%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO383^5 : 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 : 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 09:54:05 AM UTC 2026
% Result : Theorem 1.57s 1.39s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 394 ( 80 equ; 0 cnn)
% Maximal formula atoms : 23 ( 10 avg)
% Number of connectives : 500 ( 96 ~; 63 |; 42 &; 296 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 107 ( 0 ^; 107 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_1: $i > $i > $o ).
thf(func_def_3,type,
cQ_1: $i > $i > $i > $o ).
thf(f44,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f33,f38,f43]) ).
thf(f43,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f42]) ).
thf(f42,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f40,f14]) ).
thf(f14,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_2 @ X1 @ X0 @ X2 )
!= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X3: $i] :
( ( cP_1 @ d @ X3 )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ X4 ) @ X5 )
= $true )
| ( ( cP_1 @ X4 @ X5 )
!= $true ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( ( ( cP_1 @ ( f @ X7 ) @ X8 )
!= $true )
| ( $true
= ( cQ_2 @ X11 @ X8 @ X6 ) )
| ( ( cP_1 @ ( f @ X10 ) @ X6 )
!= $true )
| ( ( cQ_1 @ X9 @ X7 @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X11 )
!= $true ) )
& ( ( cP_1 @ a @ a )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_2 @ X1 @ X0 @ X2 )
!= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ! [X3: $i] :
( ( cP_1 @ d @ X3 )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X11: $i,X10: $i] :
( ( ( cP_1 @ ( f @ X11 ) @ X10 )
= $true )
| ( ( cP_1 @ X11 @ X10 )
!= $true ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X4: $i,X7: $i,X5: $i,X9: $i,X6: $i,X8: $i] :
( ( ( cP_1 @ ( f @ X7 ) @ X5 )
!= $true )
| ( $true
= ( cQ_2 @ X8 @ X5 @ X4 ) )
| ( ( cP_1 @ ( f @ X6 ) @ X4 )
!= $true )
| ( $true
!= ( cQ_1 @ X9 @ X7 @ X6 ) )
| ( ( cP_1 @ ( f @ X9 ) @ X8 )
!= $true ) )
& ( ( cP_1 @ a @ a )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ( ( cP_1 @ c @ c )
= $true )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_2 @ X1 @ X0 @ X2 )
!= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X3: $i] :
( ( cP_1 @ d @ X3 )
= $true )
& ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ( ( cP_1 @ ( f @ X7 ) @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ X6 ) @ X4 )
!= $true )
| ( $true
!= ( cQ_1 @ X9 @ X7 @ X6 ) )
| ( ( cP_1 @ ( f @ X9 ) @ X8 )
!= $true )
| ( $true
= ( cQ_2 @ X8 @ X5 @ X4 ) ) )
& ! [X10: $i,X11: $i] :
( ( ( cP_1 @ ( f @ X11 ) @ X10 )
= $true )
| ( ( cP_1 @ X11 @ X10 )
!= $true ) )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_1 @ a @ a )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ( cP_1 @ c @ c )
& ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_2 @ X1 @ X0 @ X2 )
& ( cQ_1 @ a @ b @ c )
& ! [X3: $i] : ( cP_1 @ d @ X3 )
& ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ~ ( cP_1 @ ( f @ X7 ) @ X5 )
| ~ ( cP_1 @ ( f @ X6 ) @ X4 )
| ~ ( cQ_1 @ X9 @ X7 @ X6 )
| ~ ( cP_1 @ ( f @ X9 ) @ X8 )
| ( cQ_2 @ X8 @ X5 @ X4 ) )
& ! [X10: $i,X11: $i] :
( ( cP_1 @ ( f @ X11 ) @ X10 )
| ~ ( cP_1 @ X11 @ X10 ) )
& ( cP_1 @ b @ b )
& ( cP_1 @ a @ a ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ( cP_1 @ c @ c )
& ! [X1: $i,X0: $i,X2: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ( cQ_1 @ a @ b @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X5: $i,X4: $i,X2: $i,X1: $i,X3: $i,X0: $i] :
( ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ! [X1: $i,X0: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ( cP_1 @ b @ b )
& ( cP_1 @ a @ a ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ( cP_1 @ c @ c )
& ! [X1: $i,X0: $i,X2: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ( cQ_1 @ a @ b @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X5: $i,X4: $i,X2: $i,X1: $i,X3: $i,X0: $i] :
( ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ( cQ_2 @ X3 @ X4 @ X5 ) )
& ! [X1: $i,X0: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ( cP_1 @ b @ b )
& ( cP_1 @ a @ a ) ),
file('/export/starexec/sandbox2/tmp/tmp.oGc6dB4AOk/DTF2THF_3076.p',cTHM409_1) ).
thf(f40,plain,
( ! [X0: $i] :
( ( cP_1 @ c @ X0 )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ! [X0: $i] :
( ( ( cP_1 @ c @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f21,f11]) ).
thf(f11,plain,
! [X4: $i,X5: $i] :
( ( ( cP_1 @ ( f @ X4 ) @ X5 )
= $true )
| ( ( cP_1 @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f21,plain,
( ! [X2: $i] :
( ( cP_1 @ ( f @ c ) @ X2 )
!= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl0_1
<=> ! [X2: $i] :
( ( cP_1 @ ( f @ c ) @ X2 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f38,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f35,f8]) ).
thf(f8,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f35,plain,
( ! [X0: $i] :
( ( cP_1 @ a @ X0 )
!= $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ! [X0: $i] :
( ( ( cP_1 @ a @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f27,f11]) ).
thf(f27,plain,
( ! [X0: $i] :
( ( cP_1 @ ( f @ a ) @ X0 )
!= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_3
<=> ! [X0: $i] :
( ( cP_1 @ ( f @ a ) @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f33,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f30,f10]) ).
thf(f10,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f30,plain,
( ! [X0: $i] :
( ( cP_1 @ b @ X0 )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP_1 @ b @ X0 )
!= $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f24,f11]) ).
thf(f24,plain,
( ! [X1: $i] :
( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl0_2
<=> ! [X1: $i] :
( ( cP_1 @ ( f @ b ) @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f28,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f18,f26,f23,f20]) ).
thf(f18,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ c ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP_1 @ ( f @ b ) @ X1 )
!= $true )
| ( $true != $true )
| ( ( cP_1 @ ( f @ c ) @ X2 )
!= $true )
| ( ( cP_1 @ ( f @ a ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f16,f12]) ).
thf(f12,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f16,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( cQ_1 @ X9 @ X7 @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X11 )
!= $true )
| ( ( cP_1 @ ( f @ X7 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ X10 ) @ X6 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f9,f15]) ).
thf(f15,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( cQ_2 @ X1 @ X0 @ X2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f9,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( cP_1 @ ( f @ X7 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X11 )
!= $true )
| ( ( cP_1 @ ( f @ X10 ) @ X6 )
!= $true )
| ( ( cQ_1 @ X9 @ X7 @ X10 )
!= $true )
| ( $true
= ( cQ_2 @ X11 @ X8 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO383^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n017.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 14:27:56 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SYO383^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Syntactic
% 0.17/0.40 % Problem : TPS problem THM409-1
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0166 [Bro09]
% 0.17/0.40 % : THM409-1 [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % 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 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% 0.17/0.40 % Number of atoms : 13 ( 0 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 13 ( 13 avg)
% 0.17/0.40 % Number of connectives : 53 ( 7 ~; 5 |; 7 &; 34 @)
% 0.17/0.40 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 23 ( 23 avg)
% 0.17/0.40 % Number of types : 2 ( 0 usr)
% 0.17/0.40 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 8 ( 8 usr; 4 con; 0-3 aty)
% 0.17/0.40 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.17/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(cQ_2,type,
% 0.17/0.40 cQ_2: $i > $i > $i > $o ).
% 0.17/0.40
% 0.17/0.40 thf(f,type,
% 0.17/0.40 f: $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(cP_1,type,
% 0.17/0.40 cP_1: $i > $i > $o ).
% 0.17/0.40
% 0.17/0.40 thf(cQ_1,type,
% 0.17/0.40 cQ_1: $i > $i > $i > $o ).
% 0.17/0.40
% 0.17/0.40 thf(d,type,
% 0.17/0.40 d: $i ).
% 0.17/0.40
% 0.17/0.40 thf(c,type,
% 0.17/0.40 c: $i ).
% 0.17/0.40
% 0.17/0.40 thf(b,type,
% 0.17/0.40 b: $i ).
% 0.17/0.40
% 0.17/0.40 thf(a,type,
% 0.17/0.40 a: $i ).
% 0.17/0.40
% 0.17/0.40 thf(cTHM409_1,conjecture,
% 0.17/0.40 ~ ( ( cQ_1 @ a @ b @ c )
% 0.17/0.40 & ( cP_1 @ a @ a )
% 0.17/0.40 & ( cP_1 @ b @ b )
% 0.17/0.40 & ( cP_1 @ c @ c )
% 0.17/0.40 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 0.17/0.40 & ! [Xx: $i,Xy: $i] :
% 0.17/0.40 ( ~ ( cP_1 @ Xx @ Xy )
% 0.17/0.40 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 0.17/0.40 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 0.17/0.40 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 0.17/0.40 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 0.17/0.40 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 0.17/0.40 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 0.17/0.40 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 0.17/0.40 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.40 ~ ( cQ_2 @ Xx @ Xy @ Xz ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.57/1.35 ---- Embedded in THF ---
% 1.57/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.35 %%% Generated on Tue Feb 24 14:27:57 EST 2026
% 1.57/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.35 %%% Logic specification used:
% 1.57/1.35 %%% thf(spec, logic, $$dhol).
% 1.57/1.35
% 1.57/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oGc6dB4AOk/DTF2DTF3076.p
% See solution above
% 1.57/1.35 ------------------------
% 1.57/1.36 ---- Cleaned THF ---
% 1.57/1.36 thf(cQ_2,type,
% 1.57/1.36 cQ_2: $i > $i > $i > $o ).
% 1.57/1.36
% 1.57/1.36 thf(f,type,
% 1.57/1.36 f: $i > $i ).
% 1.57/1.36
% 1.57/1.36 thf(cP_1,type,
% 1.57/1.36 cP_1: $i > $i > $o ).
% 1.57/1.36
% 1.57/1.36 thf(cQ_1,type,
% 1.57/1.36 cQ_1: $i > $i > $i > $o ).
% 1.57/1.36
% 1.57/1.36 thf(d,type,
% 1.57/1.36 d: $i ).
% 1.57/1.36
% 1.57/1.36 thf(c,type,
% 1.57/1.36 c: $i ).
% 1.57/1.36
% 1.57/1.36 thf(b,type,
% 1.57/1.36 b: $i ).
% 1.57/1.36
% 1.57/1.36 thf(a,type,
% 1.57/1.36 a: $i ).
% 1.57/1.36
% 1.57/1.36 thf(cTHM409_1,conjecture,
% 1.57/1.36 ~ ( ( cQ_1 @ a @ b @ c )
% 1.57/1.36 & ( cP_1 @ a @ a )
% 1.57/1.36 & ( cP_1 @ b @ b )
% 1.57/1.36 & ( cP_1 @ c @ c )
% 1.57/1.36 & ! [Xx: $i] : ( cP_1 @ d @ Xx )
% 1.57/1.36 & ! [Xx: $i,Xy: $i] :
% 1.57/1.36 ( ~ ( cP_1 @ Xx @ Xy )
% 1.57/1.36 | ( cP_1 @ ( f @ Xx ) @ Xy ) )
% 1.57/1.36 & ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
% 1.57/1.36 ( ~ ( cQ_1 @ Xx @ Xy @ Xz )
% 1.57/1.36 | ~ ( cP_1 @ ( f @ Xx ) @ Xu )
% 1.57/1.36 | ~ ( cP_1 @ ( f @ Xy ) @ Xv )
% 1.57/1.36 | ~ ( cP_1 @ ( f @ Xz ) @ Xw )
% 1.57/1.36 | ( cQ_2 @ Xu @ Xv @ Xw ) )
% 1.57/1.36 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.57/1.36 ~ ( cQ_2 @ Xx @ Xy @ Xz ) ) ).
% 1.57/1.36 ------------------------
% 1.57/1.38 % (3207)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3076 for (2999ds/2Mi)
% 1.57/1.38 % (3210)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3076 for (2999ds/18Mi)
% 1.57/1.38 % (3204)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3076 for (2999ds/183Mi)
% 1.57/1.38 % (3208)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_3076 for (2999ds/2Mi)
% 1.57/1.38 % (3209)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_3076 for (2999ds/275Mi)
% 1.57/1.38 % (3205)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_3076 for (2999ds/4Mi)
% 1.57/1.38 % (3207)Instruction limit reached!
% 1.57/1.38 % (3207)------------------------------
% 1.57/1.38 % (3207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.38 % (3207)Termination reason: Unknown
% 1.57/1.38 % (3207)Termination phase: Property scanning
% 1.57/1.38
% 1.57/1.38 % (3208)Instruction limit reached!
% 1.57/1.38 % (3208)------------------------------
% 1.57/1.38 % (3208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.38 % (3208)Termination reason: Unknown
% 1.57/1.38 % (3208)Termination phase: Property scanning
% 1.57/1.38
% 1.57/1.38 % (3208)Memory used [KB]: 895
% 1.57/1.38 % (3208)Time elapsed: 0.003 s
% 1.57/1.38 % (3208)Instructions burned: 2 (million)
% 1.57/1.38 % (3208)------------------------------
% 1.57/1.38 % (3208)------------------------------
% 1.57/1.38 % (3207)Memory used [KB]: 895
% 1.57/1.38 % (3207)Time elapsed: 0.003 s
% 1.57/1.38 % (3207)Instructions burned: 2 (million)
% 1.57/1.38 % (3207)------------------------------
% 1.57/1.38 % (3207)------------------------------
% 1.57/1.38 % (3206)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_3076 for (2999ds/27Mi)
% 1.57/1.39 % (3205)Instruction limit reached!
% 1.57/1.39 % (3205)------------------------------
% 1.57/1.39 % (3205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.39 % (3205)Termination reason: Unknown
% 1.57/1.39 % (3205)Termination phase: Saturation
% 1.57/1.39
% 1.57/1.39 % (3205)Memory used [KB]: 5500
% 1.57/1.39 % (3205)Time elapsed: 0.005 s
% 1.57/1.39 % (3205)Instructions burned: 4 (million)
% 1.57/1.39 % (3205)------------------------------
% 1.57/1.39 % (3205)------------------------------
% 1.57/1.39 % (3204)First to succeed.
% 1.57/1.39 % (3209)Also succeeded, but the first one will report.
% 1.57/1.39 % (3204)Refutation found. Thanks to Tanya!
% 1.57/1.39 % SZS status Theorem for DTF2THF_3076
% 1.57/1.39 % SZS output start Proof for DTF2THF_3076
% 1.57/1.39 thf(func_def_0, type, cQ_2: $i > $i > $i > $o).
% 1.57/1.39 thf(func_def_1, type, f: $i > $i).
% 1.57/1.39 thf(func_def_2, type, cP_1: $i > $i > $o).
% 1.57/1.39 thf(func_def_3, type, cQ_1: $i > $i > $i > $o).
% 1.57/1.39 thf(f44,plain,(
% 1.57/1.39 $false),
% 1.57/1.39 inference(avatar_sat_refutation,[status(thm)],[f28,f33,f38,f43])).
% 1.57/1.39 thf(f43,plain,(
% 1.57/1.39 ~spl0_1),
% 1.57/1.39 inference(avatar_contradiction_clause,[status(thm)],[f42])).
% 1.57/1.39 thf(f42,plain,(
% 1.57/1.39 $false | ~spl0_1),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.57/1.39 thf(f41,plain,(
% 1.57/1.39 ($true != $true) | ~spl0_1),
% 1.57/1.39 inference(superposition,[status(thm)],[f40,f14])).
% 1.57/1.39 thf(f14,plain,(
% 1.57/1.39 ((cP_1 @ c @ c) = $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 thf(f7,plain,(
% 1.57/1.39 ! [X0 : $i,X1 : $i,X2 : $i] : ((cQ_2 @ X1 @ X0 @ X2) != $true) & ((cP_1 @ c @ c) = $true) & ! [X3 : $i] : ((cP_1 @ d @ X3) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X4 : $i,X5 : $i] : (((cP_1 @ (f @ X4) @ X5) = $true) | ((cP_1 @ X4 @ X5) != $true)) & ((cP_1 @ b @ b) = $true) & ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i,X11 : $i] : (((cP_1 @ (f @ X7) @ X8) != $true) | ($true = (cQ_2 @ X11 @ X8 @ X6)) | ((cP_1 @ (f @ X10) @ X6) != $true) | ((cQ_1 @ X9 @ X7 @ X10) != $true) | ((cP_1 @ (f @ X9) @ X11) != $true)) & ((cP_1 @ a @ a) = $true)),
% 1.57/1.39 inference(rectify,[status(thm)],[f6])).
% 1.57/1.39 thf(f6,plain,(
% 1.57/1.39 ! [X0 : $i,X1 : $i,X2 : $i] : ((cQ_2 @ X1 @ X0 @ X2) != $true) & ((cP_1 @ c @ c) = $true) & ! [X3 : $i] : ((cP_1 @ d @ X3) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X11 : $i,X10 : $i] : (((cP_1 @ (f @ X11) @ X10) = $true) | ((cP_1 @ X11 @ X10) != $true)) & ((cP_1 @ b @ b) = $true) & ! [X4 : $i,X7 : $i,X5 : $i,X9 : $i,X6 : $i,X8 : $i] : (((cP_1 @ (f @ X7) @ X5) != $true) | ($true = (cQ_2 @ X8 @ X5 @ X4)) | ((cP_1 @ (f @ X6) @ X4) != $true) | ($true != (cQ_1 @ X9 @ X7 @ X6)) | ((cP_1 @ (f @ X9) @ X8) != $true)) & ((cP_1 @ a @ a) = $true)),
% 1.57/1.39 inference(flattening,[status(thm)],[f5])).
% 1.57/1.39 thf(f5,plain,(
% 1.57/1.39 ~~(((cP_1 @ c @ c) = $true) & ! [X0 : $i,X1 : $i,X2 : $i] : ~((cQ_2 @ X1 @ X0 @ X2) = $true) & ((cQ_1 @ a @ b @ c) = $true) & ! [X3 : $i] : ((cP_1 @ d @ X3) = $true) & ! [X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i,X9 : $i] : (~((cP_1 @ (f @ X7) @ X5) = $true) | ~((cP_1 @ (f @ X6) @ X4) = $true) | ~($true = (cQ_1 @ X9 @ X7 @ X6)) | ~((cP_1 @ (f @ X9) @ X8) = $true) | ($true = (cQ_2 @ X8 @ X5 @ X4))) & ! [X10 : $i,X11 : $i] : (((cP_1 @ (f @ X11) @ X10) = $true) | ~((cP_1 @ X11 @ X10) = $true)) & ((cP_1 @ b @ b) = $true) & ((cP_1 @ a @ a) = $true))),
% 1.57/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.39 thf(f4,plain,(
% 1.57/1.39 ~~((cP_1 @ c @ c) & ! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_2 @ X1 @ X0 @ X2) & (cQ_1 @ a @ b @ c) & ! [X3 : $i] : (cP_1 @ d @ X3) & ! [X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i,X9 : $i] : (~(cP_1 @ (f @ X7) @ X5) | ~(cP_1 @ (f @ X6) @ X4) | ~(cQ_1 @ X9 @ X7 @ X6) | ~(cP_1 @ (f @ X9) @ X8) | (cQ_2 @ X8 @ X5 @ X4)) & ! [X10 : $i,X11 : $i] : ((cP_1 @ (f @ X11) @ X10) | ~(cP_1 @ X11 @ X10)) & (cP_1 @ b @ b) & (cP_1 @ a @ a))),
% 1.57/1.39 inference(rectify,[status(thm)],[f2])).
% 1.57/1.39 thf(f2,negated_conjecture,(
% 1.57/1.39 ~~((cP_1 @ c @ c) & ! [X1 : $i,X0 : $i,X2 : $i] : ~(cQ_2 @ X0 @ X1 @ X2) & (cQ_1 @ a @ b @ c) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X5 : $i,X4 : $i,X2 : $i,X1 : $i,X3 : $i,X0 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | ~(cQ_1 @ X0 @ X1 @ X2) | ~(cP_1 @ (f @ X0) @ X3) | (cQ_2 @ X3 @ X4 @ X5)) & ! [X1 : $i,X0 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & (cP_1 @ b @ b) & (cP_1 @ a @ a))),
% 1.57/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.39 thf(f1,conjecture,(
% 1.57/1.39 ~((cP_1 @ c @ c) & ! [X1 : $i,X0 : $i,X2 : $i] : ~(cQ_2 @ X0 @ X1 @ X2) & (cQ_1 @ a @ b @ c) & ! [X0 : $i] : (cP_1 @ d @ X0) & ! [X5 : $i,X4 : $i,X2 : $i,X1 : $i,X3 : $i,X0 : $i] : (~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X2) @ X5) | ~(cQ_1 @ X0 @ X1 @ X2) | ~(cP_1 @ (f @ X0) @ X3) | (cQ_2 @ X3 @ X4 @ X5)) & ! [X1 : $i,X0 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & (cP_1 @ b @ b) & (cP_1 @ a @ a))),
% 1.57/1.39 file('/export/starexec/sandbox2/tmp/tmp.oGc6dB4AOk/DTF2THF_3076.p',cTHM409_1)).
% 1.57/1.39 thf(f40,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (((cP_1 @ c @ X0) != $true)) ) | ~spl0_1),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.57/1.39 thf(f39,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (((cP_1 @ c @ X0) != $true) | ($true != $true)) ) | ~spl0_1),
% 1.57/1.39 inference(superposition,[status(thm)],[f21,f11])).
% 1.57/1.39 thf(f11,plain,(
% 1.57/1.39 ( ! [X4 : $i,X5 : $i] : (((cP_1 @ (f @ X4) @ X5) = $true) | ((cP_1 @ X4 @ X5) != $true)) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 thf(f21,plain,(
% 1.57/1.39 ( ! [X2 : $i] : (((cP_1 @ (f @ c) @ X2) != $true)) ) | ~spl0_1),
% 1.57/1.39 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.57/1.39 thf(f20,definition,(
% 1.57/1.39 spl0_1 <=> ! [X2 : $i] : ((cP_1 @ (f @ c) @ X2) != $true)),
% 1.57/1.39 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.57/1.39 thf(f38,plain,(
% 1.57/1.39 ~spl0_3),
% 1.57/1.39 inference(avatar_contradiction_clause,[status(thm)],[f37])).
% 1.57/1.39 thf(f37,plain,(
% 1.57/1.39 $false | ~spl0_3),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.57/1.39 thf(f36,plain,(
% 1.57/1.39 ($true != $true) | ~spl0_3),
% 1.57/1.39 inference(superposition,[status(thm)],[f35,f8])).
% 1.57/1.39 thf(f8,plain,(
% 1.57/1.39 ((cP_1 @ a @ a) = $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 thf(f35,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (((cP_1 @ a @ X0) != $true)) ) | ~spl0_3),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.57/1.39 thf(f34,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (((cP_1 @ a @ X0) != $true) | ($true != $true)) ) | ~spl0_3),
% 1.57/1.39 inference(superposition,[status(thm)],[f27,f11])).
% 1.57/1.39 thf(f27,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (((cP_1 @ (f @ a) @ X0) != $true)) ) | ~spl0_3),
% 1.57/1.39 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.57/1.39 thf(f26,definition,(
% 1.57/1.39 spl0_3 <=> ! [X0 : $i] : ((cP_1 @ (f @ a) @ X0) != $true)),
% 1.57/1.39 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.57/1.39 thf(f33,plain,(
% 1.57/1.39 ~spl0_2),
% 1.57/1.39 inference(avatar_contradiction_clause,[status(thm)],[f32])).
% 1.57/1.39 thf(f32,plain,(
% 1.57/1.39 $false | ~spl0_2),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.57/1.39 thf(f31,plain,(
% 1.57/1.39 ($true != $true) | ~spl0_2),
% 1.57/1.39 inference(superposition,[status(thm)],[f30,f10])).
% 1.57/1.39 thf(f10,plain,(
% 1.57/1.39 ((cP_1 @ b @ b) = $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 thf(f30,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.57/1.39 thf(f29,plain,(
% 1.57/1.39 ( ! [X0 : $i] : (($true != $true) | ((cP_1 @ b @ X0) != $true)) ) | ~spl0_2),
% 1.57/1.39 inference(superposition,[status(thm)],[f24,f11])).
% 1.57/1.39 thf(f24,plain,(
% 1.57/1.39 ( ! [X1 : $i] : (((cP_1 @ (f @ b) @ X1) != $true)) ) | ~spl0_2),
% 1.57/1.39 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.57/1.39 thf(f23,definition,(
% 1.57/1.39 spl0_2 <=> ! [X1 : $i] : ((cP_1 @ (f @ b) @ X1) != $true)),
% 1.57/1.39 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.57/1.39 thf(f28,plain,(
% 1.57/1.39 spl0_1 | spl0_2 | spl0_3),
% 1.57/1.39 inference(avatar_split_clause,[status(thm)],[f18,f26,f23,f20])).
% 1.57/1.39 thf(f18,plain,(
% 1.57/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_1 @ (f @ c) @ X2) != $true) | ((cP_1 @ (f @ b) @ X1) != $true) | ((cP_1 @ (f @ a) @ X0) != $true)) )),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.57/1.39 thf(f17,plain,(
% 1.57/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP_1 @ (f @ b) @ X1) != $true) | ($true != $true) | ((cP_1 @ (f @ c) @ X2) != $true) | ((cP_1 @ (f @ a) @ X0) != $true)) )),
% 1.57/1.39 inference(superposition,[status(thm)],[f16,f12])).
% 1.57/1.39 thf(f12,plain,(
% 1.57/1.39 ((cQ_1 @ a @ b @ c) = $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 thf(f16,plain,(
% 1.57/1.39 ( ! [X10 : $i,X11 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((cQ_1 @ X9 @ X7 @ X10) != $true) | ((cP_1 @ (f @ X9) @ X11) != $true) | ((cP_1 @ (f @ X7) @ X8) != $true) | ((cP_1 @ (f @ X10) @ X6) != $true)) )),
% 1.57/1.39 inference(subsumption_resolution,[status(thm)],[f9,f15])).
% 1.57/1.39 thf(f15,plain,(
% 1.57/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cQ_2 @ X1 @ X0 @ X2) != $true)) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 thf(f9,plain,(
% 1.57/1.39 ( ! [X10 : $i,X11 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (((cP_1 @ (f @ X7) @ X8) != $true) | ((cP_1 @ (f @ X9) @ X11) != $true) | ((cP_1 @ (f @ X10) @ X6) != $true) | ((cQ_1 @ X9 @ X7 @ X10) != $true) | ($true = (cQ_2 @ X11 @ X8 @ X6))) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.39 % SZS output end Proof for DTF2THF_3076
% 1.57/1.39 % (3204)------------------------------
% 1.57/1.39 % (3204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.39 % (3204)Termination reason: Refutation
% 1.57/1.39
% 1.57/1.39 % (3204)Memory used [KB]: 5500
% 1.57/1.39 % (3204)Time elapsed: 0.006 s
% 1.57/1.39 % (3204)Instructions burned: 5 (million)
% 1.57/1.39 % (3204)------------------------------
% 1.57/1.39 % (3204)------------------------------
% 1.57/1.39 % (3203)Success in time 0.022 s
%------------------------------------------------------------------------------