%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO160^5 : 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 : n003.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 09:53:32 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 318 ( 67 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 255 ( 59 ~; 66 |; 25 &; 88 @)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cR: $i > $o ).
thf(func_def_4,type,
cQ: $i > $o ).
thf(func_def_5,type,
cP: $i > $o ).
thf(f55,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f32,f37,f42,f46,f48,f52,f54]) ).
thf(f54,plain,
( spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| spl0_2
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f20,f49]) ).
thf(f49,plain,
( ! [X2: $i] :
( $true
= ( cR @ X2 ) )
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f10,f31]) ).
thf(f31,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_5
<=> ! [X0: $i] :
( ( cQ @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f10,plain,
! [X2: $i] :
( ( $true
!= ( cQ @ X2 ) )
| ( $true
= ( cR @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( ( cR @ c )
!= $true )
| ( ( cR @ b )
!= $true )
| ( ( cR @ a )
!= $true ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ! [X1: $i] :
( $true
= ( cP @ X1 ) ) )
& ! [X2: $i] :
( ( $true
!= ( cQ @ X2 ) )
| ( $true
= ( cR @ X2 ) ) )
& ! [X3: $i] :
( ( ( cR @ X3 )
= $true )
| ( $true
!= ( cP @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( cR @ c )
!= $true )
| ( ( cR @ b )
!= $true )
| ( ( cR @ a )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cQ @ X2 ) )
| ! [X1: $i] :
( $true
= ( cP @ X1 ) ) )
& ! [X3: $i] :
( ( $true
!= ( cQ @ X3 ) )
| ( ( cR @ X3 )
= $true ) )
& ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( ( cP @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ( cR @ c )
!= $true )
| ( ( cR @ b )
!= $true )
| ( ( cR @ a )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( cQ @ X3 ) )
| ( ( cR @ X3 )
= $true ) )
& ( ! [X2: $i] :
( $true
= ( cQ @ X2 ) )
| ! [X1: $i] :
( $true
= ( cP @ X1 ) ) )
& ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( ( cP @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X3: $i] :
( ( $true
= ( cQ @ X3 ) )
=> ( ( cR @ X3 )
= $true ) )
& ( ! [X2: $i] :
( $true
= ( cQ @ X2 ) )
| ! [X1: $i] :
( $true
= ( cP @ X1 ) ) )
& ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( cR @ X0 )
= $true ) ) )
=> ( ( ( cR @ b )
= $true )
& ( ( cR @ c )
= $true )
& ( ( cR @ a )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
& ( ! [X1: $i] : ( cP @ X1 )
| ! [X2: $i] : ( cQ @ X2 ) )
& ! [X3: $i] :
( ( cQ @ X3 )
=> ( cR @ X3 ) ) )
=> ( ( cR @ c )
& ( cR @ b )
& ( cR @ a ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
& ( ! [X0: $i] : ( cP @ X0 )
| ! [X0: $i] : ( cQ @ X0 ) )
& ! [X0: $i] :
( ( cQ @ X0 )
=> ( cR @ X0 ) ) )
=> ( ( cR @ c )
& ( cR @ b )
& ( cR @ a ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
& ( ! [X0: $i] : ( cP @ X0 )
| ! [X0: $i] : ( cQ @ X0 ) )
& ! [X0: $i] :
( ( cQ @ X0 )
=> ( cR @ X0 ) ) )
=> ( ( cR @ c )
& ( cR @ b )
& ( cR @ a ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K6vWZcmasC/DTF2THF_31027.p',cDISJ_THIRD) ).
thf(f20,plain,
( ( ( cR @ a )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl0_2
<=> ( ( cR @ a )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f52,plain,
( spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true != $true )
| spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f24,f49]) ).
thf(f24,plain,
( ( ( cR @ c )
!= $true )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl0_3
<=> ( ( cR @ c )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f48,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f24,f43]) ).
thf(f43,plain,
( ! [X3: $i] :
( ( cR @ X3 )
= $true )
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f9,f28]) ).
thf(f28,plain,
( ! [X1: $i] :
( $true
= ( cP @ X1 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_4
<=> ! [X1: $i] :
( $true
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f9,plain,
! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( cR @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f46,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true != $true )
| spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f20,f43]) ).
thf(f42,plain,
( spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f16,f39]) ).
thf(f39,plain,
( ! [X0: $i] :
( ( cR @ X0 )
= $true )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ X0 )
= $true ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f10,f31]) ).
thf(f16,plain,
( ( ( cR @ b )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f14]) ).
thf(f14,definition,
( spl0_1
<=> ( ( cR @ b )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f37,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true != $true )
| spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f16,f34]) ).
thf(f34,plain,
( ! [X0: $i] :
( ( cR @ X0 )
= $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f9,f28]) ).
thf(f32,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f11,f30,f27]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( cQ @ X0 )
= $true )
| ( $true
= ( cP @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f25,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f12,f22,f18,f14]) ).
thf(f12,plain,
( ( ( cR @ b )
!= $true )
| ( ( cR @ a )
!= $true )
| ( ( cR @ c )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO160^5 : TPTP v9.2.1. Released v4.0.0.
% 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n003.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:24:41 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.44 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYO160^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : TPS problem from BASIC-FO-THMS
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0861 [Bro09]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.29/0.45 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 9 ( 9 avg)
% 0.29/0.45 % Number of connectives : 17 ( 0 ~; 1 |; 4 &; 9 @)
% 0.29/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 6 ( 6 usr; 3 con; 0-1 aty)
% 0.29/0.45 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.29/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(c,type,
% 0.29/0.45 c: $i ).
% 0.29/0.45
% 0.29/0.45 thf(cR,type,
% 0.29/0.45 cR: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(b,type,
% 0.29/0.45 b: $i ).
% 0.29/0.45
% 0.29/0.45 thf(a,type,
% 0.29/0.45 a: $i ).
% 0.29/0.45
% 0.29/0.45 thf(cQ,type,
% 0.29/0.45 cQ: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cP,type,
% 0.29/0.45 cP: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cDISJ_THIRD,conjecture,
% 0.29/0.45 ( ( ( ! [Xx: $i] : ( cP @ Xx )
% 0.29/0.45 | ! [Xx: $i] : ( cQ @ Xx ) )
% 0.29/0.45 & ! [Xx: $i] :
% 0.29/0.45 ( ( cP @ Xx )
% 0.29/0.45 => ( cR @ Xx ) )
% 0.29/0.45 & ! [Xx: $i] :
% 0.29/0.45 ( ( cQ @ Xx )
% 0.29/0.45 => ( cR @ Xx ) ) )
% 0.29/0.45 => ( ( cR @ a )
% 0.29/0.45 & ( cR @ b )
% 0.29/0.45 & ( cR @ c ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 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 14:24:41 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.K6vWZcmasC/DTF2DTF31027.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.28 thf(c,type,
% 1.48/1.28 c: $i ).
% 1.48/1.28
% 1.48/1.28 thf(cR,type,
% 1.48/1.28 cR: $i > $o ).
% 1.48/1.28
% 1.48/1.28 thf(b,type,
% 1.48/1.28 b: $i ).
% 1.48/1.28
% 1.48/1.28 thf(a,type,
% 1.48/1.28 a: $i ).
% 1.48/1.28
% 1.48/1.28 thf(cQ,type,
% 1.48/1.28 cQ: $i > $o ).
% 1.48/1.28
% 1.48/1.28 thf(cP,type,
% 1.48/1.28 cP: $i > $o ).
% 1.48/1.28
% 1.48/1.28 thf(cDISJ_THIRD,conjecture,
% 1.48/1.28 ( ( ( ! [Xx: $i] : ( cP @ Xx )
% 1.48/1.28 | ! [Xx: $i] : ( cQ @ Xx ) )
% 1.48/1.28 & ! [Xx: $i] :
% 1.48/1.28 ( ( cP @ Xx )
% 1.48/1.28 => ( cR @ Xx ) )
% 1.48/1.28 & ! [Xx: $i] :
% 1.48/1.28 ( ( cQ @ Xx )
% 1.48/1.28 => ( cR @ Xx ) ) )
% 1.48/1.28 => ( ( cR @ a )
% 1.48/1.28 & ( cR @ b )
% 1.48/1.28 & ( cR @ c ) ) ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (31179)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31027 for (2999ds/18Mi)
% 1.48/1.29 % (31178)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_31027 for (2999ds/275Mi)
% 1.48/1.29 % (31179)First to succeed.
% 1.48/1.29 % (31178)Also succeeded, but the first one will report.
% 1.48/1.29 % (31179)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_31027
% 1.48/1.29 % SZS output start Proof for DTF2THF_31027
% 1.48/1.29 thf(func_def_1, type, cR: $i > $o).
% 1.48/1.29 thf(func_def_4, type, cQ: $i > $o).
% 1.48/1.29 thf(func_def_5, type, cP: $i > $o).
% 1.48/1.29 thf(f55,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(avatar_sat_refutation,[status(thm)],[f25,f32,f37,f42,f46,f48,f52,f54])).
% 1.48/1.29 thf(f54,plain,(
% 1.48/1.29 spl0_2 | ~spl0_5),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.48/1.29 thf(f53,plain,(
% 1.48/1.29 $false | (spl0_2 | ~spl0_5)),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f20,f49])).
% 1.48/1.29 thf(f49,plain,(
% 1.48/1.29 ( ! [X2 : $i] : (($true = (cR @ X2))) ) | ~spl0_5),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f10,f31])).
% 1.48/1.29 thf(f31,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (((cQ @ X0) = $true)) ) | ~spl0_5),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.48/1.29 thf(f30,definition,(
% 1.48/1.29 spl0_5 <=> ! [X0 : $i] : ((cQ @ X0) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ( ! [X2 : $i] : (($true != (cQ @ X2)) | ($true = (cR @ X2))) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 (((cR @ c) != $true) | ((cR @ b) != $true) | ((cR @ a) != $true)) & (! [X0 : $i] : ((cQ @ X0) = $true) | ! [X1 : $i] : ($true = (cP @ X1))) & ! [X2 : $i] : (($true != (cQ @ X2)) | ($true = (cR @ X2))) & ! [X3 : $i] : (((cR @ X3) = $true) | ($true != (cP @ X3)))),
% 1.48/1.29 inference(rectify,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 (((cR @ c) != $true) | ((cR @ b) != $true) | ((cR @ a) != $true)) & (! [X2 : $i] : ($true = (cQ @ X2)) | ! [X1 : $i] : ($true = (cP @ X1))) & ! [X3 : $i] : (($true != (cQ @ X3)) | ((cR @ X3) = $true)) & ! [X0 : $i] : (((cR @ X0) = $true) | ((cP @ X0) != $true))),
% 1.48/1.29 inference(flattening,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 (((cR @ c) != $true) | ((cR @ b) != $true) | ((cR @ a) != $true)) & (! [X3 : $i] : (($true != (cQ @ X3)) | ((cR @ X3) = $true)) & (! [X2 : $i] : ($true = (cQ @ X2)) | ! [X1 : $i] : ($true = (cP @ X1))) & ! [X0 : $i] : (((cR @ X0) = $true) | ((cP @ X0) != $true)))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ~((! [X3 : $i] : (($true = (cQ @ X3)) => ((cR @ X3) = $true)) & (! [X2 : $i] : ($true = (cQ @ X2)) | ! [X1 : $i] : ($true = (cP @ X1))) & ! [X0 : $i] : (((cP @ X0) = $true) => ((cR @ X0) = $true))) => (((cR @ b) = $true) & ((cR @ c) = $true) & ((cR @ a) = $true)))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,plain,(
% 1.48/1.29 ~((! [X0 : $i] : ((cP @ X0) => (cR @ X0)) & (! [X1 : $i] : (cP @ X1) | ! [X2 : $i] : (cQ @ X2)) & ! [X3 : $i] : ((cQ @ X3) => (cR @ X3))) => ((cR @ c) & (cR @ b) & (cR @ a)))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,negated_conjecture,(
% 1.48/1.29 ~((! [X0 : $i] : ((cP @ X0) => (cR @ X0)) & (! [X0 : $i] : (cP @ X0) | ! [X0 : $i] : (cQ @ X0)) & ! [X0 : $i] : ((cQ @ X0) => (cR @ X0))) => ((cR @ c) & (cR @ b) & (cR @ a)))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.29 thf(f1,conjecture,(
% 1.48/1.29 (! [X0 : $i] : ((cP @ X0) => (cR @ X0)) & (! [X0 : $i] : (cP @ X0) | ! [X0 : $i] : (cQ @ X0)) & ! [X0 : $i] : ((cQ @ X0) => (cR @ X0))) => ((cR @ c) & (cR @ b) & (cR @ a))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.K6vWZcmasC/DTF2THF_31027.p',cDISJ_THIRD)).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 ((cR @ a) != $true) | spl0_2),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.48/1.29 thf(f18,definition,(
% 1.48/1.29 spl0_2 <=> ((cR @ a) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.48/1.29 thf(f52,plain,(
% 1.48/1.29 spl0_3 | ~spl0_5),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.48/1.29 thf(f51,plain,(
% 1.48/1.29 $false | (spl0_3 | ~spl0_5)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.48/1.29 thf(f50,plain,(
% 1.48/1.29 ($true != $true) | (spl0_3 | ~spl0_5)),
% 1.48/1.29 inference(superposition,[status(thm)],[f24,f49])).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 ((cR @ c) != $true) | spl0_3),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,definition,(
% 1.48/1.29 spl0_3 <=> ((cR @ c) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.48/1.29 thf(f48,plain,(
% 1.48/1.29 spl0_3 | ~spl0_4),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f47])).
% 1.48/1.29 thf(f47,plain,(
% 1.48/1.29 $false | (spl0_3 | ~spl0_4)),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f24,f43])).
% 1.48/1.29 thf(f43,plain,(
% 1.48/1.29 ( ! [X3 : $i] : (((cR @ X3) = $true)) ) | ~spl0_4),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f9,f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($true = (cP @ X1))) ) | ~spl0_4),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.48/1.29 thf(f27,definition,(
% 1.48/1.29 spl0_4 <=> ! [X1 : $i] : ($true = (cP @ X1))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ( ! [X3 : $i] : (($true != (cP @ X3)) | ((cR @ X3) = $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.29 thf(f46,plain,(
% 1.48/1.29 spl0_2 | ~spl0_4),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.48/1.29 thf(f45,plain,(
% 1.48/1.29 $false | (spl0_2 | ~spl0_4)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.48/1.29 thf(f44,plain,(
% 1.48/1.29 ($true != $true) | (spl0_2 | ~spl0_4)),
% 1.48/1.29 inference(superposition,[status(thm)],[f20,f43])).
% 1.48/1.29 thf(f42,plain,(
% 1.48/1.29 spl0_1 | ~spl0_5),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.48/1.29 thf(f41,plain,(
% 1.48/1.29 $false | (spl0_1 | ~spl0_5)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.48/1.29 thf(f40,plain,(
% 1.48/1.29 ($true != $true) | (spl0_1 | ~spl0_5)),
% 1.48/1.29 inference(superposition,[status(thm)],[f16,f39])).
% 1.48/1.29 thf(f39,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (((cR @ X0) = $true)) ) | ~spl0_5),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.48/1.29 thf(f38,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (($true != $true) | ((cR @ X0) = $true)) ) | ~spl0_5),
% 1.48/1.29 inference(superposition,[status(thm)],[f10,f31])).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 ((cR @ b) != $true) | spl0_1),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f14])).
% 1.48/1.29 thf(f14,definition,(
% 1.48/1.29 spl0_1 <=> ((cR @ b) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.48/1.29 thf(f37,plain,(
% 1.48/1.29 spl0_1 | ~spl0_4),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.48/1.29 thf(f36,plain,(
% 1.48/1.29 $false | (spl0_1 | ~spl0_4)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.48/1.29 thf(f35,plain,(
% 1.48/1.29 ($true != $true) | (spl0_1 | ~spl0_4)),
% 1.48/1.29 inference(superposition,[status(thm)],[f16,f34])).
% 1.48/1.29 thf(f34,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (((cR @ X0) = $true)) ) | ~spl0_4),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.48/1.29 thf(f33,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (((cR @ X0) = $true) | ($true != $true)) ) | ~spl0_4),
% 1.48/1.29 inference(superposition,[status(thm)],[f9,f28])).
% 1.48/1.29 thf(f32,plain,(
% 1.48/1.29 spl0_4 | spl0_5),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f11,f30,f27])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ( ! [X0 : $i,X1 : $i] : (((cQ @ X0) = $true) | ($true = (cP @ X1))) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.29 thf(f25,plain,(
% 1.48/1.29 ~spl0_1 | ~spl0_2 | ~spl0_3),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f12,f22,f18,f14])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ((cR @ b) != $true) | ((cR @ a) != $true) | ((cR @ c) != $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_31027
% 1.48/1.29 % (31179)------------------------------
% 1.48/1.29 % (31179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (31179)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (31179)Memory used [KB]: 5500
% 1.48/1.29 % (31179)Time elapsed: 0.005 s
% 1.48/1.29 % (31179)Instructions burned: 5 (million)
% 1.48/1.29 % (31179)------------------------------
% 1.48/1.29 % (31179)------------------------------
% 1.48/1.29 % (31170)Success in time 0.015 s
%------------------------------------------------------------------------------