%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO169^5 : 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 : n017.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 09:53:34 AM UTC 2026
% Result : Theorem 1.23s 1.04s
% Output : Refutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 436 ( 94 equ; 0 cnn)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 481 ( 60 ~; 53 |; 31 &; 320 @)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-3 aty)
% Number of variables : 121 ( 0 ^; 121 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
cP: $i > $i > $i > $o ).
thf(func_def_4,type,
cPx: $i > $i > $o ).
thf(f190,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f131,f183,f189]) ).
thf(f189,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f188]) ).
thf(f188,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f127,f46]) ).
thf(f46,plain,
! [X0: $i] :
( ( cPx @ e @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cPx @ e @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f38,f9]) ).
thf(f9,plain,
! [X8: $i] :
( $true
= ( cP @ X8 @ X8 @ e ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( cPx @ X0 @ X5 )
= ( cP @ X2 @ X1 @ X5 ) )
| ( ( cP @ X3 @ X1 @ X0 )
!= $true )
| ( ( cP @ X4 @ X3 @ X2 )
!= $true ) )
& ! [X6: $i] :
( ( cP @ e @ X6 @ X6 )
= $true )
& ( ( cP @ b @ a @ ab )
!= $true )
& ( ( cP @ a @ b @ ab )
= $true )
& ! [X7: $i] :
( ( cP @ X7 @ e @ X7 )
= $true )
& ! [X8: $i] :
( $true
= ( cP @ X8 @ X8 @ e ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X3: $i,X5: $i,X2: $i,X4: $i,X7: $i,X6: $i] :
( ( ( cPx @ X3 @ X6 )
= ( cP @ X2 @ X5 @ X6 ) )
| ( ( cP @ X4 @ X5 @ X3 )
!= $true )
| ( ( cP @ X7 @ X4 @ X2 )
!= $true ) )
& ! [X8: $i] :
( ( cP @ e @ X8 @ X8 )
= $true )
& ( ( cP @ b @ a @ ab )
!= $true )
& ( ( cP @ a @ b @ ab )
= $true )
& ! [X1: $i] :
( ( cP @ X1 @ e @ X1 )
= $true )
& ! [X0: $i] :
( ( cP @ X0 @ X0 @ e )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP @ b @ a @ ab )
!= $true )
& ( ( cP @ a @ b @ ab )
= $true )
& ! [X8: $i] :
( ( cP @ e @ X8 @ X8 )
= $true )
& ! [X0: $i] :
( ( cP @ X0 @ X0 @ e )
= $true )
& ! [X1: $i] :
( ( cP @ X1 @ e @ X1 )
= $true )
& ! [X6: $i,X5: $i,X3: $i,X2: $i,X7: $i,X4: $i] :
( ( ( cPx @ X3 @ X6 )
= ( cP @ X2 @ X5 @ X6 ) )
| ( ( cP @ X4 @ X5 @ X3 )
!= $true )
| ( ( cP @ X7 @ X4 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X8: $i] :
( ( cP @ e @ X8 @ X8 )
= $true )
& ! [X0: $i] :
( ( cP @ X0 @ X0 @ e )
= $true )
& ! [X1: $i] :
( ( cP @ X1 @ e @ X1 )
= $true )
& ! [X6: $i,X5: $i,X3: $i,X2: $i,X7: $i,X4: $i] :
( ( ( ( cP @ X4 @ X5 @ X3 )
= $true )
& ( ( cP @ X7 @ X4 @ X2 )
= $true ) )
=> ( ( cPx @ X3 @ X6 )
= ( cP @ X2 @ X5 @ X6 ) ) ) )
=> ( ( ( cP @ a @ b @ ab )
= $true )
=> ( ( cP @ b @ a @ ab )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] : ( cP @ X0 @ X0 @ e )
& ! [X1: $i] : ( cP @ X1 @ e @ X1 )
& ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( cP @ X4 @ X5 @ X3 )
& ( cP @ X7 @ X4 @ X2 ) )
=> ( ( cPx @ X3 @ X6 )
<=> ( cP @ X2 @ X5 @ X6 ) ) )
& ! [X8: $i] : ( cP @ e @ X8 @ X8 ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i] : ( cP @ X2 @ X2 @ e )
& ! [X1: $i] : ( cP @ X1 @ e @ X1 )
& ! [X3: $i,X4: $i,X1: $i,X2: $i,X5: $i,X0: $i] :
( ( ( cP @ X1 @ X2 @ X4 )
& ( cP @ X0 @ X1 @ X3 ) )
=> ( ( cPx @ X4 @ X5 )
<=> ( cP @ X3 @ X2 @ X5 ) ) )
& ! [X0: $i] : ( cP @ e @ X0 @ X0 ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: $i] : ( cP @ X2 @ X2 @ e )
& ! [X1: $i] : ( cP @ X1 @ e @ X1 )
& ! [X3: $i,X4: $i,X1: $i,X2: $i,X5: $i,X0: $i] :
( ( ( cP @ X1 @ X2 @ X4 )
& ( cP @ X0 @ X1 @ X3 ) )
=> ( ( cPx @ X4 @ X5 )
<=> ( cP @ X3 @ X2 @ X5 ) ) )
& ! [X0: $i] : ( cP @ e @ X0 @ X0 ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gI90SRPZVk/DTF2THF_19786.p',cGRP_COMM) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP @ X0 @ X2 @ X1 ) )
| ( $true
= ( cPx @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cPx @ X1 @ X2 ) )
| ( $true
!= ( cP @ X0 @ X2 @ X1 ) ) ),
inference(superposition,[status(thm)],[f29,f9]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP @ X3 @ X1 @ e )
!= $true )
| ( $true
= ( cPx @ X2 @ X0 ) )
| ( ( cP @ X1 @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP @ X3 @ X1 @ e )
!= $true )
| ( $true = $false )
| ( ( cP @ X1 @ X0 @ X2 )
!= $true )
| ( $true
= ( cPx @ X2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f15,f13]) ).
thf(f13,plain,
! [X6: $i] :
( ( cP @ e @ X6 @ X6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f15,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cP @ X2 @ X1 @ X5 )
= $false )
| ( ( cP @ X3 @ X1 @ X0 )
!= $true )
| ( ( cP @ X4 @ X3 @ X2 )
!= $true )
| ( $true
= ( cPx @ X0 @ X5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( cPx @ X0 @ X5 )
= ( cP @ X2 @ X1 @ X5 ) )
| ( ( cP @ X4 @ X3 @ X2 )
!= $true )
| ( ( cP @ X3 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f127,plain,
( ( ( cPx @ e @ ab )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f125]) ).
thf(f125,definition,
( spl0_1
<=> ( ( cPx @ e @ ab )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f183,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f182]) ).
thf(f182,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f164,f46]) ).
thf(f164,plain,
( ( ( cPx @ e @ b )
= $false )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f160]) ).
thf(f160,plain,
( ( $true != $true )
| ( ( cPx @ e @ b )
= $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f158,f9]) ).
thf(f158,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP @ X0 @ a @ X1 )
!= $true )
| ( ( cPx @ X1 @ b )
= $false ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ! [X0: $i,X1: $i] :
( ( ( cP @ X0 @ a @ X1 )
!= $true )
| ( $true != $true )
| ( ( cPx @ X1 @ b )
= $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f142,f13]) ).
thf(f142,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP @ X1 @ X2 @ X0 ) )
| ( ( cPx @ X3 @ b )
= $false )
| ( ( cP @ X2 @ a @ X3 )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cP @ X1 @ X2 @ X0 ) )
| ( ( cP @ X2 @ a @ X3 )
!= $true )
| ( ( cPx @ X3 @ b )
= $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f130,f16]) ).
thf(f16,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( cP @ X2 @ X1 @ X5 ) )
| ( ( cP @ X4 @ X3 @ X2 )
!= $true )
| ( ( cP @ X3 @ X1 @ X0 )
!= $true )
| ( ( cPx @ X0 @ X5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f130,plain,
( ! [X0: $i] :
( $true
!= ( cP @ X0 @ a @ b ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl0_2
<=> ! [X0: $i] :
( $true
!= ( cP @ X0 @ a @ b ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f131,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f123,f129,f125]) ).
thf(f123,plain,
! [X0: $i] :
( ( $true
!= ( cP @ X0 @ a @ b ) )
| ( ( cPx @ e @ ab )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
! [X0: $i] :
( ( ( cPx @ e @ ab )
= $false )
| ( $true
!= ( cP @ X0 @ a @ b ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f59,f9]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP @ X1 @ a @ X2 ) )
| ( ( cPx @ X2 @ ab )
= $false )
| ( ( cP @ X0 @ X1 @ b )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X0 @ X1 @ b )
!= $true )
| ( $true != $true )
| ( ( cPx @ X2 @ ab )
= $false )
| ( $true
!= ( cP @ X1 @ a @ X2 ) ) ),
inference(superposition,[status(thm)],[f12,f16]) ).
thf(f12,plain,
( ( cP @ b @ a @ ab )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO169^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n017.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 14:23:55 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.40 ---- Original DTF file ---
% 0.15/0.40 thf(spec,logic,$$dhol).
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 % File : SYO169^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.40 % Domain : Syntactic
% 0.15/0.40 % Problem : TPS problem from BASIC-FO-THMS
% 0.15/0.40 % Version : Especial.
% 0.15/0.40 % English :
% 0.15/0.40
% 0.15/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.40 % Source : [Bro09]
% 0.15/0.40 % Names : tps_0991 [Bro09]
% 0.15/0.40
% 0.15/0.40 % Status : Theorem
% 0.15/0.40 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.1.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.15/0.40 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.15/0.40 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.15/0.40 % Maximal formula atoms : 9 ( 9 avg)
% 0.15/0.40 % Number of connectives : 34 ( 0 ~; 0 |; 4 &; 26 @)
% 0.15/0.40 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.15/0.40 % Maximal formula depth : 16 ( 16 avg)
% 0.15/0.40 % Number of types : 2 ( 0 usr)
% 0.15/0.40 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.15/0.40 % Number of symbols : 6 ( 6 usr; 4 con; 0-3 aty)
% 0.15/0.40 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.15/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.40
% 0.15/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 thf(ab,type,
% 0.15/0.40 ab: $i ).
% 0.15/0.40
% 0.15/0.40 thf(a,type,
% 0.15/0.40 a: $i ).
% 0.15/0.40
% 0.15/0.40 thf(b,type,
% 0.15/0.40 b: $i ).
% 0.15/0.40
% 0.15/0.40 thf(cP,type,
% 0.15/0.40 cP: $i > $i > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(cPx,type,
% 0.15/0.40 cPx: $i > $i > $o ).
% 0.15/0.40
% 0.15/0.40 thf(e,type,
% 0.15/0.40 e: $i ).
% 0.15/0.40
% 0.15/0.40 thf(cGRP_COMM,conjecture,
% 0.15/0.40 ( ( ! [Xx: $i] : ( cP @ e @ Xx @ Xx )
% 0.15/0.40 & ! [Xy: $i] : ( cP @ Xy @ e @ Xy )
% 0.15/0.40 & ! [Xz: $i] : ( cP @ Xz @ Xz @ e )
% 0.15/0.40 & ! [Xx: $i,Xy: $i,Xz: $i,Xxy: $i,Xyz: $i,Xxyz: $i] :
% 0.15/0.40 ( ( ( cP @ Xx @ Xy @ Xxy )
% 0.15/0.40 & ( cP @ Xy @ Xz @ Xyz ) )
% 0.15/0.40 => ( ( cP @ Xxy @ Xz @ Xxyz )
% 0.15/0.40 <=> ( cPx @ Xyz @ Xxyz ) ) ) )
% 0.15/0.40 => ( ( cP @ a @ b @ ab )
% 0.15/0.40 => ( cP @ b @ a @ ab ) ) ) ).
% 0.15/0.40
% 0.15/0.40 %------------------------------------------------------------------------------
% 0.15/0.40 ------------------------
% 0.98/1.01 ---- Embedded in THF ---
% 0.98/1.01 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.98/1.01 %%% Generated on Tue Feb 24 14:23:56 EST 2026
% 0.98/1.01 %%% using '$$dhol' embedding, version 1.3.0.
% 0.98/1.01 %%% Logic specification used:
% 0.98/1.01 %%% thf(spec, logic, $$dhol).
% 0.98/1.01
% 0.98/1.01 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gI90SRPZVk/DTF2DTF19786.p
% See solution above
% 0.98/1.01 ------------------------
% 0.98/1.01 ---- Cleaned THF ---
% 0.98/1.01 thf(ab,type,
% 0.98/1.01 ab: $i ).
% 0.98/1.01
% 0.98/1.01 thf(a,type,
% 0.98/1.01 a: $i ).
% 0.98/1.01
% 0.98/1.01 thf(b,type,
% 0.98/1.01 b: $i ).
% 0.98/1.01
% 0.98/1.01 thf(cP,type,
% 0.98/1.01 cP: $i > $i > $i > $o ).
% 0.98/1.01
% 0.98/1.01 thf(cPx,type,
% 0.98/1.01 cPx: $i > $i > $o ).
% 0.98/1.01
% 0.98/1.01 thf(e,type,
% 0.98/1.01 e: $i ).
% 0.98/1.01
% 0.98/1.01 thf(cGRP_COMM,conjecture,
% 0.98/1.01 ( ( ! [Xx: $i] : ( cP @ e @ Xx @ Xx )
% 0.98/1.01 & ! [Xy: $i] : ( cP @ Xy @ e @ Xy )
% 0.98/1.01 & ! [Xz: $i] : ( cP @ Xz @ Xz @ e )
% 0.98/1.01 & ! [Xx: $i,Xy: $i,Xz: $i,Xxy: $i,Xyz: $i,Xxyz: $i] :
% 0.98/1.01 ( ( ( cP @ Xx @ Xy @ Xxy )
% 0.98/1.01 & ( cP @ Xy @ Xz @ Xyz ) )
% 0.98/1.01 => ( ( cP @ Xxy @ Xz @ Xxyz )
% 0.98/1.01 <=> ( cPx @ Xyz @ Xxyz ) ) ) )
% 0.98/1.01 => ( ( cP @ a @ b @ ab )
% 0.98/1.01 => ( cP @ b @ a @ ab ) ) ) ).
% 0.98/1.01 ------------------------
% 1.23/1.03 % (19926)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19786 for (3000ds/183Mi)
% 1.23/1.03 % (19929)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19786 for (3000ds/2Mi)
% 1.23/1.03 % (19931)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_19786 for (3000ds/275Mi)
% 1.23/1.03 % (19927)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_19786 for (3000ds/4Mi)
% 1.23/1.03 % (19930)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_19786 for (3000ds/2Mi)
% 1.23/1.03 % (19928)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_19786 for (3000ds/27Mi)
% 1.23/1.03 % (19932)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19786 for (3000ds/18Mi)
% 1.23/1.03 % (19929)Instruction limit reached!
% 1.23/1.03 % (19929)------------------------------
% 1.23/1.03 % (19929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.23/1.03 % (19929)Termination reason: Unknown
% 1.23/1.03 % (19930)Instruction limit reached!
% 1.23/1.03 % (19930)------------------------------
% 1.23/1.03 % (19930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.23/1.03 % (19930)Termination reason: Unknown
% 1.23/1.03 % (19930)Termination phase: Property scanning
% 1.23/1.03
% 1.23/1.03 % (19930)Memory used [KB]: 895
% 1.23/1.03 % (19930)Time elapsed: 0.002 s
% 1.23/1.03 % (19930)Instructions burned: 2 (million)
% 1.23/1.03 % (19930)------------------------------
% 1.23/1.03 % (19930)------------------------------
% 1.23/1.03 % (19929)Termination phase: Saturation
% 1.23/1.03
% 1.23/1.03 % (19929)Memory used [KB]: 5500
% 1.23/1.03 % (19929)Time elapsed: 0.003 s
% 1.23/1.03 % (19929)Instructions burned: 2 (million)
% 1.23/1.03 % (19929)------------------------------
% 1.23/1.03 % (19929)------------------------------
% 1.23/1.03 % (19927)Instruction limit reached!
% 1.23/1.03 % (19927)------------------------------
% 1.23/1.03 % (19927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.23/1.03 % (19927)Termination reason: Unknown
% 1.23/1.03 % (19927)Termination phase: Saturation
% 1.23/1.03
% 1.23/1.03 % (19927)Memory used [KB]: 5500
% 1.23/1.03 % (19927)Time elapsed: 0.004 s
% 1.23/1.03 % (19927)Instructions burned: 5 (million)
% 1.23/1.03 % (19927)------------------------------
% 1.23/1.03 % (19927)------------------------------
% 1.23/1.04 % (19926)First to succeed.
% 1.23/1.04 % (19926)Refutation found. Thanks to Tanya!
% 1.23/1.04 % SZS status Theorem for DTF2THF_19786
% 1.23/1.04 % SZS output start Proof for DTF2THF_19786
% 1.23/1.04 thf(func_def_3, type, cP: $i > $i > $i > $o).
% 1.23/1.04 thf(func_def_4, type, cPx: $i > $i > $o).
% 1.23/1.04 thf(f190,plain,(
% 1.23/1.04 $false),
% 1.23/1.04 inference(avatar_sat_refutation,[status(thm)],[f131,f183,f189])).
% 1.23/1.04 thf(f189,plain,(
% 1.23/1.04 ~spl0_1),
% 1.23/1.04 inference(avatar_contradiction_clause,[status(thm)],[f188])).
% 1.23/1.04 thf(f188,plain,(
% 1.23/1.04 $false | ~spl0_1),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.23/1.04 thf(f184,plain,(
% 1.23/1.04 ($true = $false) | ~spl0_1),
% 1.23/1.04 inference(superposition,[status(thm)],[f127,f46])).
% 1.23/1.04 thf(f46,plain,(
% 1.23/1.04 ( ! [X0 : $i] : (((cPx @ e @ X0) = $true)) )),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.23/1.04 thf(f41,plain,(
% 1.23/1.04 ( ! [X0 : $i] : (($true != $true) | ((cPx @ e @ X0) = $true)) )),
% 1.23/1.04 inference(superposition,[status(thm)],[f38,f9])).
% 1.23/1.04 thf(f9,plain,(
% 1.23/1.04 ( ! [X8 : $i] : (($true = (cP @ X8 @ X8 @ e))) )),
% 1.23/1.04 inference(cnf_transformation,[status(thm)],[f8])).
% 1.23/1.04 thf(f8,plain,(
% 1.23/1.04 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : (((cPx @ X0 @ X5) = (cP @ X2 @ X1 @ X5)) | ((cP @ X3 @ X1 @ X0) != $true) | ((cP @ X4 @ X3 @ X2) != $true)) & ! [X6 : $i] : ((cP @ e @ X6 @ X6) = $true) & ((cP @ b @ a @ ab) != $true) & ((cP @ a @ b @ ab) = $true) & ! [X7 : $i] : ((cP @ X7 @ e @ X7) = $true) & ! [X8 : $i] : ($true = (cP @ X8 @ X8 @ e))),
% 1.23/1.04 inference(rectify,[status(thm)],[f7])).
% 1.23/1.04 thf(f7,plain,(
% 1.23/1.04 ! [X3 : $i,X5 : $i,X2 : $i,X4 : $i,X7 : $i,X6 : $i] : (((cPx @ X3 @ X6) = (cP @ X2 @ X5 @ X6)) | ((cP @ X4 @ X5 @ X3) != $true) | ((cP @ X7 @ X4 @ X2) != $true)) & ! [X8 : $i] : ((cP @ e @ X8 @ X8) = $true) & ((cP @ b @ a @ ab) != $true) & ((cP @ a @ b @ ab) = $true) & ! [X1 : $i] : ((cP @ X1 @ e @ X1) = $true) & ! [X0 : $i] : ((cP @ X0 @ X0 @ e) = $true)),
% 1.23/1.04 inference(flattening,[status(thm)],[f6])).
% 1.23/1.04 thf(f6,plain,(
% 1.23/1.04 (((cP @ b @ a @ ab) != $true) & ((cP @ a @ b @ ab) = $true)) & (! [X8 : $i] : ((cP @ e @ X8 @ X8) = $true) & ! [X0 : $i] : ((cP @ X0 @ X0 @ e) = $true) & ! [X1 : $i] : ((cP @ X1 @ e @ X1) = $true) & ! [X6 : $i,X5 : $i,X3 : $i,X2 : $i,X7 : $i,X4 : $i] : (((cPx @ X3 @ X6) = (cP @ X2 @ X5 @ X6)) | (((cP @ X4 @ X5 @ X3) != $true) | ((cP @ X7 @ X4 @ X2) != $true))))),
% 1.23/1.04 inference(ennf_transformation,[status(thm)],[f5])).
% 1.23/1.04 thf(f5,plain,(
% 1.23/1.04 ~((! [X8 : $i] : ((cP @ e @ X8 @ X8) = $true) & ! [X0 : $i] : ((cP @ X0 @ X0 @ e) = $true) & ! [X1 : $i] : ((cP @ X1 @ e @ X1) = $true) & ! [X6 : $i,X5 : $i,X3 : $i,X2 : $i,X7 : $i,X4 : $i] : ((((cP @ X4 @ X5 @ X3) = $true) & ((cP @ X7 @ X4 @ X2) = $true)) => ((cPx @ X3 @ X6) = (cP @ X2 @ X5 @ X6)))) => (((cP @ a @ b @ ab) = $true) => ((cP @ b @ a @ ab) = $true)))),
% 1.23/1.04 inference(fool_elimination,[status(thm)],[f4])).
% 1.23/1.04 thf(f4,plain,(
% 1.23/1.04 ~((! [X0 : $i] : (cP @ X0 @ X0 @ e) & ! [X1 : $i] : (cP @ X1 @ e @ X1) & ! [X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((cP @ X4 @ X5 @ X3) & (cP @ X7 @ X4 @ X2)) => ((cPx @ X3 @ X6) <=> (cP @ X2 @ X5 @ X6))) & ! [X8 : $i] : (cP @ e @ X8 @ X8)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))),
% 1.23/1.04 inference(rectify,[status(thm)],[f2])).
% 1.23/1.04 thf(f2,negated_conjecture,(
% 1.23/1.04 ~((! [X2 : $i] : (cP @ X2 @ X2 @ e) & ! [X1 : $i] : (cP @ X1 @ e @ X1) & ! [X3 : $i,X4 : $i,X1 : $i,X2 : $i,X5 : $i,X0 : $i] : (((cP @ X1 @ X2 @ X4) & (cP @ X0 @ X1 @ X3)) => ((cPx @ X4 @ X5) <=> (cP @ X3 @ X2 @ X5))) & ! [X0 : $i] : (cP @ e @ X0 @ X0)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))),
% 1.23/1.04 inference(negated_conjecture,[status(cth)],[f1])).
% 1.23/1.04 thf(f1,conjecture,(
% 1.23/1.04 (! [X2 : $i] : (cP @ X2 @ X2 @ e) & ! [X1 : $i] : (cP @ X1 @ e @ X1) & ! [X3 : $i,X4 : $i,X1 : $i,X2 : $i,X5 : $i,X0 : $i] : (((cP @ X1 @ X2 @ X4) & (cP @ X0 @ X1 @ X3)) => ((cPx @ X4 @ X5) <=> (cP @ X3 @ X2 @ X5))) & ! [X0 : $i] : (cP @ e @ X0 @ X0)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab))),
% 1.23/1.04 file('/export/starexec/sandbox/tmp/tmp.gI90SRPZVk/DTF2THF_19786.p',cGRP_COMM)).
% 1.23/1.04 thf(f38,plain,(
% 1.23/1.04 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cP @ X0 @ X2 @ X1)) | ($true = (cPx @ X1 @ X2))) )),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.23/1.04 thf(f34,plain,(
% 1.23/1.04 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = (cPx @ X1 @ X2)) | ($true != (cP @ X0 @ X2 @ X1))) )),
% 1.23/1.04 inference(superposition,[status(thm)],[f29,f9])).
% 1.23/1.04 thf(f29,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP @ X3 @ X1 @ e) != $true) | ($true = (cPx @ X2 @ X0)) | ((cP @ X1 @ X0 @ X2) != $true)) )),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.23/1.04 thf(f20,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((cP @ X3 @ X1 @ e) != $true) | ($true = $false) | ((cP @ X1 @ X0 @ X2) != $true) | ($true = (cPx @ X2 @ X0))) )),
% 1.23/1.04 inference(superposition,[status(thm)],[f15,f13])).
% 1.23/1.04 thf(f13,plain,(
% 1.23/1.04 ( ! [X6 : $i] : (((cP @ e @ X6 @ X6) = $true)) )),
% 1.23/1.04 inference(cnf_transformation,[status(thm)],[f8])).
% 1.23/1.04 thf(f15,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cP @ X2 @ X1 @ X5) = $false) | ((cP @ X3 @ X1 @ X0) != $true) | ((cP @ X4 @ X3 @ X2) != $true) | ($true = (cPx @ X0 @ X5))) )),
% 1.23/1.04 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.23/1.04 thf(f14,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((cPx @ X0 @ X5) = (cP @ X2 @ X1 @ X5)) | ((cP @ X4 @ X3 @ X2) != $true) | ((cP @ X3 @ X1 @ X0) != $true)) )),
% 1.23/1.04 inference(cnf_transformation,[status(thm)],[f8])).
% 1.23/1.04 thf(f127,plain,(
% 1.23/1.04 ((cPx @ e @ ab) = $false) | ~spl0_1),
% 1.23/1.04 inference(avatar_component_clause,[status(thm)],[f125])).
% 1.23/1.04 thf(f125,definition,(
% 1.23/1.04 spl0_1 <=> ((cPx @ e @ ab) = $false)),
% 1.23/1.04 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.23/1.04 thf(f183,plain,(
% 1.23/1.04 ~spl0_2),
% 1.23/1.04 inference(avatar_contradiction_clause,[status(thm)],[f182])).
% 1.23/1.04 thf(f182,plain,(
% 1.23/1.04 $false | ~spl0_2),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.23/1.04 thf(f178,plain,(
% 1.23/1.04 ($true = $false) | ~spl0_2),
% 1.23/1.04 inference(superposition,[status(thm)],[f164,f46])).
% 1.23/1.04 thf(f164,plain,(
% 1.23/1.04 ((cPx @ e @ b) = $false) | ~spl0_2),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f160])).
% 1.23/1.04 thf(f160,plain,(
% 1.23/1.04 ($true != $true) | ((cPx @ e @ b) = $false) | ~spl0_2),
% 1.23/1.04 inference(superposition,[status(thm)],[f158,f9])).
% 1.23/1.04 thf(f158,plain,(
% 1.23/1.04 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ a @ X1) != $true) | ((cPx @ X1 @ b) = $false)) ) | ~spl0_2),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.23/1.04 thf(f154,plain,(
% 1.23/1.04 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ a @ X1) != $true) | ($true != $true) | ((cPx @ X1 @ b) = $false)) ) | ~spl0_2),
% 1.23/1.04 inference(superposition,[status(thm)],[f142,f13])).
% 1.23/1.04 thf(f142,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (cP @ X1 @ X2 @ X0)) | ((cPx @ X3 @ b) = $false) | ((cP @ X2 @ a @ X3) != $true)) ) | ~spl0_2),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.23/1.04 thf(f140,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (cP @ X1 @ X2 @ X0)) | ((cP @ X2 @ a @ X3) != $true) | ((cPx @ X3 @ b) = $false)) ) | ~spl0_2),
% 1.23/1.04 inference(superposition,[status(thm)],[f130,f16])).
% 1.23/1.04 thf(f16,plain,(
% 1.23/1.04 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (cP @ X2 @ X1 @ X5)) | ((cP @ X4 @ X3 @ X2) != $true) | ((cP @ X3 @ X1 @ X0) != $true) | ((cPx @ X0 @ X5) = $false)) )),
% 1.23/1.04 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.23/1.04 thf(f130,plain,(
% 1.23/1.04 ( ! [X0 : $i] : (($true != (cP @ X0 @ a @ b))) ) | ~spl0_2),
% 1.23/1.04 inference(avatar_component_clause,[status(thm)],[f129])).
% 1.23/1.04 thf(f129,definition,(
% 1.23/1.04 spl0_2 <=> ! [X0 : $i] : ($true != (cP @ X0 @ a @ b))),
% 1.23/1.04 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.23/1.04 thf(f131,plain,(
% 1.23/1.04 spl0_1 | spl0_2),
% 1.23/1.04 inference(avatar_split_clause,[status(thm)],[f123,f129,f125])).
% 1.23/1.04 thf(f123,plain,(
% 1.23/1.04 ( ! [X0 : $i] : (($true != (cP @ X0 @ a @ b)) | ((cPx @ e @ ab) = $false)) )),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.23/1.04 thf(f117,plain,(
% 1.23/1.04 ( ! [X0 : $i] : (((cPx @ e @ ab) = $false) | ($true != (cP @ X0 @ a @ b)) | ($true != $true)) )),
% 1.23/1.04 inference(superposition,[status(thm)],[f59,f9])).
% 1.23/1.04 thf(f59,plain,(
% 1.23/1.04 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (cP @ X1 @ a @ X2)) | ((cPx @ X2 @ ab) = $false) | ((cP @ X0 @ X1 @ b) != $true)) )),
% 1.23/1.04 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.23/1.04 thf(f54,plain,(
% 1.23/1.04 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP @ X0 @ X1 @ b) != $true) | ($true != $true) | ((cPx @ X2 @ ab) = $false) | ($true != (cP @ X1 @ a @ X2))) )),
% 1.23/1.04 inference(superposition,[status(thm)],[f12,f16])).
% 1.23/1.04 thf(f12,plain,(
% 1.23/1.04 ((cP @ b @ a @ ab) != $true)),
% 1.23/1.04 inference(cnf_transformation,[status(thm)],[f8])).
% 1.23/1.04 % SZS output end Proof for DTF2THF_19786
% 1.23/1.04 % (19926)------------------------------
% 1.23/1.04 % (19926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.23/1.04 % (19926)Termination reason: Refutation
% 1.23/1.04
% 1.23/1.04 % (19926)Memory used [KB]: 5756
% 1.23/1.04 % (19926)Time elapsed: 0.013 s
% 1.23/1.04 % (19926)Instructions burned: 31 (million)
% 1.23/1.04 % (19926)------------------------------
% 1.23/1.04 % (19926)------------------------------
% 1.23/1.04 % (19925)Success in time 0.021 s
%------------------------------------------------------------------------------