%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG282^5 : 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 : n020.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 08:37:49 AM UTC 2026
% Result : Theorem 1.64s 1.32s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 180 ( 13 ~; 0 |; 18 &; 145 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 61 !; 11 ?; 72 :)
% 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(f55,plain,
$false,
inference(equality_resolution,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: a] : ( sK0 != X0 ),
inference(superposition,[status(thm)],[f51,f10]) ).
thf(f10,plain,
! [X7: a] :
( ( cP @ cE @ X7 )
= X7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X3: a] :
( sK0
!= ( cP @ X3 @ sK1 ) )
& ! [X4: a,X5: a,X6: a] :
( ( cP @ ( cP @ X4 @ X6 ) @ X5 )
= ( cP @ X4 @ ( cP @ X6 @ X5 ) ) )
& ! [X7: a] :
( ( cP @ cE @ X7 )
= X7 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X1: a,X2: a] :
! [X3: a] :
( ( cP @ X3 @ X2 )
!= X1 )
=> ! [X3: a] :
( sK0
!= ( cP @ X3 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ? [X1: a,X2: a] :
! [X3: a] :
( ( cP @ X3 @ X2 )
!= X1 )
& ! [X4: a,X5: a,X6: a] :
( ( cP @ ( cP @ X4 @ X6 ) @ X5 )
= ( cP @ X4 @ ( cP @ X6 @ X5 ) ) )
& ! [X7: a] :
( ( cP @ cE @ X7 )
= X7 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ? [X6: a,X5: a] :
! [X7: a] :
( ( cP @ X7 @ X5 )
!= X6 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X2 @ X4 ) @ X3 )
= ( cP @ X2 @ ( cP @ X4 @ X3 ) ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ? [X6: a,X5: a] :
! [X7: a] :
( ( cP @ X7 @ X5 )
!= X6 )
& ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X2 @ X4 ) @ X3 )
= ( cP @ X2 @ ( cP @ X4 @ X3 ) ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X2 @ X4 ) @ X3 )
= ( cP @ X2 @ ( cP @ X4 @ X3 ) ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 ) )
=> ! [X5: a,X6: a] :
? [X7: a] :
( ( cP @ X7 @ X5 )
= X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: a,X2: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X3: a,X4: a] :
? [X5: a] :
( ( cP @ X5 @ X3 )
= X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: a,X2: a,X1: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X3: a,X4: a] :
? [X5: a] :
( ( cP @ X5 @ X3 )
= X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HbTLdFqmZG/DTF2THF_28315.p',cTHM21_pme) ).
thf(f51,plain,
! [X0: a] :
( ( cP @ cE @ X0 )
!= sK0 ),
inference(superposition,[status(thm)],[f21,f36]) ).
thf(f36,plain,
! [X0: a] :
( ( cP @ cE @ X0 )
= ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE ) ),
inference(superposition,[status(thm)],[f17,f13]) ).
thf(f13,plain,
! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f17,plain,
! [X0: a,X1: a] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f11,f13]) ).
thf(f11,plain,
! [X6: a,X4: a,X5: a] :
( ( cP @ ( cP @ X4 @ X6 ) @ X5 )
= ( cP @ X4 @ ( cP @ X6 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f21,plain,
! [X0: a] :
( sK0
!= ( cP @ X0 @ cE ) ),
inference(superposition,[status(thm)],[f19,f13]) ).
thf(f19,plain,
! [X0: a,X1: a] :
( sK0
!= ( cP @ X0 @ ( cP @ X1 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f12,f11]) ).
thf(f12,plain,
! [X3: a] :
( sK0
!= ( cP @ X3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG282^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 03:42:42 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : ALG282^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : General Algebra
% 0.29/0.47 % Problem : TPS problem from GRP-THMS
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0920 [Bro09]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % 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, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 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
% 0.29/0.47 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.29/0.47 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.47 % Number of connectives : 18 ( 0 ~; 0 |; 2 &; 15 @)
% 0.29/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.29/0.47 % Number of types : 1 ( 1 usr)
% 0.29/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 8 ( 0 ^; 7 !; 1 ?; 8 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(a_type,type,
% 0.29/0.47 a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(cP,type,
% 0.29/0.47 cP: a > a > a ).
% 0.29/0.47
% 0.29/0.47 thf(cE,type,
% 0.29/0.47 cE: a ).
% 0.29/0.47
% 0.29/0.47 thf(cJ,type,
% 0.29/0.47 cJ: a > a ).
% 0.29/0.47
% 0.29/0.47 thf(cTHM21_pme,conjecture,
% 0.29/0.47 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.29/0.47 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.29/0.47 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.29/0.47 & ! [Xx: a] :
% 0.29/0.47 ( ( cP @ cE @ Xx )
% 0.29/0.47 = Xx )
% 0.29/0.47 & ! [Xy: a] :
% 0.29/0.47 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 0.29/0.47 = cE ) )
% 0.29/0.47 => ! [X: a,Y: a] :
% 0.29/0.47 ? [W: a] :
% 0.29/0.47 ( ( cP @ W @ X )
% 0.29/0.47 = Y ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 03:42:43 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.HbTLdFqmZG/DTF2DTF28315.p
% See solution above
% 1.47/1.29 ------------------------
% 1.64/1.30 ---- Cleaned THF ---
% 1.64/1.30 thf(a_type,type,
% 1.64/1.30 a: $tType ).
% 1.64/1.30
% 1.64/1.30 thf(cP,type,
% 1.64/1.30 cP: a > a > a ).
% 1.64/1.30
% 1.64/1.30 thf(cE,type,
% 1.64/1.30 cE: a ).
% 1.64/1.30
% 1.64/1.30 thf(cJ,type,
% 1.64/1.30 cJ: a > a ).
% 1.64/1.30
% 1.64/1.30 thf(cTHM21_pme,conjecture,
% 1.64/1.30 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.64/1.30 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 1.64/1.30 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 1.64/1.30 & ! [Xx: a] :
% 1.64/1.30 ( ( cP @ cE @ Xx )
% 1.64/1.30 = Xx )
% 1.64/1.30 & ! [Xy: a] :
% 1.64/1.30 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 1.64/1.30 = cE ) )
% 1.64/1.30 => ! [X: a,Y: a] :
% 1.64/1.30 ? [W: a] :
% 1.64/1.30 ( ( cP @ W @ X )
% 1.64/1.30 = Y ) ) ).
% 1.64/1.30 ------------------------
% 1.64/1.32 % (28429)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28315 for (2999ds/183Mi)
% 1.64/1.32 % (28433)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_28315 for (2999ds/2Mi)
% 1.64/1.32 % (28433)Instruction limit reached!
% 1.64/1.32 % (28433)------------------------------
% 1.64/1.32 % (28433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (28433)Termination reason: Unknown
% 1.64/1.32 % (28433)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (28433)Memory used [KB]: 5500
% 1.64/1.32 % (28433)Time elapsed: 0.002 s
% 1.64/1.32 % (28433)Instructions burned: 3 (million)
% 1.64/1.32 % (28433)------------------------------
% 1.64/1.32 % (28433)------------------------------
% 1.64/1.32 % (28429)First to succeed.
% 1.64/1.32 % (28429)Refutation found. Thanks to Tanya!
% 1.64/1.32 % SZS status Theorem for DTF2THF_28315
% 1.64/1.32 % SZS output start Proof for DTF2THF_28315
% 1.64/1.32 thf(type_def_5, type, a: $tType).
% 1.64/1.32 thf(func_def_0, type, a: $tType).
% 1.64/1.32 thf(func_def_1, type, cP: a > a > a).
% 1.64/1.32 thf(func_def_2, type, cE: a).
% 1.64/1.32 thf(func_def_3, type, cJ: a > a).
% 1.64/1.32 thf(func_def_7, type, sK0: a).
% 1.64/1.32 thf(func_def_8, type, sK1: a).
% 1.64/1.32 thf(f55,plain,(
% 1.64/1.32 $false),
% 1.64/1.32 inference(equality_resolution,[status(thm)],[f54])).
% 1.64/1.32 thf(f54,plain,(
% 1.64/1.32 ( ! [X0 : a] : ((sK0 != X0)) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f51,f10])).
% 1.64/1.32 thf(f10,plain,(
% 1.64/1.32 ( ! [X7 : a] : (((cP @ cE @ X7) = X7)) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f9,plain,(
% 1.64/1.32 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ! [X3 : a] : (sK0 != (cP @ X3 @ sK1)) & ! [X4 : a,X5 : a,X6 : a] : ((cP @ (cP @ X4 @ X6) @ X5) = (cP @ X4 @ (cP @ X6 @ X5))) & ! [X7 : a] : ((cP @ cE @ X7) = X7)),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.64/1.32 thf(f8,plain,(
% 1.64/1.32 ? [X1 : a,X2 : a] : ! [X3 : a] : ((cP @ X3 @ X2) != X1) => ! [X3 : a] : (sK0 != (cP @ X3 @ sK1))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f7,plain,(
% 1.64/1.32 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ? [X1 : a,X2 : a] : ! [X3 : a] : ((cP @ X3 @ X2) != X1) & ! [X4 : a,X5 : a,X6 : a] : ((cP @ (cP @ X4 @ X6) @ X5) = (cP @ X4 @ (cP @ X6 @ X5))) & ! [X7 : a] : ((cP @ cE @ X7) = X7)),
% 1.64/1.32 inference(rectify,[status(thm)],[f6])).
% 1.64/1.32 thf(f6,plain,(
% 1.64/1.32 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ? [X6 : a,X5 : a] : ! [X7 : a] : ((cP @ X7 @ X5) != X6) & ! [X2 : a,X3 : a,X4 : a] : ((cP @ (cP @ X2 @ X4) @ X3) = (cP @ X2 @ (cP @ X4 @ X3))) & ! [X1 : a] : ((cP @ cE @ X1) = X1)),
% 1.64/1.32 inference(flattening,[status(thm)],[f5])).
% 1.64/1.32 thf(f5,plain,(
% 1.64/1.32 ? [X6 : a,X5 : a] : ! [X7 : a] : ((cP @ X7 @ X5) != X6) & (! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ! [X2 : a,X3 : a,X4 : a] : ((cP @ (cP @ X2 @ X4) @ X3) = (cP @ X2 @ (cP @ X4 @ X3))) & ! [X1 : a] : ((cP @ cE @ X1) = X1))),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f4])).
% 1.64/1.32 thf(f4,plain,(
% 1.64/1.32 ~((! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ! [X2 : a,X3 : a,X4 : a] : ((cP @ (cP @ X2 @ X4) @ X3) = (cP @ X2 @ (cP @ X4 @ X3))) & ! [X1 : a] : ((cP @ cE @ X1) = X1)) => ! [X5 : a,X6 : a] : ? [X7 : a] : ((cP @ X7 @ X5) = X6))),
% 1.64/1.32 inference(rectify,[status(thm)],[f2])).
% 1.64/1.32 thf(f2,negated_conjecture,(
% 1.64/1.32 ~((! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1)) & ! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X0 : a,X2 : a,X1 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2)))) => ! [X3 : a,X4 : a] : ? [X5 : a] : ((cP @ X5 @ X3) = X4))),
% 1.64/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.32 thf(f1,conjecture,(
% 1.64/1.32 (! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1)) & ! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X0 : a,X2 : a,X1 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2)))) => ! [X3 : a,X4 : a] : ? [X5 : a] : ((cP @ X5 @ X3) = X4)),
% 1.64/1.32 file('/export/starexec/sandbox2/tmp/tmp.HbTLdFqmZG/DTF2THF_28315.p',cTHM21_pme)).
% 1.64/1.32 thf(f51,plain,(
% 1.64/1.32 ( ! [X0 : a] : (((cP @ cE @ X0) != sK0)) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f21,f36])).
% 1.64/1.32 thf(f36,plain,(
% 1.64/1.32 ( ! [X0 : a] : (((cP @ cE @ X0) = (cP @ (cJ @ (cJ @ X0)) @ cE))) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f17,f13])).
% 1.64/1.32 thf(f13,plain,(
% 1.64/1.32 ( ! [X0 : a] : ((cE = (cP @ (cJ @ X0) @ X0))) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f17,plain,(
% 1.64/1.32 ( ! [X0 : a,X1 : a] : (((cP @ cE @ X1) = (cP @ (cJ @ X0) @ (cP @ X0 @ X1)))) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f11,f13])).
% 1.64/1.32 thf(f11,plain,(
% 1.64/1.32 ( ! [X6 : a,X4 : a,X5 : a] : (((cP @ (cP @ X4 @ X6) @ X5) = (cP @ X4 @ (cP @ X6 @ X5)))) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f21,plain,(
% 1.64/1.32 ( ! [X0 : a] : ((sK0 != (cP @ X0 @ cE))) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f19,f13])).
% 1.64/1.32 thf(f19,plain,(
% 1.64/1.32 ( ! [X0 : a,X1 : a] : ((sK0 != (cP @ X0 @ (cP @ X1 @ sK1)))) )),
% 1.64/1.32 inference(superposition,[status(thm)],[f12,f11])).
% 1.64/1.32 thf(f12,plain,(
% 1.64/1.32 ( ! [X3 : a] : ((sK0 != (cP @ X3 @ sK1))) )),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 % SZS output end Proof for DTF2THF_28315
% 1.64/1.32 % (28429)------------------------------
% 1.64/1.32 % (28429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (28429)Termination reason: Refutation
% 1.64/1.32
% 1.64/1.32 % (28429)Memory used [KB]: 5500
% 1.64/1.32 % (28429)Time elapsed: 0.005 s
% 1.64/1.32 % (28429)Instructions burned: 7 (million)
% 1.64/1.32 % (28429)------------------------------
% 1.64/1.32 % (28429)------------------------------
% 1.64/1.32 % (28428)Success in time 0.004 s
%------------------------------------------------------------------------------