thf(func_def_8, type, ph3: !>[X0: $tType]:(X0)).
% 1.58/1.20 thf(func_def_9, type, sK4: b).
% 1.58/1.20 thf(func_def_10, type, sK5: a).
% 1.58/1.20 thf(f69,plain,(
% 1.58/1.20 $false),
% 1.58/1.20 inference(avatar_sat_refutation,[status(thm)],[f26,f35,f41,f47,f54,f66])).
% 1.58/1.20 thf(f66,plain,(
% 1.58/1.20 ~spl2_1 | spl2_2),
% 1.58/1.20 inference(avatar_contradiction_clause,[status(thm)],[f65])).
% 1.58/1.20 thf(f65,plain,(
% 1.58/1.20 $false | (~spl2_1 | spl2_2)),
% 1.58/1.20 inference(subsumption_resolution,[status(thm)],[f61,f24])).
% 1.58/1.20 thf(f24,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) != $true) | spl2_2),
% 1.58/1.20 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.58/1.20 thf(f23,definition,(
% 1.58/1.20 spl2_2 <=> ((sK1 @ sK4 @ sK5) = $true)),
% 1.58/1.20 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.58/1.20 thf(f61,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) = $true) | ~spl2_1),
% 1.58/1.20 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.58/1.20 thf(f57,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) = $true) | ($false = $true) | ~spl2_1),
% 1.58/1.20 inference(superposition,[status(thm)],[f13,f21])).
% 1.58/1.20 thf(f21,plain,(
% 1.58/1.20 ((sK0 @ sK4 @ sK5) = $true) | ~spl2_1),
% 1.58/1.20 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.58/1.20 thf(f19,definition,(
% 1.58/1.20 spl2_1 <=> ((sK0 @ sK4 @ sK5) = $true)),
% 1.58/1.20 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.58/1.20 thf(f13,plain,(
% 1.58/1.20 ( ! [X2 : b,X3 : a] : (($false = (sK0 @ X2 @ X3)) | ((sK1 @ X2 @ X3) = $true)) )),
% 1.58/1.20 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.58/1.20 thf(f10,plain,(
% 1.58/1.20 ( ! [X2 : b,X3 : a] : (((sK0 @ X2 @ X3) = (sK1 @ X2 @ X3))) )),
% 1.58/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.20 thf(f9,plain,(
% 1.58/1.20 (sK1 != sK0) & ! [X2 : b,X3 : a] : ((sK0 @ X2 @ X3) = (sK1 @ X2 @ X3))),
% 1.58/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.58/1.20 thf(f8,plain,(
% 1.58/1.20 ? [X0 : b > a > $o,X1 : b > a > $o] : ((X0 != X1) & ! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) = (X1 @ X2 @ X3))) => ((sK1 != sK0) & ! [X3 : a,X2 : b] : ((sK0 @ X2 @ X3) = (sK1 @ X2 @ X3)))),
% 1.58/1.20 introduced(definition,[],[choice_axiom])).
% 1.58/1.20 thf(f7,plain,(
% 1.58/1.20 ? [X0 : b > a > $o,X1 : b > a > $o] : ((X0 != X1) & ! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) = (X1 @ X2 @ X3)))),
% 1.58/1.20 inference(rectify,[status(thm)],[f6])).
% 1.58/1.20 thf(f6,plain,(
% 1.58/1.20 ? [X1 : b > a > $o,X0 : b > a > $o] : ((X0 != X1) & ! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) = (X1 @ X2 @ X3)))),
% 1.58/1.20 inference(ennf_transformation,[status(thm)],[f5])).
% 1.58/1.20 thf(f5,plain,(
% 1.58/1.20 ~! [X0 : b > a > $o,X1 : b > a > $o] : (! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) = (X1 @ X2 @ X3)) => (X0 = X1))),
% 1.58/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.20 thf(f4,plain,(
% 1.58/1.20 ~! [X0 : b > a > $o,X1 : b > a > $o] : (! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) <=> (X1 @ X2 @ X3)) => (X0 = X1))),
% 1.58/1.20 inference(rectify,[status(thm)],[f2])).
% 1.58/1.20 thf(f2,negated_conjecture,(
% 1.58/1.20 ~! [X0 : b > a > $o,X1 : b > a > $o] : (! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) <=> (X1 @ X2 @ X3)) => (X0 = X1))),
% 1.58/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.20 thf(f1,conjecture,(
% 1.58/1.20 ! [X0 : b > a > $o,X1 : b > a > $o] : (! [X2 : b,X3 : a] : ((X0 @ X2 @ X3) <=> (X1 @ X2 @ X3)) => (X0 = X1))),
% 1.58/1.20 file('/export/starexec/sandbox/tmp/tmp.q6kx8vptmx/DTF2THF_30615.p',cTHM174)).
% 1.58/1.20 thf(f54,plain,(
% 1.58/1.20 ~spl2_2 | ~spl2_4),
% 1.58/1.20 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.58/1.20 thf(f53,plain,(
% 1.58/1.20 $false | (~spl2_2 | ~spl2_4)),
% 1.58/1.20 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.58/1.20 thf(f49,plain,(
% 1.58/1.20 ($false = $true) | (~spl2_2 | ~spl2_4)),
% 1.58/1.20 inference(superposition,[status(thm)],[f34,f25])).
% 1.58/1.20 thf(f25,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) = $true) | ~spl2_2),
% 1.58/1.20 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.58/1.20 thf(f34,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) = $false) | ~spl2_4),
% 1.58/1.20 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.58/1.20 thf(f32,definition,(
% 1.58/1.20 spl2_4 <=> ((sK1 @ sK4 @ sK5) = $false)),
% 1.58/1.20 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.58/1.20 thf(f47,plain,(
% 1.58/1.20 ~spl2_1 | ~spl2_3),
% 1.58/1.20 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.58/1.20 thf(f46,plain,(
% 1.58/1.20 $false | (~spl2_1 | ~spl2_3)),
% 1.58/1.20 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.58/1.20 thf(f42,plain,(
% 1.58/1.20 ($false = $true) | (~spl2_1 | ~spl2_3)),
% 1.58/1.20 inference(superposition,[status(thm)],[f21,f30])).
% 1.58/1.20 thf(f30,plain,(
% 1.58/1.20 ($false = (sK0 @ sK4 @ sK5)) | ~spl2_3),
% 1.58/1.20 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.58/1.20 thf(f28,definition,(
% 1.58/1.20 spl2_3 <=> ($false = (sK0 @ sK4 @ sK5))),
% 1.58/1.20 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.58/1.20 thf(f41,plain,(
% 1.58/1.20 spl2_1 | ~spl2_2),
% 1.58/1.20 inference(avatar_split_clause,[status(thm)],[f38,f23,f19])).
% 1.58/1.20 thf(f38,plain,(
% 1.58/1.20 ((sK0 @ sK4 @ sK5) = $true) | ~spl2_2),
% 1.58/1.20 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.58/1.20 thf(f36,plain,(
% 1.58/1.20 ((sK0 @ sK4 @ sK5) = $true) | ($false = $true) | ~spl2_2),
% 1.58/1.20 inference(superposition,[status(thm)],[f12,f25])).
% 1.58/1.20 thf(f12,plain,(
% 1.58/1.20 ( ! [X2 : b,X3 : a] : (($false = (sK1 @ X2 @ X3)) | ((sK0 @ X2 @ X3) = $true)) )),
% 1.58/1.20 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.58/1.20 thf(f35,plain,(
% 1.58/1.20 spl2_3 | spl2_4),
% 1.58/1.20 inference(avatar_split_clause,[status(thm)],[f17,f32,f28])).
% 1.58/1.20 thf(f17,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) = $false) | ($false = (sK0 @ sK4 @ sK5))),
% 1.58/1.20 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.58/1.20 thf(f15,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) != (sK0 @ sK4 @ sK5))),
% 1.58/1.20 inference(negative_extensionality,[status(thm)],[f14])).
% 1.58/1.20 thf(f14,plain,(
% 1.58/1.20 ((sK0 @ sK4) != (sK1 @ sK4))),
% 1.58/1.20 inference(negative_extensionality,[status(thm)],[f11])).
% 1.58/1.20 thf(f11,plain,(
% 1.58/1.20 (sK1 != sK0)),
% 1.58/1.20 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.20 thf(f26,plain,(
% 1.58/1.20 spl2_1 | spl2_2),
% 1.58/1.20 inference(avatar_split_clause,[status(thm)],[f16,f23,f19])).
% 1.58/1.20 thf(f16,plain,(
% 1.58/1.20 ((sK1 @ sK4 @ sK5) = $true) | ((sK0 @ sK4 @ sK5) = $true)),
% 1.58/1.20 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.58/1.20 % SZS output end Proof for DTF2THF_30615
% 1.58/1.20 % (30803)------------------------------
% 1.58/1.20 % (30803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.20 % (30803)Termination reason: Refutation
% 1.58/1.20
% 1.58/1.20 % (30803)Memory used [KB]: 5500
% 1.58/1.20 % (30803)Time elapsed: 0.003 s
% 1.58/1.20 % (30803)Instructions burned: 1 (million)
% 1.58/1.20 % (30803)------------------------------
% 1.58/1.20 % (30803)------------------------------
% 1.58/1.20 % (30802)Success in time 0.004 s
%------------------------------------------------------------------------------