%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO023^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 09:53:09 AM UTC 2026
% Result : Theorem 1.49s 1.24s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 193 ( 58 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 135 ( 66 ~; 46 |; 17 &; 4 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 32 ^; 0 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f46,f52]) ).
thf(f52,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f35,f27]) ).
thf(f27,plain,
sK3 = $true,
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( sK3 = $true )
| ( sK3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( sK3 = $true )
| ( $true
= ( sK3
& sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ~ sK3 ) = $false )
| ( $true
= ( sK3
& sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( ~ sK3
| ~ sK2 ) )
| ( $true
= ( sK3
& sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ~ ( ~ sK3
| ~ sK2 ) )
= $true )
| ( $true
= ( sK3
& sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( ~ sK3
| ~ sK2 ) )
!= ( sK3
& sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: $o] :
( Y0
& sK2 )
@ sK3 )
!= ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK2 )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK2 ) )
!= ( ^ [Y0: $o] :
( Y0
& sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 )
@ sK2 )
!= ( ^ [Y0: $o,Y1: $o] :
( Y1
& Y0 )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: $o,Y1: $o] :
( Y1
& Y0 ) )
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: $o,Y1: $o] :
( Y1
& Y0 ) )
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: $o,Y1: $o] :
( Y1
& Y0 ) )
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: $o,X1: $o] :
~ ( ~ X0
| ~ X1 ) )
!= ( ^ [X2: $o,X3: $o] :
( X2
& X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X2: $o,X3: $o] :
~ ( ~ X2
| ~ X3 ) )
!= ( ^ [X0: $o,X1: $o] :
( X0
& X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X2: $o,X3: $o] :
~ ( ~ X2
| ~ X3 ) )
= ( ^ [X0: $o,X1: $o] :
( X0
& X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KLr33Pv0LG/DTF2THF_15603.p',conj) ).
thf(f35,plain,
( ( sK3 = $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_1
<=> ( sK3 = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f46,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f31,f39]) ).
thf(f39,plain,
( ( $false = sK2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl0_2
<=> ( $false = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f31,plain,
$true = sK2,
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true = sK2 )
| ( $true = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
= ( sK3
& sK2 ) )
| ( $true = sK2 ) ),
inference(not_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ~ sK2 ) = $false )
| ( $true
= ( sK3
& sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f37,f33]) ).
thf(f20,plain,
( ( $false = sK2 )
| ( sK3 = $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false = sK2 )
| ( sK3 = $false )
| ( sK3 = $false ) ),
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false = sK2 )
| ( sK3 = $false )
| ( ( ~ sK3 ) = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false = sK2 )
| ( ( ~ sK3 ) = $true )
| ( $false = sK2 )
| ( sK3 = $false ) ),
inference(not_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false = sK2 )
| ( ( ~ sK2 ) = $true )
| ( ( ~ sK3 ) = $true )
| ( sK3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK3 = $false )
| ( $true
= ( ~ sK3
| ~ sK2 ) )
| ( $false = sK2 ) ),
inference(not_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ~ ( ~ sK3
| ~ sK2 ) )
= $false )
| ( $false = sK2 )
| ( sK3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( sK3
& sK2 ) )
| ( ( ~ ( ~ sK3
| ~ sK2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO023^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n013.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 14:21:23 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
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO023^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : De Morgan lambda terms by Leibnitz
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.18/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Ben09]
% 0.18/0.45 % Names : Example 20c [BB05]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % : Without Boolean extensionality : CounterSatisfiable
% 0.18/0.45 % : Without xi extensionality : CounterSatisfiable
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 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, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.18/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.45 % Number of connectives : 5 ( 3 ~; 1 |; 1 &; 0 @)
% 0.18/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 1 ( 1 avg)
% 0.18/0.45 % Number of types : 1 ( 0 usr)
% 0.18/0.45 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.45 % Number of variables : 4 ( 4 ^; 0 !; 0 ?; 4 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(conj,conjecture,
% 0.18/0.45 ( ( ^ [U: $o,V: $o] :
% 0.18/0.45 ( U
% 0.18/0.45 & V ) )
% 0.18/0.45 = ( ^ [X: $o,Y: $o] :
% 0.18/0.45 ~ ( ~ X
% 0.18/0.45 | ~ Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.49/1.21 ---- Embedded in THF ---
% 1.49/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.22 %%% Generated on Tue Feb 24 14:21:24 EST 2026
% 1.49/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.22 %%% Logic specification used:
% 1.49/1.22 %%% thf(spec, logic, $$dhol).
% 1.49/1.22
% 1.49/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KLr33Pv0LG/DTF2DTF15603.p
% See solution above
% 1.49/1.22 ------------------------
% 1.49/1.23 ---- Cleaned THF ---
% 1.49/1.23 thf(conj,conjecture,
% 1.49/1.23 ( ( ^ [U: $o,V: $o] :
% 1.49/1.23 ( U
% 1.49/1.23 & V ) )
% 1.49/1.23 = ( ^ [X: $o,Y: $o] :
% 1.49/1.23 ~ ( ~ X
% 1.49/1.23 | ~ Y ) ) ) ).
% 1.49/1.23 ------------------------
% 1.49/1.24 % (15717)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15603 for (2999ds/183Mi)
% 1.49/1.24 % (15719)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_15603 for (2999ds/27Mi)
% 1.49/1.24 % (15717)First to succeed.
% 1.49/1.24 % (15719)Also succeeded, but the first one will report.
% 1.49/1.24 % (15717)Refutation found. Thanks to Tanya!
% 1.49/1.24 % SZS status Theorem for DTF2THF_15603
% 1.49/1.24 % SZS output start Proof for DTF2THF_15603
% 1.49/1.24 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.24 thf(f53,plain,(
% 1.49/1.24 $false),
% 1.49/1.24 inference(avatar_sat_refutation,[status(thm)],[f40,f46,f52])).
% 1.49/1.24 thf(f52,plain,(
% 1.49/1.24 ~spl0_1),
% 1.49/1.24 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.49/1.24 thf(f51,plain,(
% 1.49/1.24 $false | ~spl0_1),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.49/1.24 thf(f47,plain,(
% 1.49/1.24 ($true = $false) | ~spl0_1),
% 1.49/1.24 inference(superposition,[status(thm)],[f35,f27])).
% 1.49/1.24 thf(f27,plain,(
% 1.49/1.24 (sK3 = $true)),
% 1.49/1.24 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.49/1.24 thf(f26,plain,(
% 1.49/1.24 (sK3 = $true) | (sK3 = $true)),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.49/1.24 thf(f24,plain,(
% 1.49/1.24 (sK3 = $true) | ($true = (sK3 & sK2))),
% 1.49/1.24 inference(not_proxy_clausification,[status(thm)],[f23])).
% 1.49/1.24 thf(f23,plain,(
% 1.49/1.24 ((~ sK3) = $false) | ($true = (sK3 & sK2))),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.49/1.24 thf(f21,plain,(
% 1.49/1.24 ($false = ((~ sK3) | (~ sK2))) | ($true = (sK3 & sK2))),
% 1.49/1.24 inference(not_proxy_clausification,[status(thm)],[f12])).
% 1.49/1.24 thf(f12,plain,(
% 1.49/1.24 ((~ ((~ sK3) | (~ sK2))) = $true) | ($true = (sK3 & sK2))),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.49/1.24 thf(f11,plain,(
% 1.49/1.24 ((~ ((~ sK3) | (~ sK2))) != (sK3 & sK2))),
% 1.49/1.24 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.49/1.24 thf(f10,plain,(
% 1.49/1.24 (((^[Y0 : $o]: (Y0 & sK2)) @ sK3) != ((^[Y0 : $o]: (~ ((~ Y0) | (~ sK2)))) @ sK3))),
% 1.49/1.24 inference(negative_extensionality,[status(thm)],[f9])).
% 1.49/1.24 thf(f9,plain,(
% 1.49/1.24 ((^[Y0 : $o]: (~ ((~ Y0) | (~ sK2)))) != (^[Y0 : $o]: (Y0 & sK2)))),
% 1.49/1.24 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.49/1.24 thf(f8,plain,(
% 1.49/1.24 (((^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))) @ sK2) != ((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 & Y0)))) @ sK2))),
% 1.49/1.24 inference(negative_extensionality,[status(thm)],[f7])).
% 1.49/1.24 thf(f7,plain,(
% 1.49/1.24 ((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 & Y0)))) != (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))))),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f6])).
% 1.49/1.24 thf(f6,plain,(
% 1.49/1.24 ((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 & Y0)))) != (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))))),
% 1.49/1.24 inference(flattening,[status(thm)],[f5])).
% 1.49/1.24 thf(f5,plain,(
% 1.49/1.24 ~((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 & Y0)))) = (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.24 thf(f4,plain,(
% 1.49/1.24 ~((^[X0 : $o, X1 : $o] : (~(~X0 | ~X1))) = (^[X2 : $o, X3 : $o] : (X2 & X3)))),
% 1.49/1.24 inference(rectify,[status(thm)],[f2])).
% 1.49/1.24 thf(f2,negated_conjecture,(
% 1.49/1.24 ~((^[X2 : $o, X3 : $o] : (~(~X2 | ~X3))) = (^[X0 : $o, X1 : $o] : (X0 & X1)))),
% 1.49/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.24 thf(f1,conjecture,(
% 1.49/1.24 ((^[X2 : $o, X3 : $o] : (~(~X2 | ~X3))) = (^[X0 : $o, X1 : $o] : (X0 & X1)))),
% 1.49/1.24 file('/export/starexec/sandbox2/tmp/tmp.KLr33Pv0LG/DTF2THF_15603.p',conj)).
% 1.49/1.24 thf(f35,plain,(
% 1.49/1.24 (sK3 = $false) | ~spl0_1),
% 1.49/1.24 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.49/1.24 thf(f33,definition,(
% 1.49/1.24 spl0_1 <=> (sK3 = $false)),
% 1.49/1.24 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.49/1.24 thf(f46,plain,(
% 1.49/1.24 ~spl0_2),
% 1.49/1.24 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.49/1.24 thf(f45,plain,(
% 1.49/1.24 $false | ~spl0_2),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.49/1.24 thf(f41,plain,(
% 1.49/1.24 ($true = $false) | ~spl0_2),
% 1.49/1.24 inference(superposition,[status(thm)],[f31,f39])).
% 1.49/1.24 thf(f39,plain,(
% 1.49/1.24 ($false = sK2) | ~spl0_2),
% 1.49/1.24 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.49/1.24 thf(f37,definition,(
% 1.49/1.24 spl0_2 <=> ($false = sK2)),
% 1.49/1.24 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.49/1.24 thf(f31,plain,(
% 1.49/1.24 ($true = sK2)),
% 1.49/1.24 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.49/1.24 thf(f29,plain,(
% 1.49/1.24 ($true = sK2) | ($true = sK2)),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.49/1.24 thf(f28,plain,(
% 1.49/1.24 ($true = (sK3 & sK2)) | ($true = sK2)),
% 1.49/1.24 inference(not_proxy_clausification,[status(thm)],[f22])).
% 1.49/1.24 thf(f22,plain,(
% 1.49/1.24 ((~ sK2) = $false) | ($true = (sK3 & sK2))),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.49/1.24 thf(f40,plain,(
% 1.49/1.24 spl0_1 | spl0_2),
% 1.49/1.24 inference(avatar_split_clause,[status(thm)],[f20,f37,f33])).
% 1.49/1.24 thf(f20,plain,(
% 1.49/1.24 ($false = sK2) | (sK3 = $false)),
% 1.49/1.24 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.49/1.24 thf(f19,plain,(
% 1.49/1.24 ($false = sK2) | (sK3 = $false) | (sK3 = $false)),
% 1.49/1.24 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.49/1.24 thf(f18,plain,(
% 1.49/1.24 ($false = sK2) | (sK3 = $false) | ((~ sK3) = $true)),
% 1.49/1.24 inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.49/1.24 thf(f17,plain,(
% 1.49/1.24 ($false = sK2) | ((~ sK3) = $true) | ($false = sK2) | (sK3 = $false)),
% 1.49/1.24 inference(not_proxy_clausification,[status(thm)],[f16])).
% 1.49/1.24 thf(f16,plain,(
% 1.49/1.24 ($false = sK2) | ((~ sK2) = $true) | ((~ sK3) = $true) | (sK3 = $false)),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.49/1.24 thf(f15,plain,(
% 1.49/1.24 (sK3 = $false) | ($true = ((~ sK3) | (~ sK2))) | ($false = sK2)),
% 1.49/1.24 inference(not_proxy_clausification,[status(thm)],[f14])).
% 1.49/1.24 thf(f14,plain,(
% 1.49/1.24 ((~ ((~ sK3) | (~ sK2))) = $false) | ($false = sK2) | (sK3 = $false)),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.49/1.24 thf(f13,plain,(
% 1.49/1.24 ($false = (sK3 & sK2)) | ((~ ((~ sK3) | (~ sK2))) = $false)),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.49/1.24 % SZS output end Proof for DTF2THF_15603
% 1.49/1.24 % (15717)------------------------------
% 1.49/1.24 % (15717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (15717)Termination reason: Refutation
% 1.49/1.24
% 1.49/1.24 % (15717)Memory used [KB]: 5500
% 1.49/1.24 % (15717)Time elapsed: 0.003 s
% 1.49/1.24 % (15717)Instructions burned: 1 (million)
% 1.49/1.24 % (15717)------------------------------
% 1.49/1.24 % (15717)------------------------------
% 1.49/1.24 % (15716)Success in time 0.004 s
%------------------------------------------------------------------------------