%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO375^5 : 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 : n007.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 09:54:04 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 159 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 140 ( 32 ~; 28 |; 4 &; 60 @)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 23 !; 8 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(func_def_5,type,
sK1: $i > $o ).
thf(f55,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f33,f39,f42,f46,f54]) ).
thf(f54,plain,
( spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f51,f30,f26]) ).
thf(f26,definition,
( spl3_3
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f30,definition,
( spl3_4
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f51,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true = $false )
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f13,f32]) ).
thf(f32,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f13,plain,
! [X2: $i] :
( ( $true
= ( sK0 @ X2 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: $i] :
( ( sK1 @ X2 )
= ( sK0 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X2: $i] :
( ( sK1 @ X2 )
= ( sK0 @ X2 ) )
& ( ( sK0 @ sK2 )
!= ( sK1 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
& ? [X3: $i] :
( ( X0 @ X3 )
!= ( X1 @ X3 ) ) )
=> ( ! [X2: $i] :
( ( sK1 @ X2 )
= ( sK0 @ X2 ) )
& ? [X3: $i] :
( ( sK0 @ X3 )
!= ( sK1 @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X3: $i] :
( ( sK0 @ X3 )
!= ( sK1 @ X3 ) )
=> ( ( sK0 @ sK2 )
!= ( sK1 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
& ? [X3: $i] :
( ( X0 @ X3 )
!= ( X1 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
= ( X1 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X0 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
<=> ( X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
<=> ( X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H5aKqVBESJ/DTF2THF_25514.p',cEXT_SET1) ).
thf(f46,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f19,f28]) ).
thf(f28,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f19,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl3_1
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f42,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f23,f32]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl3_2
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f39,plain,
( spl3_4
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f36,f26,f30]) ).
thf(f36,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true = $false )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f28,f12]) ).
thf(f12,plain,
! [X2: $i] :
( ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f33,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f15,f30,f26]) ).
thf(f15,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK0 @ sK2 )
!= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f24,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO375^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n007.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 14:28:23 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SYO375^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.44 % Domain : Syntactic
% 0.19/0.44 % Problem : TPS problem from EXTENSIONALITY
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English :
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro09]
% 0.19/0.44 % Names : tps_0769 [Bro09]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.19/0.44 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.19/0.44 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.44 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.19/0.44 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.44 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.19/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(cEXT_SET1,conjecture,
% 0.19/0.44 ! [X: $i > $o,Y: $i > $o] :
% 0.19/0.44 ( ! [W: $i] :
% 0.19/0.44 ( ( X @ W )
% 0.19/0.44 <=> ( Y @ W ) )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( X @ Xx )
% 0.19/0.44 <=> ( Y @ Xx ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 14:28:24 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.H5aKqVBESJ/DTF2DTF25514.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(cEXT_SET1,conjecture,
% 1.48/1.27 ! [X: $i > $o,Y: $i > $o] :
% 1.48/1.27 ( ! [W: $i] :
% 1.48/1.27 ( ( X @ W )
% 1.48/1.27 <=> ( Y @ W ) )
% 1.48/1.27 => ! [Xx: $i] :
% 1.48/1.27 ( ( X @ Xx )
% 1.48/1.27 <=> ( Y @ Xx ) ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.29 % (25716)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_25514 for (2999ds/27Mi)
% 1.48/1.29 % (25715)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_25514 for (2999ds/4Mi)
% 1.48/1.29 % (25716)First to succeed.
% 1.48/1.29 % (25715)Also succeeded, but the first one will report.
% 1.48/1.29 % (25716)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_25514
% 1.48/1.29 % SZS output start Proof for DTF2THF_25514
% 1.48/1.29 thf(func_def_1, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.29 thf(func_def_4, type, sK0: $i > $o).
% 1.48/1.29 thf(func_def_5, type, sK1: $i > $o).
% 1.48/1.29 thf(f55,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(avatar_sat_refutation,[status(thm)],[f24,f33,f39,f42,f46,f54])).
% 1.48/1.29 thf(f54,plain,(
% 1.48/1.29 spl3_3 | ~spl3_4),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f51,f30,f26])).
% 1.48/1.29 thf(f26,definition,(
% 1.48/1.29 spl3_3 <=> ($false = (sK1 @ sK2))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.48/1.29 thf(f30,definition,(
% 1.48/1.29 spl3_4 <=> ($false = (sK0 @ sK2))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.48/1.29 thf(f51,plain,(
% 1.48/1.29 ($false = (sK1 @ sK2)) | ~spl3_4),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.48/1.29 thf(f49,plain,(
% 1.48/1.29 ($false = (sK1 @ sK2)) | ($true = $false) | ~spl3_4),
% 1.48/1.29 inference(superposition,[status(thm)],[f13,f32])).
% 1.48/1.29 thf(f32,plain,(
% 1.48/1.29 ($false = (sK0 @ sK2)) | ~spl3_4),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 ( ! [X2 : $i] : (($true = (sK0 @ X2)) | ($false = (sK1 @ X2))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ( ! [X2 : $i] : (((sK1 @ X2) = (sK0 @ X2))) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ! [X2 : $i] : ((sK1 @ X2) = (sK0 @ X2)) & ((sK0 @ sK2) != (sK1 @ sK2))),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) & ? [X3 : $i] : ((X0 @ X3) != (X1 @ X3))) => (! [X2 : $i] : ((sK1 @ X2) = (sK0 @ X2)) & ? [X3 : $i] : ((sK0 @ X3) != (sK1 @ X3)))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 ? [X3 : $i] : ((sK0 @ X3) != (sK1 @ X3)) => ((sK0 @ sK2) != (sK1 @ sK2))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) & ? [X3 : $i] : ((X0 @ X3) != (X1 @ X3)))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ~! [X1 : $i > $o,X0 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) = (X1 @ X2)) => ! [X3 : $i] : ((X0 @ X3) = (X1 @ X3)))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,plain,(
% 1.48/1.29 ~! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) <=> (X1 @ X2)) => ! [X3 : $i] : ((X1 @ X3) <=> (X0 @ X3)))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,negated_conjecture,(
% 1.48/1.29 ~! [X1 : $i > $o,X0 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) <=> (X0 @ X2)) => ! [X3 : $i] : ((X0 @ X3) <=> (X1 @ X3)))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.29 thf(f1,conjecture,(
% 1.48/1.29 ! [X1 : $i > $o,X0 : $i > $o] : (! [X2 : $i] : ((X1 @ X2) <=> (X0 @ X2)) => ! [X3 : $i] : ((X0 @ X3) <=> (X1 @ X3)))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.H5aKqVBESJ/DTF2THF_25514.p',cEXT_SET1)).
% 1.48/1.29 thf(f46,plain,(
% 1.48/1.29 ~spl3_1 | ~spl3_3),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.48/1.29 thf(f45,plain,(
% 1.48/1.29 $false | (~spl3_1 | ~spl3_3)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.48/1.29 thf(f44,plain,(
% 1.48/1.29 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 1.48/1.29 inference(forward_demodulation,[status(thm)],[f19,f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ($false = (sK1 @ sK2)) | ~spl3_3),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 ($true = (sK1 @ sK2)) | ~spl3_1),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.48/1.29 thf(f17,definition,(
% 1.48/1.29 spl3_1 <=> ($true = (sK1 @ sK2))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.48/1.29 thf(f42,plain,(
% 1.48/1.29 ~spl3_2 | ~spl3_4),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.48/1.29 thf(f41,plain,(
% 1.48/1.29 $false | (~spl3_2 | ~spl3_4)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.48/1.29 thf(f40,plain,(
% 1.48/1.29 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 1.48/1.29 inference(backward_demodulation,[status(thm)],[f23,f32])).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 ($true = (sK0 @ sK2)) | ~spl3_2),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.48/1.29 thf(f21,definition,(
% 1.48/1.29 spl3_2 <=> ($true = (sK0 @ sK2))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.48/1.29 thf(f39,plain,(
% 1.48/1.29 spl3_4 | ~spl3_3),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f36,f26,f30])).
% 1.48/1.29 thf(f36,plain,(
% 1.48/1.29 ($false = (sK0 @ sK2)) | ~spl3_3),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.48/1.29 thf(f35,plain,(
% 1.48/1.29 ($false = (sK0 @ sK2)) | ($true = $false) | ~spl3_3),
% 1.48/1.29 inference(superposition,[status(thm)],[f28,f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ( ! [X2 : $i] : (($true = (sK1 @ X2)) | ($false = (sK0 @ X2))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.48/1.29 thf(f33,plain,(
% 1.48/1.29 spl3_3 | spl3_4),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f15,f30,f26])).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 ($false = (sK1 @ sK2)) | ($false = (sK0 @ sK2))),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ((sK0 @ sK2) != (sK1 @ sK2))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 spl3_1 | spl3_2),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2))),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_25514
% 1.48/1.29 % (25716)------------------------------
% 1.48/1.29 % (25716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (25716)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (25716)Memory used [KB]: 5500
% 1.48/1.29 % (25716)Time elapsed: 0.003 s
% 1.48/1.29 % (25716)Instructions burned: 2 (million)
% 1.48/1.29 % (25716)------------------------------
% 1.48/1.29 % (25716)------------------------------
% 1.48/1.29 % (25713)Success in time 0.013 s
%------------------------------------------------------------------------------