%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO371^5 : 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 : n005.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 1.65s 1.45s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 147 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 80 ( 24 ~; 26 |; 1 &; 14 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f74,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f19,f28,f62,f65,f73]) ).
thf(f73,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f70,f27]) ).
thf(f27,plain,
( ( cP = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl0_4
<=> ( cP = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f70,plain,
( ( cP = $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $false = $true )
| ( cP = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f40,f18]) ).
thf(f18,plain,
( ( cQ = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl0_2
<=> ( cQ = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f40,plain,
( ( cQ = $false )
| ( cP = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
cP = cQ,
inference(leibniz_equality_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $o > $o] :
( ( ( X0 @ cQ )
= $true )
| ( ( X0 @ cP )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( cP != cQ )
& ! [X0: $o > $o] :
( ( ( X0 @ cQ )
= $true )
| ( ( X0 @ cP )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $o > $o] :
( ( ( X0 @ cP )
= $true )
=> ( ( X0 @ cQ )
= $true ) )
=> ( cP = cQ ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $o > $o] :
( ( X0 @ cP )
=> ( X0 @ cQ ) )
=> ( cP
<=> cQ ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $o > $o] :
( ( X0 @ cP )
=> ( X0 @ cQ ) )
=> ( cP
<=> cQ ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $o > $o] :
( ( X0 @ cP )
=> ( X0 @ cQ ) )
=> ( cP
<=> cQ ) ),
file('/export/starexec/sandbox/tmp/tmp.QbT9KEe5tC/DTF2THF_2576.p',cEXT_O_LEIB) ).
thf(f65,plain,
( spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f44,f12,f16]) ).
thf(f12,definition,
( spl0_1
<=> ( cP = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f44,plain,
( ( cP != $true )
| ( cQ = $true ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true
!= ( ^ [Y0: $o] : Y0
@ cP ) )
| ( $true
= ( ^ [Y0: $o] : Y0
@ cQ ) ) ),
inference(primitive_instantiation,[status(thm)],[f7]) ).
thf(f62,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f61,f21,f25]) ).
thf(f21,definition,
( spl0_3
<=> ( cQ = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f61,plain,
( ( cP = $false )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( cP = $false )
| ( $false = $true )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f41,f23]) ).
thf(f23,plain,
( ( cQ = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f41,plain,
( ( cQ = $true )
| ( cP = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f28,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f10,f25,f21]) ).
thf(f10,plain,
( ( cQ = $false )
| ( cP = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
cP != cQ,
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f19,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f9,f16,f12]) ).
thf(f9,plain,
( ( cP = $true )
| ( cQ = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO371^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:28:59 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SYO371^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.49 % Domain : Syntactic
% 0.32/0.49 % Problem : TPS problem from EXTENSIONALITY
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English :
% 0.32/0.49
% 0.32/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.49 % Source : [Bro09]
% 0.32/0.49 % Names : tps_0650 [Bro09]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v5.4.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.32/0.49 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.32/0.49 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 4 ( 4 avg)
% 0.32/0.49 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 2 @)
% 0.32/0.49 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 5 ( 5 avg)
% 0.32/0.49 % Number of types : 1 ( 0 usr)
% 0.32/0.49 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.32/0.49 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.32/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(cQ,type,
% 0.32/0.49 cQ: $o ).
% 0.32/0.49
% 0.32/0.49 thf(cP,type,
% 0.32/0.49 cP: $o ).
% 0.32/0.49
% 0.32/0.49 thf(cEXT_O_LEIB,conjecture,
% 0.32/0.49 ( ! [R: $o > $o] :
% 0.32/0.49 ( ( R @ cP )
% 0.32/0.49 => ( R @ cQ ) )
% 0.32/0.49 => ( cP
% 0.32/0.49 <=> cQ ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.65/1.42 ---- Embedded in THF ---
% 1.65/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.42 %%% Generated on Tue Feb 24 14:29:00 EST 2026
% 1.65/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.42 %%% Logic specification used:
% 1.65/1.42 %%% thf(spec, logic, $$dhol).
% 1.65/1.42
% 1.65/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QbT9KEe5tC/DTF2DTF2576.p
% See solution above
% 1.65/1.42 ------------------------
% 1.65/1.43 ---- Cleaned THF ---
% 1.65/1.43 thf(cQ,type,
% 1.65/1.43 cQ: $o ).
% 1.65/1.43
% 1.65/1.43 thf(cP,type,
% 1.65/1.43 cP: $o ).
% 1.65/1.43
% 1.65/1.43 thf(cEXT_O_LEIB,conjecture,
% 1.65/1.43 ( ! [R: $o > $o] :
% 1.65/1.43 ( ( R @ cP )
% 1.65/1.43 => ( R @ cQ ) )
% 1.65/1.43 => ( cP
% 1.65/1.43 <=> cQ ) ) ).
% 1.65/1.43 ------------------------
% 1.65/1.45 % (2707)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_2576 for (3000ds/4Mi)
% 1.65/1.45 % (2710)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_2576 for (3000ds/2Mi)
% 1.65/1.45 % (2712)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2576 for (3000ds/18Mi)
% 1.65/1.45 % (2708)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_2576 for (3000ds/27Mi)
% 1.65/1.45 % (2709)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2576 for (3000ds/2Mi)
% 1.65/1.45 % (2706)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2576 for (3000ds/183Mi)
% 1.65/1.45 % (2711)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_2576 for (3000ds/275Mi)
% 1.65/1.45 % (2709)Instruction limit reached!
% 1.65/1.45 % (2709)------------------------------
% 1.65/1.45 % (2709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (2709)Termination reason: Unknown
% 1.65/1.45 % (2710)Instruction limit reached!
% 1.65/1.45 % (2710)------------------------------
% 1.65/1.45 % (2710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (2709)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (2709)Memory used [KB]: 5500
% 1.65/1.45 % (2709)Time elapsed: 0.003 s
% 1.65/1.45 % (2709)Instructions burned: 2 (million)
% 1.65/1.45 % (2709)------------------------------
% 1.65/1.45 % (2709)------------------------------
% 1.65/1.45 % (2710)Termination reason: Unknown
% 1.65/1.45 % (2710)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (2710)Memory used [KB]: 5500
% 1.65/1.45 % (2710)Time elapsed: 0.003 s
% 1.65/1.45 % (2710)Instructions burned: 2 (million)
% 1.65/1.45 % (2710)------------------------------
% 1.65/1.45 % (2710)------------------------------
% 1.65/1.45 % (2708)Refutation not found, incomplete strategy
% 1.65/1.45 % (2708)------------------------------
% 1.65/1.45 % (2708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (2708)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.45
% 1.65/1.45
% 1.65/1.45 % (2708)Memory used [KB]: 5500
% 1.65/1.45 % (2708)Time elapsed: 0.003 s
% 1.65/1.45 % (2708)Instructions burned: 1 (million)
% 1.65/1.45 % (2708)------------------------------
% 1.65/1.45 % (2708)------------------------------
% 1.65/1.45 % (2711)First to succeed.
% 1.65/1.45 % (2707)Instruction limit reached!
% 1.65/1.45 % (2707)------------------------------
% 1.65/1.45 % (2707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (2707)Termination reason: Unknown
% 1.65/1.45 % (2707)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (2707)Memory used [KB]: 5500
% 1.65/1.45 % (2707)Time elapsed: 0.005 s
% 1.65/1.45 % (2707)Instructions burned: 5 (million)
% 1.65/1.45 % (2707)------------------------------
% 1.65/1.45 % (2707)------------------------------
% 1.65/1.45 % (2712)Also succeeded, but the first one will report.
% 1.65/1.45 % (2711)Refutation found. Thanks to Tanya!
% 1.65/1.45 % SZS status Theorem for DTF2THF_2576
% 1.65/1.45 % SZS output start Proof for DTF2THF_2576
% 1.65/1.45 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.65/1.45 thf(f74,plain,(
% 1.65/1.45 $false),
% 1.65/1.45 inference(avatar_sat_refutation,[status(thm)],[f19,f28,f62,f65,f73])).
% 1.65/1.45 thf(f73,plain,(
% 1.65/1.45 ~spl0_2 | ~spl0_4),
% 1.65/1.45 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.65/1.45 thf(f72,plain,(
% 1.65/1.45 $false | (~spl0_2 | ~spl0_4)),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.65/1.45 thf(f71,plain,(
% 1.65/1.45 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 1.65/1.45 inference(forward_demodulation,[status(thm)],[f70,f27])).
% 1.65/1.45 thf(f27,plain,(
% 1.65/1.45 (cP = $false) | ~spl0_4),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.65/1.45 thf(f25,definition,(
% 1.65/1.45 spl0_4 <=> (cP = $false)),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.65/1.45 thf(f70,plain,(
% 1.65/1.45 (cP = $true) | ~spl0_2),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.65/1.45 thf(f69,plain,(
% 1.65/1.45 ($false = $true) | (cP = $true) | ~spl0_2),
% 1.65/1.45 inference(forward_demodulation,[status(thm)],[f40,f18])).
% 1.65/1.45 thf(f18,plain,(
% 1.65/1.45 (cQ = $true) | ~spl0_2),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.65/1.45 thf(f16,definition,(
% 1.65/1.45 spl0_2 <=> (cQ = $true)),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.45 thf(f40,plain,(
% 1.65/1.45 (cQ = $false) | (cP = $true)),
% 1.65/1.45 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.65/1.45 thf(f30,plain,(
% 1.65/1.45 (cP = cQ)),
% 1.65/1.45 inference(leibniz_equality_elimination,[status(thm)],[f7])).
% 1.65/1.45 thf(f7,plain,(
% 1.65/1.45 ( ! [X0 : $o > $o] : (((X0 @ cQ) = $true) | ((X0 @ cP) != $true)) )),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f6])).
% 1.65/1.45 thf(f6,plain,(
% 1.65/1.45 (cP != cQ) & ! [X0 : $o > $o] : (((X0 @ cQ) = $true) | ((X0 @ cP) != $true))),
% 1.65/1.45 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.45 thf(f5,plain,(
% 1.65/1.45 ~(! [X0 : $o > $o] : (((X0 @ cP) = $true) => ((X0 @ cQ) = $true)) => (cP = cQ))),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.45 thf(f4,plain,(
% 1.65/1.45 ~(! [X0 : $o > $o] : ((X0 @ cP) => (X0 @ cQ)) => (cP <=> cQ))),
% 1.65/1.45 inference(rectify,[status(thm)],[f2])).
% 1.65/1.45 thf(f2,negated_conjecture,(
% 1.65/1.45 ~(! [X0 : $o > $o] : ((X0 @ cP) => (X0 @ cQ)) => (cP <=> cQ))),
% 1.65/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.45 thf(f1,conjecture,(
% 1.65/1.45 ! [X0 : $o > $o] : ((X0 @ cP) => (X0 @ cQ)) => (cP <=> cQ)),
% 1.65/1.45 file('/export/starexec/sandbox/tmp/tmp.QbT9KEe5tC/DTF2THF_2576.p',cEXT_O_LEIB)).
% 1.65/1.45 thf(f65,plain,(
% 1.65/1.45 spl0_2 | ~spl0_1),
% 1.65/1.45 inference(avatar_split_clause,[status(thm)],[f44,f12,f16])).
% 1.65/1.45 thf(f12,definition,(
% 1.65/1.45 spl0_1 <=> (cP = $true)),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.45 thf(f44,plain,(
% 1.65/1.45 (cP != $true) | (cQ = $true)),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.65/1.45 thf(f31,plain,(
% 1.65/1.45 ($true != ((^[Y0 : $o]: (Y0)) @ cP)) | ($true = ((^[Y0 : $o]: (Y0)) @ cQ))),
% 1.65/1.45 inference(primitive_instantiation,[status(thm)],[f7])).
% 1.65/1.45 thf(f62,plain,(
% 1.65/1.45 spl0_4 | ~spl0_3),
% 1.65/1.45 inference(avatar_split_clause,[status(thm)],[f61,f21,f25])).
% 1.65/1.45 thf(f21,definition,(
% 1.65/1.45 spl0_3 <=> (cQ = $false)),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.65/1.45 thf(f61,plain,(
% 1.65/1.45 (cP = $false) | ~spl0_3),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.65/1.45 thf(f60,plain,(
% 1.65/1.45 (cP = $false) | ($false = $true) | ~spl0_3),
% 1.65/1.45 inference(forward_demodulation,[status(thm)],[f41,f23])).
% 1.65/1.45 thf(f23,plain,(
% 1.65/1.45 (cQ = $false) | ~spl0_3),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.65/1.45 thf(f41,plain,(
% 1.65/1.45 (cQ = $true) | (cP = $false)),
% 1.65/1.45 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.65/1.45 thf(f28,plain,(
% 1.65/1.45 spl0_3 | spl0_4),
% 1.65/1.45 inference(avatar_split_clause,[status(thm)],[f10,f25,f21])).
% 1.65/1.45 thf(f10,plain,(
% 1.65/1.45 (cQ = $false) | (cP = $false)),
% 1.65/1.45 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.65/1.45 thf(f8,plain,(
% 1.65/1.45 (cP != cQ)),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f6])).
% 1.65/1.45 thf(f19,plain,(
% 1.65/1.45 spl0_1 | spl0_2),
% 1.65/1.45 inference(avatar_split_clause,[status(thm)],[f9,f16,f12])).
% 1.65/1.45 thf(f9,plain,(
% 1.65/1.45 (cP = $true) | (cQ = $true)),
% 1.65/1.45 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.65/1.45 % SZS output end Proof for DTF2THF_2576
% 1.65/1.45 % (2711)------------------------------
% 1.65/1.45 % (2711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (2711)Termination reason: Refutation
% 1.65/1.45
% 1.65/1.45 % (2711)Memory used [KB]: 5500
% 1.65/1.45 % (2711)Time elapsed: 0.004 s
% 1.65/1.45 % (2711)Instructions burned: 3 (million)
% 1.65/1.45 % (2711)------------------------------
% 1.65/1.45 % (2711)------------------------------
% 1.65/1.45 % (2705)Success in time 0.017 s
%------------------------------------------------------------------------------