%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG285^5 : 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 : n028.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 08:37:50 AM UTC 2026
% Result : Theorem 1.53s 1.45s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 92 ( 71 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 393 ( 39 ~; 22 |; 24 &; 300 @)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 118 ( 0 ^; 92 !; 26 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cP: a > a > a ).
thf(func_def_2,type,
cE: a ).
thf(func_def_3,type,
cJ: a > a ).
thf(func_def_7,type,
sK0: a ).
thf(func_def_8,type,
sK1: a ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_10,type,
sK3: a ).
thf(func_def_11,type,
sK4: a ).
thf(f217,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f27,f210,f216]) ).
thf(f216,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[status(thm)],[f215]) ).
thf(f215,plain,
( $false
| ~ spl5_2 ),
inference(equality_resolution,[status(thm)],[f213]) ).
thf(f213,plain,
( ! [X0: a] : ( sK4 != X0 )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f21,f108]) ).
thf(f108,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ ( cP @ X1 @ ( cJ @ X0 ) ) ) @ X1 )
= X0 ),
inference(forward_demodulation,[status(thm)],[f78,f64]) ).
thf(f64,plain,
! [X0: a] :
( ( cP @ X0 @ cE )
= X0 ),
inference(superposition,[status(thm)],[f37,f35]) ).
thf(f35,plain,
! [X0: a] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(superposition,[status(thm)],[f33,f14]) ).
thf(f14,plain,
! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: a,X2: a,X3: a] :
( ( cP @ X3 @ ( cP @ X2 @ X1 ) )
= ( cP @ ( cP @ X3 @ X2 ) @ X1 ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 )
& ( ( ( cP @ ( cP @ sK0 @ sK1 ) @ sK2 )
!= ( cP @ sK0 @ ( cP @ sK1 @ sK2 ) ) )
| ! [X10: a] :
( sK4
!= ( cP @ sK3 @ X10 ) )
| ! [X11: a] :
( sK4
!= ( cP @ X11 @ sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X5: a,X6: a,X7: a] :
( ( cP @ ( cP @ X5 @ X6 ) @ X7 )
!= ( cP @ X5 @ ( cP @ X6 @ X7 ) ) )
=> ( ( cP @ ( cP @ sK0 @ sK1 ) @ sK2 )
!= ( cP @ sK0 @ ( cP @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X8: a,X9: a] :
( ! [X10: a] :
( ( cP @ X8 @ X10 )
!= X9 )
| ! [X11: a] :
( ( cP @ X11 @ X8 )
!= X9 ) )
=> ( ! [X10: a] :
( sK4
!= ( cP @ sK3 @ X10 ) )
| ! [X11: a] :
( sK4
!= ( cP @ X11 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: a,X2: a,X3: a] :
( ( cP @ X3 @ ( cP @ X2 @ X1 ) )
= ( cP @ ( cP @ X3 @ X2 ) @ X1 ) )
& ! [X4: a] :
( ( cP @ cE @ X4 )
= X4 )
& ( ? [X5: a,X6: a,X7: a] :
( ( cP @ ( cP @ X5 @ X6 ) @ X7 )
!= ( cP @ X5 @ ( cP @ X6 @ X7 ) ) )
| ? [X8: a,X9: a] :
( ! [X10: a] :
( ( cP @ X8 @ X10 )
!= X9 )
| ! [X11: a] :
( ( cP @ X11 @ X8 )
!= X9 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X4: a] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) )
& ! [X2: a,X3: a,X1: a] :
( ( cP @ X1 @ ( cP @ X3 @ X2 ) )
= ( cP @ ( cP @ X1 @ X3 ) @ X2 ) )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ( ? [X7: a,X6: a,X5: a] :
( ( cP @ X7 @ ( cP @ X6 @ X5 ) )
!= ( cP @ ( cP @ X7 @ X6 ) @ X5 ) )
| ? [X9: a,X8: a] :
( ! [X11: a] :
( ( cP @ X9 @ X11 )
!= X8 )
| ! [X10: a] :
( ( cP @ X10 @ X9 )
!= X8 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ? [X7: a,X6: a,X5: a] :
( ( cP @ X7 @ ( cP @ X6 @ X5 ) )
!= ( cP @ ( cP @ X7 @ X6 ) @ X5 ) )
| ? [X9: a,X8: a] :
( ! [X11: a] :
( ( cP @ X9 @ X11 )
!= X8 )
| ! [X10: a] :
( ( cP @ X10 @ X9 )
!= X8 ) ) )
& ! [X2: a,X3: a,X1: a] :
( ( cP @ X1 @ ( cP @ X3 @ X2 ) )
= ( cP @ ( cP @ X1 @ X3 ) @ X2 ) )
& ! [X4: a] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X2: a,X3: a,X1: a] :
( ( cP @ X1 @ ( cP @ X3 @ X2 ) )
= ( cP @ ( cP @ X1 @ X3 ) @ X2 ) )
& ! [X4: a] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 ) )
=> ( ! [X9: a,X8: a] :
( ? [X11: a] :
( ( cP @ X9 @ X11 )
= X8 )
& ? [X10: a] :
( ( cP @ X10 @ X9 )
= X8 ) )
& ! [X7: a,X6: a,X5: a] :
( ( cP @ X7 @ ( cP @ X6 @ X5 ) )
= ( cP @ ( cP @ X7 @ X6 ) @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: a,X2: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) )
=> ( ! [X2: a,X1: a,X0: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X4: a,X3: a] :
( ? [X6: a] :
( ( cP @ X6 @ X3 )
= X4 )
& ? [X5: a] :
( ( cP @ X3 @ X5 )
= X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: a,X2: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) )
=> ( ! [X2: a,X1: a,X0: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X4: a,X3: a] :
( ? [X6: a] :
( ( cP @ X6 @ X3 )
= X4 )
& ? [X5: a] :
( ( cP @ X3 @ X5 )
= X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oP4skSro89/DTF2THF_22476.p',cTHM22_pme) ).
thf(f33,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[status(thm)],[f29,f12]) ).
thf(f12,plain,
! [X4: a] :
( ( cP @ cE @ X4 )
= X4 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f29,plain,
! [X0: a,X1: a] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f13,f14]) ).
thf(f13,plain,
! [X2: a,X3: a,X1: a] :
( ( cP @ X3 @ ( cP @ X2 @ X1 ) )
= ( cP @ ( cP @ X3 @ X2 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f37,plain,
! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
= ( cP @ ( cJ @ ( cJ @ X0 ) ) @ X1 ) ),
inference(superposition,[status(thm)],[f33,f33]) ).
thf(f78,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ ( cP @ X1 @ ( cJ @ X0 ) ) ) @ ( cP @ X1 @ cE ) )
= X0 ),
inference(superposition,[status(thm)],[f36,f14]) ).
thf(f36,plain,
! [X2: a,X0: a,X1: a] :
( ( cP @ ( cJ @ ( cP @ X0 @ X1 ) ) @ ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
= X2 ),
inference(superposition,[status(thm)],[f33,f13]) ).
thf(f21,plain,
( ! [X11: a] :
( sK4
!= ( cP @ X11 @ sK3 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl5_2
<=> ! [X11: a] :
( sK4
!= ( cP @ X11 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f210,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[status(thm)],[f209]) ).
thf(f209,plain,
( $false
| ~ spl5_3 ),
inference(equality_resolution,[status(thm)],[f169]) ).
thf(f169,plain,
( ! [X0: a] : ( sK4 != X0 )
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f24,f65]) ).
thf(f65,plain,
! [X0: a,X1: a] :
( ( cP @ X0 @ ( cP @ ( cJ @ X0 ) @ X1 ) )
= X1 ),
inference(superposition,[status(thm)],[f37,f33]) ).
thf(f24,plain,
( ! [X10: a] :
( sK4
!= ( cP @ sK3 @ X10 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl5_3
<=> ! [X10: a] :
( sK4
!= ( cP @ sK3 @ X10 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f27,plain,
spl5_1,
inference(avatar_contradiction_clause,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
| spl5_1 ),
inference(subsumption_resolution,[status(thm)],[f18,f13]) ).
thf(f18,plain,
( ( ( cP @ ( cP @ sK0 @ sK1 ) @ sK2 )
!= ( cP @ sK0 @ ( cP @ sK1 @ sK2 ) ) )
| spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl5_1
<=> ( ( cP @ ( cP @ sK0 @ sK1 ) @ sK2 )
= ( cP @ sK0 @ ( cP @ sK1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f25,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f11,f23,f20,f16]) ).
thf(f11,plain,
! [X10: a,X11: a] :
( ( ( cP @ ( cP @ sK0 @ sK1 ) @ sK2 )
!= ( cP @ sK0 @ ( cP @ sK1 @ sK2 ) ) )
| ( sK4
!= ( cP @ sK3 @ X10 ) )
| ( sK4
!= ( cP @ X11 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG285^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Feb 24 03:42:57 EST 2026
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.43 ---- Original DTF file ---
% 0.14/0.43 thf(spec,logic,$$dhol).
% 0.14/0.43 %------------------------------------------------------------------------------
% 0.14/0.43 % File : ALG285^5 : TPTP v9.2.1. Released v4.0.0.
% 0.14/0.43 % Domain : General Algebra
% 0.14/0.43 % Problem : TPS problem from GRP-THMS
% 0.14/0.43 % Version : Especial.
% 0.14/0.43 % English :
% 0.14/0.43
% 0.14/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.14/0.43 % Source : [Bro09]
% 0.14/0.43 % Names : tps_1023 [Bro09]
% 0.14/0.43
% 0.14/0.43 % Status : Theorem
% 0.14/0.43 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.0
% 0.14/0.43 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.14/0.43 % Number of atoms : 6 ( 6 equ; 0 cnn)
% 0.14/0.43 % Maximal formula atoms : 6 ( 6 avg)
% 0.14/0.43 % Number of connectives : 30 ( 0 ~; 0 |; 4 &; 25 @)
% 0.14/0.43 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.14/0.43 % Maximal formula depth : 7 ( 7 avg)
% 0.14/0.43 % Number of types : 1 ( 1 usr)
% 0.14/0.43 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.14/0.43 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.14/0.43 % Number of variables : 12 ( 0 ^; 10 !; 2 ?; 12 :)
% 0.14/0.43 % SPC : TH0_THM_EQU_NAR
% 0.14/0.43
% 0.14/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.14/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.14/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.14/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.14/0.43 %------------------------------------------------------------------------------
% 0.14/0.43 thf(a_type,type,
% 0.14/0.43 a: $tType ).
% 0.14/0.43
% 0.14/0.43 thf(cP,type,
% 0.14/0.43 cP: a > a > a ).
% 0.14/0.43
% 0.14/0.43 thf(cE,type,
% 0.14/0.43 cE: a ).
% 0.14/0.43
% 0.14/0.43 thf(cJ,type,
% 0.14/0.43 cJ: a > a ).
% 0.14/0.43
% 0.14/0.43 thf(cTHM22_pme,conjecture,
% 0.14/0.43 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.14/0.43 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.14/0.43 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.14/0.43 & ! [Xx: a] :
% 0.14/0.43 ( ( cP @ cE @ Xx )
% 0.14/0.43 = Xx )
% 0.14/0.43 & ! [Xy: a] :
% 0.14/0.43 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 0.14/0.43 = cE ) )
% 0.14/0.43 => ( ! [Xx: a,Xy: a,Xz: a] :
% 0.14/0.43 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.14/0.43 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.14/0.43 & ! [X: a,Y: a] :
% 0.14/0.43 ( ? [U: a] :
% 0.14/0.43 ( ( cP @ X @ U )
% 0.14/0.43 = Y )
% 0.14/0.43 & ? [V: a] :
% 0.14/0.43 ( ( cP @ V @ X )
% 0.14/0.43 = Y ) ) ) ) ).
% 0.14/0.43
% 0.14/0.43 %------------------------------------------------------------------------------
% 0.14/0.43 ------------------------
% 1.48/1.32 ---- Embedded in THF ---
% 1.48/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.33 %%% Generated on Tue Feb 24 03:42:58 EST 2026
% 1.48/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.33 %%% Logic specification used:
% 1.48/1.33 %%% thf(spec, logic, $$dhol).
% 1.48/1.33
% 1.48/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oP4skSro89/DTF2DTF22476.p
% See solution above
% 1.48/1.33 ------------------------
% 1.48/1.33 ---- Cleaned THF ---
% 1.48/1.34 thf(a_type,type,
% 1.48/1.34 a: $tType ).
% 1.48/1.34
% 1.48/1.34 thf(cP,type,
% 1.48/1.34 cP: a > a > a ).
% 1.48/1.34
% 1.48/1.34 thf(cE,type,
% 1.48/1.34 cE: a ).
% 1.48/1.34
% 1.48/1.34 thf(cJ,type,
% 1.48/1.34 cJ: a > a ).
% 1.48/1.34
% 1.48/1.34 thf(cTHM22_pme,conjecture,
% 1.48/1.34 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.48/1.34 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 1.48/1.34 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 1.48/1.34 & ! [Xx: a] :
% 1.48/1.34 ( ( cP @ cE @ Xx )
% 1.48/1.34 = Xx )
% 1.48/1.34 & ! [Xy: a] :
% 1.48/1.34 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 1.48/1.34 = cE ) )
% 1.48/1.34 => ( ! [Xx: a,Xy: a,Xz: a] :
% 1.48/1.34 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 1.48/1.34 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 1.48/1.34 & ! [X: a,Y: a] :
% 1.48/1.34 ( ? [U: a] :
% 1.48/1.34 ( ( cP @ X @ U )
% 1.48/1.34 = Y )
% 1.48/1.34 & ? [V: a] :
% 1.48/1.34 ( ( cP @ V @ X )
% 1.48/1.34 = Y ) ) ) ) ).
% 1.48/1.34 ------------------------
% 1.48/1.36 % (22577)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_22476 for (2999ds/2Mi)
% 1.48/1.36 % (22573)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/183Mi)
% 1.48/1.36 % (22575)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_22476 for (2999ds/27Mi)
% 1.48/1.36 % (22578)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_22476 for (2999ds/275Mi)
% 1.48/1.36 % (22576)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/2Mi)
% 1.48/1.36 % (22579)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/18Mi)
% 1.48/1.36 % (22574)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_22476 for (2999ds/4Mi)
% 1.48/1.36 % (22576)Instruction limit reached!
% 1.48/1.36 % (22576)------------------------------
% 1.48/1.36 % (22576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.36 % (22576)Termination reason: Unknown
% 1.48/1.36 % (22577)Instruction limit reached!
% 1.48/1.36 % (22577)------------------------------
% 1.48/1.36 % (22577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.36 % (22577)Termination reason: Unknown
% 1.48/1.36 % (22577)Termination phase: Saturation
% 1.48/1.36
% 1.48/1.36 % (22577)Memory used [KB]: 5500
% 1.48/1.36 % (22577)Time elapsed: 0.003 s
% 1.48/1.36 % (22577)Instructions burned: 3 (million)
% 1.48/1.36 % (22577)------------------------------
% 1.48/1.36 % (22577)------------------------------
% 1.48/1.36 % (22576)Termination phase: Saturation
% 1.48/1.36
% 1.48/1.36 % (22576)Memory used [KB]: 5500
% 1.48/1.36 % (22576)Time elapsed: 0.003 s
% 1.48/1.36 % (22576)Instructions burned: 2 (million)
% 1.48/1.36 % (22576)------------------------------
% 1.48/1.36 % (22576)------------------------------
% 1.48/1.36 % (22574)Instruction limit reached!
% 1.48/1.36 % (22574)------------------------------
% 1.48/1.36 % (22574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.36 % (22574)Termination reason: Unknown
% 1.48/1.36 % (22574)Termination phase: Saturation
% 1.48/1.36
% 1.48/1.36 % (22574)Memory used [KB]: 5500
% 1.48/1.36 % (22574)Time elapsed: 0.005 s
% 1.48/1.36 % (22574)Instructions burned: 5 (million)
% 1.48/1.36 % (22574)------------------------------
% 1.48/1.36 % (22574)------------------------------
% 1.48/1.37 % (22579)Instruction limit reached!
% 1.48/1.37 % (22579)------------------------------
% 1.48/1.37 % (22579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.37 % (22579)Termination reason: Unknown
% 1.48/1.37 % (22579)Termination phase: Saturation
% 1.48/1.37
% 1.48/1.37 % (22579)Memory used [KB]: 5500
% 1.48/1.37 % (22579)Time elapsed: 0.012 s
% 1.48/1.37 % (22579)Instructions burned: 19 (million)
% 1.48/1.37 % (22579)------------------------------
% 1.48/1.37 % (22579)------------------------------
% 1.48/1.37 % (22575)Instruction limit reached!
% 1.48/1.37 % (22575)------------------------------
% 1.48/1.37 % (22575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.37 % (22575)Termination reason: Unknown
% 1.48/1.37 % (22575)Termination phase: Saturation
% 1.48/1.37
% 1.48/1.37 % (22575)Memory used [KB]: 5628
% 1.48/1.37 % (22575)Time elapsed: 0.016 s
% 1.48/1.37 % (22575)Instructions burned: 27 (million)
% 1.48/1.37 % (22575)------------------------------
% 1.48/1.37 % (22575)------------------------------
% 1.48/1.37 % (22580)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/3Mi)
% 1.48/1.37 % (22581)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/37Mi)
% 1.48/1.37 % (22580)Instruction limit reached!
% 1.48/1.37 % (22580)------------------------------
% 1.48/1.37 % (22580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.37 % (22580)Termination reason: Unknown
% 1.48/1.37 % (22580)Termination phase: Saturation
% 1.48/1.37
% 1.48/1.37 % (22580)Memory used [KB]: 5500
% 1.48/1.37 % (22580)Time elapsed: 0.003 s
% 1.48/1.37 % (22580)Instructions burned: 3 (million)
% 1.48/1.37 % (22580)------------------------------
% 1.48/1.37 % (22580)------------------------------
% 1.48/1.37 % (22582)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/15Mi)
% 1.48/1.38 % (22583)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/3Mi)
% 1.48/1.38 % (22582)Instruction limit reached!
% 1.48/1.38 % (22582)------------------------------
% 1.48/1.38 % (22582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.38 % (22582)Termination reason: Unknown
% 1.48/1.38 % (22582)Termination phase: Saturation
% 1.48/1.38
% 1.48/1.38 % (22582)Memory used [KB]: 5628
% 1.48/1.38 % (22582)Time elapsed: 0.010 s
% 1.48/1.38 % (22582)Instructions burned: 16 (million)
% 1.48/1.38 % (22582)------------------------------
% 1.48/1.38 % (22582)------------------------------
% 1.48/1.38 % (22583)Instruction limit reached!
% 1.48/1.38 % (22583)------------------------------
% 1.48/1.38 % (22583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.38 % (22583)Termination reason: Unknown
% 1.48/1.38 % (22583)Termination phase: Saturation
% 1.48/1.38
% 1.48/1.38 % (22583)Memory used [KB]: 5500
% 1.48/1.38 % (22583)Time elapsed: 0.003 s
% 1.48/1.38 % (22583)Instructions burned: 3 (million)
% 1.48/1.38 % (22583)------------------------------
% 1.48/1.38 % (22583)------------------------------
% 1.48/1.39 % (22584)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/1041Mi)
% 1.48/1.39 % (22585)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/7Mi)
% 1.48/1.39 % (22581)Instruction limit reached!
% 1.48/1.39 % (22581)------------------------------
% 1.48/1.39 % (22581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.39 % (22581)Termination reason: Unknown
% 1.48/1.39 % (22581)Termination phase: Saturation
% 1.48/1.39
% 1.48/1.39 % (22581)Memory used [KB]: 5756
% 1.48/1.39 % (22581)Time elapsed: 0.021 s
% 1.48/1.39 % (22581)Instructions burned: 38 (million)
% 1.48/1.39 % (22581)------------------------------
% 1.48/1.39 % (22581)------------------------------
% 1.48/1.39 % (22585)Instruction limit reached!
% 1.48/1.39 % (22585)------------------------------
% 1.48/1.39 % (22585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.39 % (22585)Termination reason: Unknown
% 1.48/1.39 % (22585)Termination phase: Saturation
% 1.48/1.39
% 1.48/1.39 % (22585)Memory used [KB]: 1023
% 1.48/1.39 % (22585)Time elapsed: 0.005 s
% 1.48/1.39 % (22585)Instructions burned: 7 (million)
% 1.48/1.39 % (22585)------------------------------
% 1.48/1.39 % (22585)------------------------------
% 1.53/1.40 % (22586)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/16Mi)
% 1.53/1.40 % (22587)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/3Mi)
% 1.53/1.40 % (22587)Instruction limit reached!
% 1.53/1.40 % (22587)------------------------------
% 1.53/1.40 % (22587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.40 % (22587)Termination reason: Unknown
% 1.53/1.40 % (22587)Termination phase: Saturation
% 1.53/1.40
% 1.53/1.40 % (22587)Memory used [KB]: 5500
% 1.53/1.40 % (22587)Time elapsed: 0.003 s
% 1.53/1.40 % (22587)Instructions burned: 3 (million)
% 1.53/1.40 % (22587)------------------------------
% 1.53/1.40 % (22587)------------------------------
% 1.53/1.41 % (22588)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/3Mi)
% 1.53/1.41 % (22586)Instruction limit reached!
% 1.53/1.41 % (22586)------------------------------
% 1.53/1.41 % (22586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.41 % (22586)Termination reason: Unknown
% 1.53/1.41 % (22586)Termination phase: Saturation
% 1.53/1.41
% 1.53/1.41 % (22586)Memory used [KB]: 5628
% 1.53/1.41 % (22586)Time elapsed: 0.011 s
% 1.53/1.41 % (22586)Instructions burned: 17 (million)
% 1.53/1.41 % (22586)------------------------------
% 1.53/1.41 % (22586)------------------------------
% 1.53/1.41 % (22589)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/7Mi)
% 1.53/1.41 % (22588)Instruction limit reached!
% 1.53/1.41 % (22588)------------------------------
% 1.53/1.41 % (22588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.41 % (22588)Termination reason: Unknown
% 1.53/1.41 % (22588)Termination phase: Saturation
% 1.53/1.41
% 1.53/1.41 % (22588)Memory used [KB]: 1023
% 1.53/1.41 % (22588)Time elapsed: 0.003 s
% 1.53/1.41 % (22588)Instructions burned: 3 (million)
% 1.53/1.41 % (22588)------------------------------
% 1.53/1.41 % (22588)------------------------------
% 1.53/1.41 % (22589)Refutation not found, incomplete strategy
% 1.53/1.41 % (22589)------------------------------
% 1.53/1.41 % (22589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.41 % (22589)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.41
% 1.53/1.41
% 1.53/1.41 % (22589)Memory used [KB]: 5500
% 1.53/1.41 % (22589)Time elapsed: 0.003 s
% 1.53/1.41 % (22589)Instructions burned: 3 (million)
% 1.53/1.41 % (22589)------------------------------
% 1.53/1.41 % (22589)------------------------------
% 1.53/1.42 % (22590)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/3Mi)
% 1.53/1.42 % (22590)Instruction limit reached!
% 1.53/1.42 % (22590)------------------------------
% 1.53/1.42 % (22590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.42 % (22590)Termination reason: Unknown
% 1.53/1.42 % (22590)Termination phase: Saturation
% 1.53/1.42
% 1.53/1.42 % (22590)Memory used [KB]: 5500
% 1.53/1.42 % (22590)Time elapsed: 0.003 s
% 1.53/1.42 % (22590)Instructions burned: 4 (million)
% 1.53/1.42 % (22590)------------------------------
% 1.53/1.42 % (22590)------------------------------
% 1.53/1.42 % (22591)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/4Mi)
% 1.53/1.43 % (22592)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/18Mi)
% 1.53/1.43 % (22591)Instruction limit reached!
% 1.53/1.43 % (22591)------------------------------
% 1.53/1.43 % (22591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.43 % (22591)Termination reason: Unknown
% 1.53/1.43 % (22591)Termination phase: Saturation
% 1.53/1.43
% 1.53/1.43 % (22591)Memory used [KB]: 5500
% 1.53/1.43 % (22591)Time elapsed: 0.004 s
% 1.53/1.43 % (22591)Instructions burned: 4 (million)
% 1.53/1.43 % (22591)------------------------------
% 1.53/1.43 % (22591)------------------------------
% 1.53/1.43 % (22593)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/710Mi)
% 1.53/1.43 % (22594)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/6Mi)
% 1.53/1.44 % (22592)Instruction limit reached!
% 1.53/1.44 % (22592)------------------------------
% 1.53/1.44 % (22592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.44 % (22592)Termination reason: Unknown
% 1.53/1.44 % (22592)Termination phase: Saturation
% 1.53/1.44
% 1.53/1.44 % (22592)Memory used [KB]: 5628
% 1.53/1.44 % (22592)Time elapsed: 0.011 s
% 1.53/1.44 % (22592)Instructions burned: 18 (million)
% 1.53/1.44 % (22592)------------------------------
% 1.53/1.44 % (22592)------------------------------
% 1.53/1.44 % (22594)Instruction limit reached!
% 1.53/1.44 % (22594)------------------------------
% 1.53/1.44 % (22594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.44 % (22594)Termination reason: Unknown
% 1.53/1.44 % (22594)Termination phase: Saturation
% 1.53/1.44
% 1.53/1.44 % (22594)Memory used [KB]: 5500
% 1.53/1.44 % (22594)Time elapsed: 0.005 s
% 1.53/1.44 % (22594)Instructions burned: 7 (million)
% 1.53/1.44 % (22594)------------------------------
% 1.53/1.44 % (22594)------------------------------
% 1.53/1.44 % (22595)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/902Mi)
% 1.53/1.44 % (22573)Instruction limit reached!
% 1.53/1.44 % (22573)------------------------------
% 1.53/1.44 % (22573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.44 % (22573)Termination reason: Unknown
% 1.53/1.44 % (22573)Termination phase: Saturation
% 1.53/1.44
% 1.53/1.44 % (22573)Memory used [KB]: 6396
% 1.53/1.44 % (22573)Time elapsed: 0.091 s
% 1.53/1.44 % (22573)Instructions burned: 183 (million)
% 1.53/1.44 % (22573)------------------------------
% 1.53/1.44 % (22573)------------------------------
% 1.53/1.45 % (22593)First to succeed.
% 1.53/1.45 % (22596)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_22476 for (2999ds/21Mi)
% 1.53/1.45 % (22593)Refutation found. Thanks to Tanya!
% 1.53/1.45 % SZS status Theorem for DTF2THF_22476
% 1.53/1.45 % SZS output start Proof for DTF2THF_22476
% 1.53/1.45 thf(type_def_5, type, a: $tType).
% 1.53/1.45 thf(func_def_0, type, a: $tType).
% 1.53/1.45 thf(func_def_1, type, cP: a > a > a).
% 1.53/1.45 thf(func_def_2, type, cE: a).
% 1.53/1.45 thf(func_def_3, type, cJ: a > a).
% 1.53/1.45 thf(func_def_7, type, sK0: a).
% 1.53/1.45 thf(func_def_8, type, sK1: a).
% 1.53/1.45 thf(func_def_9, type, sK2: a).
% 1.53/1.45 thf(func_def_10, type, sK3: a).
% 1.53/1.45 thf(func_def_11, type, sK4: a).
% 1.53/1.45 thf(f217,plain,(
% 1.53/1.45 $false),
% 1.53/1.45 inference(avatar_sat_refutation,[status(thm)],[f25,f27,f210,f216])).
% 1.53/1.45 thf(f216,plain,(
% 1.53/1.45 ~spl5_2),
% 1.53/1.45 inference(avatar_contradiction_clause,[status(thm)],[f215])).
% 1.53/1.45 thf(f215,plain,(
% 1.53/1.45 $false | ~spl5_2),
% 1.53/1.45 inference(equality_resolution,[status(thm)],[f213])).
% 1.53/1.45 thf(f213,plain,(
% 1.53/1.45 ( ! [X0 : a] : ((sK4 != X0)) ) | ~spl5_2),
% 1.53/1.45 inference(superposition,[status(thm)],[f21,f108])).
% 1.53/1.45 thf(f108,plain,(
% 1.53/1.45 ( ! [X0 : a,X1 : a] : (((cP @ (cJ @ (cP @ X1 @ (cJ @ X0))) @ X1) = X0)) )),
% 1.53/1.45 inference(forward_demodulation,[status(thm)],[f78,f64])).
% 1.53/1.45 thf(f64,plain,(
% 1.53/1.45 ( ! [X0 : a] : (((cP @ X0 @ cE) = X0)) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f37,f35])).
% 1.53/1.45 thf(f35,plain,(
% 1.53/1.45 ( ! [X0 : a] : (((cP @ (cJ @ (cJ @ X0)) @ cE) = X0)) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f33,f14])).
% 1.53/1.45 thf(f14,plain,(
% 1.53/1.45 ( ! [X0 : a] : ((cE = (cP @ (cJ @ X0) @ X0))) )),
% 1.53/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.45 thf(f10,plain,(
% 1.53/1.45 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ! [X1 : a,X2 : a,X3 : a] : ((cP @ X3 @ (cP @ X2 @ X1)) = (cP @ (cP @ X3 @ X2) @ X1)) & ! [X4 : a] : ((cP @ cE @ X4) = X4) & (((cP @ (cP @ sK0 @ sK1) @ sK2) != (cP @ sK0 @ (cP @ sK1 @ sK2))) | (! [X10 : a] : (sK4 != (cP @ sK3 @ X10)) | ! [X11 : a] : (sK4 != (cP @ X11 @ sK3))))),
% 1.53/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f7,f9,f8])).
% 1.53/1.45 thf(f8,plain,(
% 1.53/1.45 ? [X5 : a,X6 : a,X7 : a] : ((cP @ (cP @ X5 @ X6) @ X7) != (cP @ X5 @ (cP @ X6 @ X7))) => ((cP @ (cP @ sK0 @ sK1) @ sK2) != (cP @ sK0 @ (cP @ sK1 @ sK2)))),
% 1.53/1.45 introduced(definition,[],[choice_axiom])).
% 1.53/1.45 thf(f9,plain,(
% 1.53/1.45 ? [X8 : a,X9 : a] : (! [X10 : a] : ((cP @ X8 @ X10) != X9) | ! [X11 : a] : ((cP @ X11 @ X8) != X9)) => (! [X10 : a] : (sK4 != (cP @ sK3 @ X10)) | ! [X11 : a] : (sK4 != (cP @ X11 @ sK3)))),
% 1.53/1.45 introduced(definition,[],[choice_axiom])).
% 1.53/1.45 thf(f7,plain,(
% 1.53/1.45 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ! [X1 : a,X2 : a,X3 : a] : ((cP @ X3 @ (cP @ X2 @ X1)) = (cP @ (cP @ X3 @ X2) @ X1)) & ! [X4 : a] : ((cP @ cE @ X4) = X4) & (? [X5 : a,X6 : a,X7 : a] : ((cP @ (cP @ X5 @ X6) @ X7) != (cP @ X5 @ (cP @ X6 @ X7))) | ? [X8 : a,X9 : a] : (! [X10 : a] : ((cP @ X8 @ X10) != X9) | ! [X11 : a] : ((cP @ X11 @ X8) != X9)))),
% 1.53/1.45 inference(rectify,[status(thm)],[f6])).
% 1.53/1.45 thf(f6,plain,(
% 1.53/1.45 ! [X4 : a] : (cE = (cP @ (cJ @ X4) @ X4)) & ! [X2 : a,X3 : a,X1 : a] : ((cP @ X1 @ (cP @ X3 @ X2)) = (cP @ (cP @ X1 @ X3) @ X2)) & ! [X0 : a] : ((cP @ cE @ X0) = X0) & (? [X7 : a,X6 : a,X5 : a] : ((cP @ X7 @ (cP @ X6 @ X5)) != (cP @ (cP @ X7 @ X6) @ X5)) | ? [X9 : a,X8 : a] : (! [X11 : a] : ((cP @ X9 @ X11) != X8) | ! [X10 : a] : ((cP @ X10 @ X9) != X8)))),
% 1.53/1.45 inference(flattening,[status(thm)],[f5])).
% 1.53/1.45 thf(f5,plain,(
% 1.53/1.45 (? [X7 : a,X6 : a,X5 : a] : ((cP @ X7 @ (cP @ X6 @ X5)) != (cP @ (cP @ X7 @ X6) @ X5)) | ? [X9 : a,X8 : a] : (! [X11 : a] : ((cP @ X9 @ X11) != X8) | ! [X10 : a] : ((cP @ X10 @ X9) != X8))) & (! [X2 : a,X3 : a,X1 : a] : ((cP @ X1 @ (cP @ X3 @ X2)) = (cP @ (cP @ X1 @ X3) @ X2)) & ! [X4 : a] : (cE = (cP @ (cJ @ X4) @ X4)) & ! [X0 : a] : ((cP @ cE @ X0) = X0))),
% 1.53/1.45 inference(ennf_transformation,[status(thm)],[f4])).
% 1.53/1.45 thf(f4,plain,(
% 1.53/1.45 ~((! [X2 : a,X3 : a,X1 : a] : ((cP @ X1 @ (cP @ X3 @ X2)) = (cP @ (cP @ X1 @ X3) @ X2)) & ! [X4 : a] : (cE = (cP @ (cJ @ X4) @ X4)) & ! [X0 : a] : ((cP @ cE @ X0) = X0)) => (! [X9 : a,X8 : a] : (? [X11 : a] : ((cP @ X9 @ X11) = X8) & ? [X10 : a] : ((cP @ X10 @ X9) = X8)) & ! [X7 : a,X6 : a,X5 : a] : ((cP @ X7 @ (cP @ X6 @ X5)) = (cP @ (cP @ X7 @ X6) @ X5))))),
% 1.53/1.45 inference(rectify,[status(thm)],[f2])).
% 1.53/1.45 thf(f2,negated_conjecture,(
% 1.53/1.45 ~((! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X0 : a,X2 : a,X1 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1))) => (! [X2 : a,X1 : a,X0 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X4 : a,X3 : a] : (? [X6 : a] : ((cP @ X6 @ X3) = X4) & ? [X5 : a] : ((cP @ X3 @ X5) = X4))))),
% 1.53/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.45 thf(f1,conjecture,(
% 1.53/1.45 (! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X0 : a,X2 : a,X1 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1))) => (! [X2 : a,X1 : a,X0 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X4 : a,X3 : a] : (? [X6 : a] : ((cP @ X6 @ X3) = X4) & ? [X5 : a] : ((cP @ X3 @ X5) = X4)))),
% 1.53/1.45 file('/export/starexec/sandbox2/tmp/tmp.oP4skSro89/DTF2THF_22476.p',cTHM22_pme)).
% 1.53/1.45 thf(f33,plain,(
% 1.53/1.45 ( ! [X0 : a,X1 : a] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = X1)) )),
% 1.53/1.45 inference(forward_demodulation,[status(thm)],[f29,f12])).
% 1.53/1.45 thf(f12,plain,(
% 1.53/1.45 ( ! [X4 : a] : (((cP @ cE @ X4) = X4)) )),
% 1.53/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.45 thf(f29,plain,(
% 1.53/1.45 ( ! [X0 : a,X1 : a] : (((cP @ cE @ X1) = (cP @ (cJ @ X0) @ (cP @ X0 @ X1)))) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f13,f14])).
% 1.53/1.45 thf(f13,plain,(
% 1.53/1.45 ( ! [X2 : a,X3 : a,X1 : a] : (((cP @ X3 @ (cP @ X2 @ X1)) = (cP @ (cP @ X3 @ X2) @ X1))) )),
% 1.53/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.45 thf(f37,plain,(
% 1.53/1.45 ( ! [X0 : a,X1 : a] : (((cP @ X0 @ X1) = (cP @ (cJ @ (cJ @ X0)) @ X1))) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f33,f33])).
% 1.53/1.45 thf(f78,plain,(
% 1.53/1.45 ( ! [X0 : a,X1 : a] : (((cP @ (cJ @ (cP @ X1 @ (cJ @ X0))) @ (cP @ X1 @ cE)) = X0)) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f36,f14])).
% 1.53/1.45 thf(f36,plain,(
% 1.53/1.45 ( ! [X2 : a,X0 : a,X1 : a] : (((cP @ (cJ @ (cP @ X0 @ X1)) @ (cP @ X0 @ (cP @ X1 @ X2))) = X2)) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f33,f13])).
% 1.53/1.45 thf(f21,plain,(
% 1.53/1.45 ( ! [X11 : a] : ((sK4 != (cP @ X11 @ sK3))) ) | ~spl5_2),
% 1.53/1.45 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.53/1.45 thf(f20,definition,(
% 1.53/1.45 spl5_2 <=> ! [X11 : a] : (sK4 != (cP @ X11 @ sK3))),
% 1.53/1.45 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.53/1.45 thf(f210,plain,(
% 1.53/1.45 ~spl5_3),
% 1.53/1.45 inference(avatar_contradiction_clause,[status(thm)],[f209])).
% 1.53/1.45 thf(f209,plain,(
% 1.53/1.45 $false | ~spl5_3),
% 1.53/1.45 inference(equality_resolution,[status(thm)],[f169])).
% 1.53/1.45 thf(f169,plain,(
% 1.53/1.45 ( ! [X0 : a] : ((sK4 != X0)) ) | ~spl5_3),
% 1.53/1.45 inference(superposition,[status(thm)],[f24,f65])).
% 1.53/1.45 thf(f65,plain,(
% 1.53/1.45 ( ! [X0 : a,X1 : a] : (((cP @ X0 @ (cP @ (cJ @ X0) @ X1)) = X1)) )),
% 1.53/1.45 inference(superposition,[status(thm)],[f37,f33])).
% 1.53/1.45 thf(f24,plain,(
% 1.53/1.45 ( ! [X10 : a] : ((sK4 != (cP @ sK3 @ X10))) ) | ~spl5_3),
% 1.53/1.45 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.53/1.45 thf(f23,definition,(
% 1.53/1.45 spl5_3 <=> ! [X10 : a] : (sK4 != (cP @ sK3 @ X10))),
% 1.53/1.45 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.53/1.45 thf(f27,plain,(
% 1.53/1.45 spl5_1),
% 1.53/1.45 inference(avatar_contradiction_clause,[status(thm)],[f26])).
% 1.53/1.45 thf(f26,plain,(
% 1.53/1.45 $false | spl5_1),
% 1.53/1.45 inference(subsumption_resolution,[status(thm)],[f18,f13])).
% 1.53/1.45 thf(f18,plain,(
% 1.53/1.45 ((cP @ (cP @ sK0 @ sK1) @ sK2) != (cP @ sK0 @ (cP @ sK1 @ sK2))) | spl5_1),
% 1.53/1.45 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.53/1.45 thf(f16,definition,(
% 1.53/1.45 spl5_1 <=> ((cP @ (cP @ sK0 @ sK1) @ sK2) = (cP @ sK0 @ (cP @ sK1 @ sK2)))),
% 1.53/1.45 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.53/1.45 thf(f25,plain,(
% 1.53/1.45 ~spl5_1 | spl5_2 | spl5_3),
% 1.53/1.45 inference(avatar_split_clause,[status(thm)],[f11,f23,f20,f16])).
% 1.53/1.45 thf(f11,plain,(
% 1.53/1.45 ( ! [X10 : a,X11 : a] : (((cP @ (cP @ sK0 @ sK1) @ sK2) != (cP @ sK0 @ (cP @ sK1 @ sK2))) | (sK4 != (cP @ sK3 @ X10)) | (sK4 != (cP @ X11 @ sK3))) )),
% 1.53/1.45 inference(cnf_transformation,[status(thm)],[f10])).
% 1.53/1.45 % SZS output end Proof for DTF2THF_22476
% 1.53/1.45 % (22593)------------------------------
% 1.53/1.45 % (22593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.45 % (22593)Termination reason: Refutation
% 1.53/1.45
% 1.53/1.45 % (22593)Memory used [KB]: 5628
% 1.53/1.45 % (22593)Time elapsed: 0.024 s
% 1.53/1.45 % (22593)Instructions burned: 42 (million)
% 1.53/1.45 % (22593)------------------------------
% 1.53/1.45 % (22593)------------------------------
% 1.53/1.45 % (22572)Success in time 0.102 s
%------------------------------------------------------------------------------