%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO381^5 : 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 : n018.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 09:54:05 AM UTC 2026
% Result : Theorem 1.60s 1.32s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 161 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 185 ( 48 ~; 32 |; 3 &; 90 @)
% ( 8 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 42 !; 18 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $i ).
thf(func_def_5,type,
sK1: $i > $i ).
thf(f40,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f21,f28,f31,f33,f36,f39]) ).
thf(f39,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f17,f27]) ).
thf(f27,plain,
( ! [X6: $i] :
( ( cR @ sK2 @ X6 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl3_4
<=> ! [X6: $i] :
( ( cR @ sK2 @ X6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f17,plain,
( ! [X0: $i] :
( ( cR @ X0 @ ( sK0 @ X0 ) )
!= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl3_1
<=> ! [X0: $i] :
( ( cR @ X0 @ ( sK0 @ X0 ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f36,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f35]) ).
thf(f35,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f20,f27]) ).
thf(f20,plain,
( ! [X2: $i] :
( $true
!= ( cR @ X2 @ ( sK1 @ X2 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl3_2
<=> ! [X2: $i] :
( $true
!= ( cR @ X2 @ ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f33,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f17,f24]) ).
thf(f24,plain,
( ! [X0: $i,X4: $i] :
( $true
= ( cR @ X0 @ X4 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl3_3
<=> ! [X4: $i,X0: $i] :
( $true
= ( cR @ X0 @ X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f31,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true != $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f20,f24]) ).
thf(f28,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f26,f23]) ).
thf(f13,plain,
! [X0: $i,X6: $i,X4: $i] :
( ( $true
= ( cR @ X0 @ X4 ) )
| ( ( cR @ sK2 @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( ( ( cR @ X0 @ ( sK0 @ X0 ) )
!= $true )
| ! [X2: $i] :
( $true
!= ( cR @ X2 @ ( sK1 @ X2 ) ) ) )
& ( ! [X4: $i] :
( $true
= ( cR @ X0 @ X4 ) )
| ! [X6: $i] :
( ( cR @ sK2 @ X6 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
( $true
!= ( cR @ X0 @ X1 ) )
=> ( ( cR @ X0 @ ( sK0 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: $i] :
( ? [X3: $i] :
( $true
!= ( cR @ X2 @ X3 ) )
=> ( $true
!= ( cR @ X2 @ ( sK1 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: $i] :
! [X6: $i] :
( $true
= ( cR @ X5 @ X6 ) )
=> ! [X6: $i] :
( ( cR @ sK2 @ X6 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: $i] :
( ( ? [X1: $i] :
( $true
!= ( cR @ X0 @ X1 ) )
| ! [X2: $i] :
? [X3: $i] :
( $true
!= ( cR @ X2 @ X3 ) ) )
& ( ! [X4: $i] :
( $true
= ( cR @ X0 @ X4 ) )
| ? [X5: $i] :
! [X6: $i] :
( $true
= ( cR @ X5 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i] :
( ( ? [X1: $i] :
( $true
!= ( cR @ X0 @ X1 ) )
| ! [X2: $i] :
? [X3: $i] :
( $true
!= ( cR @ X2 @ X3 ) ) )
& ( ! [X1: $i] :
( $true
= ( cR @ X0 @ X1 ) )
| ? [X2: $i] :
! [X3: $i] :
( $true
= ( cR @ X2 @ X3 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i] :
( ? [X2: $i] :
! [X3: $i] :
( $true
= ( cR @ X2 @ X3 ) )
<~> ! [X1: $i] :
( $true
= ( cR @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
( ! [X1: $i] :
( $true
= ( cR @ X0 @ X1 ) )
<=> ? [X2: $i] :
! [X3: $i] :
( $true
= ( cR @ X2 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
( ! [X1: $i] : ( cR @ X0 @ X1 )
<=> ? [X2: $i] :
! [X3: $i] : ( cR @ X2 @ X3 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
( ! [X3: $i] : ( cR @ X0 @ X3 )
<=> ? [X1: $i] :
! [X2: $i] : ( cR @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
( ! [X3: $i] : ( cR @ X0 @ X3 )
<=> ? [X1: $i] :
! [X2: $i] : ( cR @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fdAeNE6K5M/DTF2THF_13643.p',cX_2002_12_17) ).
thf(f21,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f19,f16]) ).
thf(f14,plain,
! [X2: $i,X0: $i] :
( ( ( cR @ X0 @ ( sK0 @ X0 ) )
!= $true )
| ( $true
!= ( cR @ X2 @ ( sK1 @ X2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO381^5 : 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 : n018.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 14:29:01 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
% 0.24/0.46 ---- Original DTF file ---
% 0.24/0.46 thf(spec,logic,$$dhol).
% 0.24/0.46 %------------------------------------------------------------------------------
% 0.24/0.46 % File : SYO381^5 : TPTP v9.2.1. Released v4.0.0.
% 0.24/0.46 % Domain : Syntactic
% 0.24/0.46 % Problem : TPS problem X-2002-12-17
% 0.24/0.46 % Version : Especial.
% 0.24/0.46 % English : Suggested by a student's answer on a test.
% 0.24/0.46
% 0.24/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.24/0.46 % Source : [Bro09]
% 0.24/0.46 % Names : tps_0089 [Bro09]
% 0.24/0.46 % : X-2002-12-17 [TPS]
% 0.24/0.46
% 0.24/0.46 % Status : Theorem
% 0.24/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.24/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.24/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.24/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.24/0.46 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.24/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.24/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.24/0.46 % Number of types : 2 ( 0 usr)
% 0.24/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.24/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.24/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.24/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.24/0.46
% 0.24/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.24/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.24/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.24/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.24/0.46 %------------------------------------------------------------------------------
% 0.24/0.46 thf(cR,type,
% 0.24/0.46 cR: $i > $i > $o ).
% 0.24/0.46
% 0.24/0.46 thf(cX_2002_12_17,conjecture,
% 0.24/0.46 ? [Xx: $i] :
% 0.24/0.46 ( ? [Xz: $i] :
% 0.24/0.46 ! [Xy: $i] : ( cR @ Xz @ Xy )
% 0.24/0.46 <=> ! [Xw: $i] : ( cR @ Xx @ Xw ) ) ).
% 0.24/0.46
% 0.24/0.46 %------------------------------------------------------------------------------
% 0.24/0.46 ------------------------
% 1.43/1.29 ---- Embedded in THF ---
% 1.43/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.29 %%% Generated on Tue Feb 24 14:29:02 EST 2026
% 1.43/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.29 %%% Logic specification used:
% 1.43/1.29 %%% thf(spec, logic, $$dhol).
% 1.43/1.29
% 1.43/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.fdAeNE6K5M/DTF2DTF13643.p
% See solution above
% 1.43/1.29 ------------------------
% 1.60/1.30 ---- Cleaned THF ---
% 1.60/1.30 thf(cR,type,
% 1.60/1.30 cR: $i > $i > $o ).
% 1.60/1.30
% 1.60/1.30 thf(cX_2002_12_17,conjecture,
% 1.60/1.30 ? [Xx: $i] :
% 1.60/1.30 ( ? [Xz: $i] :
% 1.60/1.30 ! [Xy: $i] : ( cR @ Xz @ Xy )
% 1.60/1.30 <=> ! [Xw: $i] : ( cR @ Xx @ Xw ) ) ).
% 1.60/1.30 ------------------------
% 1.60/1.31 % (13802)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13643 for (2999ds/183Mi)
% 1.60/1.31 % (13803)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_13643 for (2999ds/4Mi)
% 1.60/1.31 % (13802)First to succeed.
% 1.60/1.32 % (13803)Also succeeded, but the first one will report.
% 1.60/1.32 % (13802)Refutation found. Thanks to Tanya!
% 1.60/1.32 % SZS status Theorem for DTF2THF_13643
% 1.60/1.32 % SZS output start Proof for DTF2THF_13643
% 1.60/1.32 thf(func_def_0, type, cR: $i > $i > $o).
% 1.60/1.32 thf(func_def_4, type, sK0: $i > $i).
% 1.60/1.32 thf(func_def_5, type, sK1: $i > $i).
% 1.60/1.32 thf(f40,plain,(
% 1.60/1.32 $false),
% 1.60/1.32 inference(avatar_sat_refutation,[status(thm)],[f21,f28,f31,f33,f36,f39])).
% 1.60/1.32 thf(f39,plain,(
% 1.60/1.32 ~spl3_1 | ~spl3_4),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.60/1.32 thf(f38,plain,(
% 1.60/1.32 $false | (~spl3_1 | ~spl3_4)),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.60/1.32 thf(f37,plain,(
% 1.60/1.32 ($true != $true) | (~spl3_1 | ~spl3_4)),
% 1.60/1.32 inference(superposition,[status(thm)],[f17,f27])).
% 1.60/1.32 thf(f27,plain,(
% 1.60/1.32 ( ! [X6 : $i] : (((cR @ sK2 @ X6) = $true)) ) | ~spl3_4),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.60/1.32 thf(f26,definition,(
% 1.60/1.32 spl3_4 <=> ! [X6 : $i] : ((cR @ sK2 @ X6) = $true)),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.60/1.32 thf(f17,plain,(
% 1.60/1.32 ( ! [X0 : $i] : (((cR @ X0 @ (sK0 @ X0)) != $true)) ) | ~spl3_1),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.60/1.32 thf(f16,definition,(
% 1.60/1.32 spl3_1 <=> ! [X0 : $i] : ((cR @ X0 @ (sK0 @ X0)) != $true)),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.60/1.32 thf(f36,plain,(
% 1.60/1.32 ~spl3_2 | ~spl3_4),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f35])).
% 1.60/1.32 thf(f35,plain,(
% 1.60/1.32 $false | (~spl3_2 | ~spl3_4)),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.60/1.32 thf(f34,plain,(
% 1.60/1.32 ($true != $true) | (~spl3_2 | ~spl3_4)),
% 1.60/1.32 inference(superposition,[status(thm)],[f20,f27])).
% 1.60/1.32 thf(f20,plain,(
% 1.60/1.32 ( ! [X2 : $i] : (($true != (cR @ X2 @ (sK1 @ X2)))) ) | ~spl3_2),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.60/1.32 thf(f19,definition,(
% 1.60/1.32 spl3_2 <=> ! [X2 : $i] : ($true != (cR @ X2 @ (sK1 @ X2)))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.60/1.32 thf(f33,plain,(
% 1.60/1.32 ~spl3_1 | ~spl3_3),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f32])).
% 1.60/1.32 thf(f32,plain,(
% 1.60/1.32 $false | (~spl3_1 | ~spl3_3)),
% 1.60/1.32 inference(subsumption_resolution,[status(thm)],[f17,f24])).
% 1.60/1.32 thf(f24,plain,(
% 1.60/1.32 ( ! [X0 : $i,X4 : $i] : (($true = (cR @ X0 @ X4))) ) | ~spl3_3),
% 1.60/1.32 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.60/1.32 thf(f23,definition,(
% 1.60/1.32 spl3_3 <=> ! [X4 : $i,X0 : $i] : ($true = (cR @ X0 @ X4))),
% 1.60/1.32 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.60/1.32 thf(f31,plain,(
% 1.60/1.32 ~spl3_2 | ~spl3_3),
% 1.60/1.32 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 1.60/1.32 thf(f30,plain,(
% 1.60/1.32 $false | (~spl3_2 | ~spl3_3)),
% 1.60/1.32 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.60/1.32 thf(f29,plain,(
% 1.60/1.32 ($true != $true) | (~spl3_2 | ~spl3_3)),
% 1.60/1.32 inference(superposition,[status(thm)],[f20,f24])).
% 1.60/1.32 thf(f28,plain,(
% 1.60/1.32 spl3_3 | spl3_4),
% 1.60/1.32 inference(avatar_split_clause,[status(thm)],[f13,f26,f23])).
% 1.60/1.32 thf(f13,plain,(
% 1.60/1.32 ( ! [X0 : $i,X6 : $i,X4 : $i] : (($true = (cR @ X0 @ X4)) | ((cR @ sK2 @ X6) = $true)) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.60/1.32 thf(f12,plain,(
% 1.60/1.32 ! [X0 : $i] : ((((cR @ X0 @ (sK0 @ X0)) != $true) | ! [X2 : $i] : ($true != (cR @ X2 @ (sK1 @ X2)))) & (! [X4 : $i] : ($true = (cR @ X0 @ X4)) | ! [X6 : $i] : ((cR @ sK2 @ X6) = $true)))),
% 1.60/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.60/1.32 thf(f9,plain,(
% 1.60/1.32 ! [X0 : $i] : (? [X1 : $i] : ($true != (cR @ X0 @ X1)) => ((cR @ X0 @ (sK0 @ X0)) != $true))),
% 1.60/1.32 introduced(definition,[],[choice_axiom])).
% 1.60/1.32 thf(f10,plain,(
% 1.60/1.32 ! [X2 : $i] : (? [X3 : $i] : ($true != (cR @ X2 @ X3)) => ($true != (cR @ X2 @ (sK1 @ X2))))),
% 1.60/1.32 introduced(definition,[],[choice_axiom])).
% 1.60/1.32 thf(f11,plain,(
% 1.60/1.32 ? [X5 : $i] : ! [X6 : $i] : ($true = (cR @ X5 @ X6)) => ! [X6 : $i] : ((cR @ sK2 @ X6) = $true)),
% 1.60/1.32 introduced(definition,[],[choice_axiom])).
% 1.60/1.32 thf(f8,plain,(
% 1.60/1.32 ! [X0 : $i] : ((? [X1 : $i] : ($true != (cR @ X0 @ X1)) | ! [X2 : $i] : ? [X3 : $i] : ($true != (cR @ X2 @ X3))) & (! [X4 : $i] : ($true = (cR @ X0 @ X4)) | ? [X5 : $i] : ! [X6 : $i] : ($true = (cR @ X5 @ X6))))),
% 1.60/1.32 inference(rectify,[status(thm)],[f7])).
% 1.60/1.32 thf(f7,plain,(
% 1.60/1.32 ! [X0 : $i] : ((? [X1 : $i] : ($true != (cR @ X0 @ X1)) | ! [X2 : $i] : ? [X3 : $i] : ($true != (cR @ X2 @ X3))) & (! [X1 : $i] : ($true = (cR @ X0 @ X1)) | ? [X2 : $i] : ! [X3 : $i] : ($true = (cR @ X2 @ X3))))),
% 1.60/1.32 inference(nnf_transformation,[status(thm)],[f6])).
% 1.60/1.32 thf(f6,plain,(
% 1.60/1.32 ! [X0 : $i] : (? [X2 : $i] : ! [X3 : $i] : ($true = (cR @ X2 @ X3)) <~> ! [X1 : $i] : ($true = (cR @ X0 @ X1)))),
% 1.60/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.60/1.32 thf(f5,plain,(
% 1.60/1.32 ~? [X0 : $i] : (! [X1 : $i] : ($true = (cR @ X0 @ X1)) <=> ? [X2 : $i] : ! [X3 : $i] : ($true = (cR @ X2 @ X3)))),
% 1.60/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.32 thf(f4,plain,(
% 1.60/1.32 ~? [X0 : $i] : (! [X1 : $i] : (cR @ X0 @ X1) <=> ? [X2 : $i] : ! [X3 : $i] : (cR @ X2 @ X3))),
% 1.60/1.32 inference(rectify,[status(thm)],[f2])).
% 1.60/1.32 thf(f2,negated_conjecture,(
% 1.60/1.32 ~? [X0 : $i] : (! [X3 : $i] : (cR @ X0 @ X3) <=> ? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2))),
% 1.60/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.32 thf(f1,conjecture,(
% 1.60/1.32 ? [X0 : $i] : (! [X3 : $i] : (cR @ X0 @ X3) <=> ? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2))),
% 1.60/1.32 file('/export/starexec/sandbox2/tmp/tmp.fdAeNE6K5M/DTF2THF_13643.p',cX_2002_12_17)).
% 1.60/1.32 thf(f21,plain,(
% 1.60/1.32 spl3_1 | spl3_2),
% 1.60/1.32 inference(avatar_split_clause,[status(thm)],[f14,f19,f16])).
% 1.60/1.32 thf(f14,plain,(
% 1.60/1.32 ( ! [X2 : $i,X0 : $i] : (((cR @ X0 @ (sK0 @ X0)) != $true) | ($true != (cR @ X2 @ (sK1 @ X2)))) )),
% 1.60/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.60/1.32 % SZS output end Proof for DTF2THF_13643
% 1.60/1.32 % (13802)------------------------------
% 1.60/1.32 % (13802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (13802)Termination reason: Refutation
% 1.60/1.32
% 1.60/1.32 % (13802)Memory used [KB]: 5500
% 1.60/1.32 % (13802)Time elapsed: 0.004 s
% 1.60/1.32 % (13802)Instructions burned: 1 (million)
% 1.60/1.32 % (13802)------------------------------
% 1.60/1.32 % (13802)------------------------------
% 1.60/1.32 % (13801)Success in time 0.015 s
%------------------------------------------------------------------------------