%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG281^5 : 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 : n001.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 1.60s 1.37s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 42 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 198 ( 10 ~; 0 |; 18 &; 166 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 52 !; 4 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cJ: $i > $i ).
thf(func_def_2,type,
cP: $i > $i > $i ).
thf(f90,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
cE != cE,
inference(superposition,[status(thm)],[f11,f74]) ).
thf(f74,plain,
! [X0: $i] :
( cE
= ( cP @ X0 @ ( cJ @ X0 ) ) ),
inference(superposition,[status(thm)],[f10,f59]) ).
thf(f59,plain,
! [X0: $i] :
( ( cJ @ ( cJ @ X0 ) )
= X0 ),
inference(superposition,[status(thm)],[f20,f53]) ).
thf(f53,plain,
! [X0: $i] :
( ( cP @ ( cJ @ ( cJ @ ( cJ @ ( cJ @ X0 ) ) ) ) @ cE )
= X0 ),
inference(superposition,[status(thm)],[f18,f29]) ).
thf(f29,plain,
! [X0: $i] :
( cE
= ( cP @ ( cJ @ ( cJ @ ( cJ @ X0 ) ) ) @ X0 ) ),
inference(superposition,[status(thm)],[f18,f20]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[status(thm)],[f15,f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ( cE
!= ( cP @ sK0 @ ( cJ @ sK0 ) ) )
& ! [X5: $i] :
( cE
= ( cP @ ( cJ @ X5 ) @ X5 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X4: $i] :
( cE
!= ( cP @ X4 @ ( cJ @ X4 ) ) )
=> ( cE
!= ( cP @ sK0 @ ( cJ @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ? [X4: $i] :
( cE
!= ( cP @ X4 @ ( cJ @ X4 ) ) )
& ! [X5: $i] :
( cE
= ( cP @ ( cJ @ X5 ) @ X5 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
& ? [X5: $i] :
( cE
!= ( cP @ X5 @ ( cJ @ X5 ) ) )
& ! [X4: $i] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ? [X5: $i] :
( cE
!= ( cP @ X5 @ ( cJ @ X5 ) ) )
& ! [X4: $i] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X4: $i] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ! [X5: $i] :
( cE
= ( cP @ X5 @ ( cJ @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) )
=> ! [X3: $i] :
( cE
= ( cP @ X3 @ ( cJ @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) )
=> ! [X3: $i] :
( cE
= ( cP @ X3 @ ( cJ @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GIJKqya41s/DTF2THF_18850.p',cTHM16_pme) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= ( cP @ cE @ X1 ) ),
inference(superposition,[status(thm)],[f12,f10]) ).
thf(f12,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f20,plain,
! [X0: $i] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(superposition,[status(thm)],[f18,f10]) ).
thf(f10,plain,
! [X5: $i] :
( cE
= ( cP @ ( cJ @ X5 ) @ X5 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( cE
!= ( cP @ sK0 @ ( cJ @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG281^5 : 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
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 03:43:20 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 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 : ALG281^5 : 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_0907 [Bro09]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.09 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, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 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 : 19 ( 0 ~; 0 |; 2 &; 16 @)
% 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 ( 0 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 : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 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(cE,type,
% 0.29/0.47 cE: $i ).
% 0.29/0.47
% 0.29/0.47 thf(cJ,type,
% 0.29/0.47 cJ: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(cP,type,
% 0.29/0.47 cP: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(cTHM16_pme,conjecture,
% 0.29/0.47 ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.29/0.47 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.29/0.47 & ! [Xx: $i] :
% 0.29/0.47 ( ( cP @ cE @ Xx )
% 0.29/0.47 = Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 0.29/0.47 = cE ) )
% 0.29/0.47 => ! [X: $i] :
% 0.29/0.47 ( ( cP @ X @ ( cJ @ X ) )
% 0.29/0.47 = cE ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.60/1.32 ---- Embedded in THF ---
% 1.60/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.32 %%% Generated on Tue Feb 24 03:43:21 EST 2026
% 1.60/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.32 %%% Logic specification used:
% 1.60/1.32 %%% thf(spec, logic, $$dhol).
% 1.60/1.32
% 1.60/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.GIJKqya41s/DTF2DTF18850.p
% See solution above
% 1.60/1.32 ------------------------
% 1.60/1.33 ---- Cleaned THF ---
% 1.60/1.33 thf(cE,type,
% 1.60/1.33 cE: $i ).
% 1.60/1.33
% 1.60/1.33 thf(cJ,type,
% 1.60/1.33 cJ: $i > $i ).
% 1.60/1.33
% 1.60/1.33 thf(cP,type,
% 1.60/1.33 cP: $i > $i > $i ).
% 1.60/1.33
% 1.60/1.33 thf(cTHM16_pme,conjecture,
% 1.60/1.33 ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.60/1.33 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 1.60/1.33 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 1.60/1.33 & ! [Xx: $i] :
% 1.60/1.33 ( ( cP @ cE @ Xx )
% 1.60/1.33 = Xx )
% 1.60/1.33 & ! [Xy: $i] :
% 1.60/1.33 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 1.60/1.33 = cE ) )
% 1.60/1.33 => ! [X: $i] :
% 1.60/1.33 ( ( cP @ X @ ( cJ @ X ) )
% 1.60/1.33 = cE ) ) ).
% 1.60/1.33 ------------------------
% 1.60/1.35 % (19130)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_18850 for (2999ds/275Mi)
% 1.60/1.35 % (19129)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_18850 for (2999ds/2Mi)
% 1.60/1.35 % (19129)Instruction limit reached!
% 1.60/1.35 % (19129)------------------------------
% 1.60/1.35 % (19129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (19129)Termination reason: Unknown
% 1.60/1.35 % (19129)Termination phase: Saturation
% 1.60/1.35
% 1.60/1.35 % (19129)Memory used [KB]: 5500
% 1.60/1.35 % (19129)Time elapsed: 0.002 s
% 1.60/1.35 % (19129)Instructions burned: 2 (million)
% 1.60/1.35 % (19129)------------------------------
% 1.60/1.35 % (19129)------------------------------
% 1.60/1.35 % (19125)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18850 for (2999ds/183Mi)
% 1.60/1.35 % (19126)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_18850 for (2999ds/4Mi)
% 1.60/1.35 % (19128)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18850 for (2999ds/2Mi)
% 1.60/1.35 % (19127)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_18850 for (2999ds/27Mi)
% 1.60/1.35 % (19131)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18850 for (2999ds/18Mi)
% 1.60/1.35 % (19128)Instruction limit reached!
% 1.60/1.35 % (19128)------------------------------
% 1.60/1.35 % (19128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (19128)Termination reason: Unknown
% 1.60/1.35 % (19128)Termination phase: Saturation
% 1.60/1.35
% 1.60/1.35 % (19128)Memory used [KB]: 5500
% 1.60/1.35 % (19128)Time elapsed: 0.004 s
% 1.60/1.35 % (19128)Instructions burned: 3 (million)
% 1.60/1.35 % (19128)------------------------------
% 1.60/1.35 % (19128)------------------------------
% 1.60/1.36 % (19126)Instruction limit reached!
% 1.60/1.36 % (19126)------------------------------
% 1.60/1.36 % (19126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (19126)Termination reason: Unknown
% 1.60/1.36 % (19126)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (19126)Memory used [KB]: 5500
% 1.60/1.36 % (19126)Time elapsed: 0.005 s
% 1.60/1.36 % (19126)Instructions burned: 4 (million)
% 1.60/1.36 % (19126)------------------------------
% 1.60/1.36 % (19126)------------------------------
% 1.60/1.36 % (19132)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18850 for (2999ds/3Mi)
% 1.60/1.36 % (19132)Instruction limit reached!
% 1.60/1.36 % (19132)------------------------------
% 1.60/1.36 % (19132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (19132)Termination reason: Unknown
% 1.60/1.36 % (19132)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (19132)Memory used [KB]: 5500
% 1.60/1.36 % (19132)Time elapsed: 0.003 s
% 1.60/1.36 % (19132)Instructions burned: 5 (million)
% 1.60/1.36 % (19132)------------------------------
% 1.60/1.36 % (19132)------------------------------
% 1.60/1.36 % (19131)First to succeed.
% 1.60/1.37 % (19127)Also succeeded, but the first one will report.
% 1.60/1.37 % (19131)Refutation found. Thanks to Tanya!
% 1.60/1.37 % SZS status Theorem for DTF2THF_18850
% 1.60/1.37 % SZS output start Proof for DTF2THF_18850
% 1.60/1.37 thf(func_def_1, type, cJ: $i > $i).
% 1.60/1.37 thf(func_def_2, type, cP: $i > $i > $i).
% 1.60/1.37 thf(f90,plain,(
% 1.60/1.37 $false),
% 1.60/1.37 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.60/1.37 thf(f85,plain,(
% 1.60/1.37 (cE != cE)),
% 1.60/1.37 inference(superposition,[status(thm)],[f11,f74])).
% 1.60/1.37 thf(f74,plain,(
% 1.60/1.37 ( ! [X0 : $i] : ((cE = (cP @ X0 @ (cJ @ X0)))) )),
% 1.60/1.37 inference(superposition,[status(thm)],[f10,f59])).
% 1.60/1.37 thf(f59,plain,(
% 1.60/1.37 ( ! [X0 : $i] : (((cJ @ (cJ @ X0)) = X0)) )),
% 1.60/1.37 inference(superposition,[status(thm)],[f20,f53])).
% 1.60/1.37 thf(f53,plain,(
% 1.60/1.37 ( ! [X0 : $i] : (((cP @ (cJ @ (cJ @ (cJ @ (cJ @ X0)))) @ cE) = X0)) )),
% 1.60/1.37 inference(superposition,[status(thm)],[f18,f29])).
% 1.60/1.37 thf(f29,plain,(
% 1.60/1.37 ( ! [X0 : $i] : ((cE = (cP @ (cJ @ (cJ @ (cJ @ X0))) @ X0))) )),
% 1.60/1.37 inference(superposition,[status(thm)],[f18,f20])).
% 1.60/1.37 thf(f18,plain,(
% 1.60/1.37 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = X1)) )),
% 1.60/1.37 inference(forward_demodulation,[status(thm)],[f15,f13])).
% 1.60/1.37 thf(f13,plain,(
% 1.60/1.37 ( ! [X0 : $i] : (((cP @ cE @ X0) = X0)) )),
% 1.60/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.60/1.37 thf(f9,plain,(
% 1.60/1.37 ! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X1 : $i,X2 : $i,X3 : $i] : ((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3))) & (cE != (cP @ sK0 @ (cJ @ sK0))) & ! [X5 : $i] : (cE = (cP @ (cJ @ X5) @ X5))),
% 1.60/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.60/1.37 thf(f8,plain,(
% 1.60/1.37 ? [X4 : $i] : (cE != (cP @ X4 @ (cJ @ X4))) => (cE != (cP @ sK0 @ (cJ @ sK0)))),
% 1.60/1.37 introduced(definition,[],[choice_axiom])).
% 1.60/1.37 thf(f7,plain,(
% 1.60/1.37 ! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X1 : $i,X2 : $i,X3 : $i] : ((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3))) & ? [X4 : $i] : (cE != (cP @ X4 @ (cJ @ X4))) & ! [X5 : $i] : (cE = (cP @ (cJ @ X5) @ X5))),
% 1.60/1.37 inference(rectify,[status(thm)],[f6])).
% 1.60/1.37 thf(f6,plain,(
% 1.60/1.37 ! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X1 : $i,X2 : $i,X3 : $i] : ((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3))) & ? [X5 : $i] : (cE != (cP @ X5 @ (cJ @ X5))) & ! [X4 : $i] : (cE = (cP @ (cJ @ X4) @ X4))),
% 1.60/1.37 inference(flattening,[status(thm)],[f5])).
% 1.60/1.37 thf(f5,plain,(
% 1.60/1.37 ? [X5 : $i] : (cE != (cP @ X5 @ (cJ @ X5))) & (! [X4 : $i] : (cE = (cP @ (cJ @ X4) @ X4)) & ! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X1 : $i,X2 : $i,X3 : $i] : ((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3))))),
% 1.60/1.37 inference(ennf_transformation,[status(thm)],[f4])).
% 1.60/1.37 thf(f4,plain,(
% 1.60/1.37 ~((! [X4 : $i] : (cE = (cP @ (cJ @ X4) @ X4)) & ! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X1 : $i,X2 : $i,X3 : $i] : ((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3)))) => ! [X5 : $i] : (cE = (cP @ X5 @ (cJ @ X5))))),
% 1.60/1.37 inference(rectify,[status(thm)],[f2])).
% 1.60/1.37 thf(f2,negated_conjecture,(
% 1.60/1.37 ~((! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X0 : $i,X1 : $i,X2 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : $i] : (cE = (cP @ (cJ @ X1) @ X1))) => ! [X3 : $i] : (cE = (cP @ X3 @ (cJ @ X3))))),
% 1.60/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.37 thf(f1,conjecture,(
% 1.60/1.37 (! [X0 : $i] : ((cP @ cE @ X0) = X0) & ! [X0 : $i,X1 : $i,X2 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : $i] : (cE = (cP @ (cJ @ X1) @ X1))) => ! [X3 : $i] : (cE = (cP @ X3 @ (cJ @ X3)))),
% 1.60/1.37 file('/export/starexec/sandbox2/tmp/tmp.GIJKqya41s/DTF2THF_18850.p',cTHM16_pme)).
% 1.60/1.37 thf(f15,plain,(
% 1.60/1.37 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = (cP @ cE @ X1))) )),
% 1.60/1.37 inference(superposition,[status(thm)],[f12,f10])).
% 1.60/1.37 thf(f12,plain,(
% 1.60/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3)))) )),
% 1.60/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.60/1.37 thf(f20,plain,(
% 1.60/1.37 ( ! [X0 : $i] : (((cP @ (cJ @ (cJ @ X0)) @ cE) = X0)) )),
% 1.60/1.37 inference(superposition,[status(thm)],[f18,f10])).
% 1.60/1.37 thf(f10,plain,(
% 1.60/1.37 ( ! [X5 : $i] : ((cE = (cP @ (cJ @ X5) @ X5))) )),
% 1.60/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.60/1.37 thf(f11,plain,(
% 1.60/1.37 (cE != (cP @ sK0 @ (cJ @ sK0)))),
% 1.60/1.37 inference(cnf_transformation,[status(thm)],[f9])).
% 1.60/1.37 % SZS output end Proof for DTF2THF_18850
% 1.60/1.37 % (19131)------------------------------
% 1.60/1.37 % (19131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.37 % (19131)Termination reason: Refutation
% 1.60/1.37
% 1.60/1.37 % (19131)Memory used [KB]: 5500
% 1.60/1.37 % (19131)Time elapsed: 0.014 s
% 1.60/1.37 % (19131)Instructions burned: 17 (million)
% 1.60/1.37 % (19131)------------------------------
% 1.60/1.37 % (19131)------------------------------
% 1.60/1.37 % (19124)Success in time 0.028 s
%------------------------------------------------------------------------------