%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG280^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 0.23s 1.34s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% 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 ( 10 ~; 0 |; 18 &; 148 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 51 !; 4 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cE: a ).
thf(func_def_2,type,
cP: a > a > a ).
thf(func_def_3,type,
cJ: a > a ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
sK0: a ).
thf(f55,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
sK0 != sK0,
inference(superposition,[status(thm)],[f12,f34]) ).
thf(f34,plain,
! [X0: a] :
( ( cP @ X0 @ cE )
= X0 ),
inference(superposition,[status(thm)],[f23,f21]) ).
thf(f21,plain,
! [X0: a] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(superposition,[status(thm)],[f17,f13]) ).
thf(f13,plain,
! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ( ( cP @ sK0 @ cE )
!= sK0 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ X3 @ ( cP @ X4 @ X2 ) )
= ( cP @ ( cP @ X3 @ X4 ) @ X2 ) )
& ! [X5: a] :
( ( cP @ cE @ X5 )
= X5 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X1: a] :
( ( cP @ X1 @ cE )
!= X1 )
=> ( ( cP @ sK0 @ cE )
!= sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ? [X1: a] :
( ( cP @ X1 @ cE )
!= X1 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ X3 @ ( cP @ X4 @ X2 ) )
= ( cP @ ( cP @ X3 @ X4 ) @ X2 ) )
& ! [X5: a] :
( ( cP @ cE @ X5 )
= X5 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ? [X5: a] :
( ( cP @ X5 @ cE )
!= X5 )
& ! [X2: a,X4: a,X3: a] :
( ( cP @ X4 @ ( cP @ X3 @ X2 ) )
= ( cP @ ( cP @ X4 @ X3 ) @ X2 ) )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ? [X5: a] :
( ( cP @ X5 @ cE )
!= X5 )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X2: a,X4: a,X3: a] :
( ( cP @ X4 @ ( cP @ X3 @ X2 ) )
= ( cP @ ( cP @ X4 @ X3 ) @ X2 ) )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X2: a,X4: a,X3: a] :
( ( cP @ X4 @ ( cP @ X3 @ X2 ) )
= ( cP @ ( cP @ X4 @ X3 ) @ X2 ) )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) )
=> ! [X5: a] :
( ( cP @ X5 @ cE )
= X5 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X2: a,X1: a,X0: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X3: a] :
( ( cP @ X3 @ cE )
= X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: a] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X2: a,X1: a,X0: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X3: a] :
( ( cP @ X3 @ cE )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.1XBRPojJXg/DTF2THF_30747.p',cTHM17_pme) ).
thf(f17,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[status(thm)],[f15,f10]) ).
thf(f10,plain,
! [X5: a] :
( ( cP @ cE @ X5 )
= X5 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f15,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= ( cP @ cE @ X1 ) ),
inference(superposition,[status(thm)],[f11,f13]) ).
thf(f11,plain,
! [X2: a,X3: a,X4: a] :
( ( cP @ X3 @ ( cP @ X4 @ X2 ) )
= ( cP @ ( cP @ X3 @ X4 ) @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f23,plain,
! [X0: a,X1: a] :
( ( cP @ X0 @ X1 )
= ( cP @ ( cJ @ ( cJ @ X0 ) ) @ X1 ) ),
inference(superposition,[status(thm)],[f17,f17]) ).
thf(f12,plain,
( ( cP @ sK0 @ cE )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG280^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n006.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 03:42:30 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.39 thf(spec,logic,$$dhol).
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 % File : ALG280^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.39 % Domain : General Algebra
% 0.19/0.39 % Problem : TPS problem from GRP-THMS
% 0.19/0.39 % Version : Especial.
% 0.19/0.39 % English :
% 0.19/0.39
% 0.19/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.39 % Source : [Bro09]
% 0.19/0.39 % Names : tps_0904 [Bro09]
% 0.19/0.39
% 0.19/0.39 % Status : Theorem
% 0.19/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 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 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.0
% 0.19/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.19/0.39 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.19/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.39 % Number of connectives : 18 ( 0 ~; 0 |; 2 &; 15 @)
% 0.19/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.39 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.39 % Number of types : 1 ( 1 usr)
% 0.19/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.39 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.39 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.19/0.39 % SPC : TH0_THM_EQU_NAR
% 0.19/0.39
% 0.19/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 thf(a_type,type,
% 0.19/0.39 a: $tType ).
% 0.19/0.39
% 0.19/0.39 thf(cE,type,
% 0.19/0.39 cE: a ).
% 0.19/0.39
% 0.19/0.39 thf(cP,type,
% 0.19/0.39 cP: a > a > a ).
% 0.19/0.39
% 0.19/0.39 thf(cJ,type,
% 0.19/0.39 cJ: a > a ).
% 0.19/0.39
% 0.19/0.39 thf(cTHM17_pme,conjecture,
% 0.19/0.39 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.19/0.39 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.19/0.39 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.19/0.39 & ! [Xx: a] :
% 0.19/0.39 ( ( cP @ cE @ Xx )
% 0.19/0.39 = Xx )
% 0.19/0.39 & ! [Xy: a] :
% 0.19/0.39 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 0.19/0.39 = cE ) )
% 0.19/0.39 => ! [X: a] :
% 0.19/0.39 ( ( cP @ X @ cE )
% 0.19/0.39 = X ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 0.23/1.30 ---- Embedded in THF ---
% 0.23/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.23/1.30 %%% Generated on Tue Feb 24 03:42:31 EST 2026
% 0.23/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.23/1.30 %%% Logic specification used:
% 0.23/1.30 %%% thf(spec, logic, $$dhol).
% 0.23/1.30
% 0.23/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1XBRPojJXg/DTF2DTF30747.p
% See solution above
% 0.23/1.30 ------------------------
% 0.23/1.31 ---- Cleaned THF ---
% 0.23/1.31 thf(a_type,type,
% 0.23/1.31 a: $tType ).
% 0.23/1.31
% 0.23/1.31 thf(cE,type,
% 0.23/1.31 cE: a ).
% 0.23/1.31
% 0.23/1.31 thf(cP,type,
% 0.23/1.31 cP: a > a > a ).
% 0.23/1.31
% 0.23/1.31 thf(cJ,type,
% 0.23/1.31 cJ: a > a ).
% 0.23/1.31
% 0.23/1.31 thf(cTHM17_pme,conjecture,
% 0.23/1.31 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.23/1.31 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.23/1.31 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.23/1.31 & ! [Xx: a] :
% 0.23/1.31 ( ( cP @ cE @ Xx )
% 0.23/1.31 = Xx )
% 0.23/1.31 & ! [Xy: a] :
% 0.23/1.31 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 0.23/1.31 = cE ) )
% 0.23/1.31 => ! [X: a] :
% 0.23/1.31 ( ( cP @ X @ cE )
% 0.23/1.31 = X ) ) ).
% 0.23/1.31 ------------------------
% 0.23/1.33 % (30849)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_30747 for (2999ds/275Mi)
% 0.23/1.33 % (30844)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30747 for (2999ds/183Mi)
% 0.23/1.33 % (30847)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30747 for (2999ds/2Mi)
% 0.23/1.33 % (30846)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_30747 for (2999ds/27Mi)
% 0.23/1.33 % (30845)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_30747 for (2999ds/4Mi)
% 0.23/1.33 % (30848)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_30747 for (2999ds/2Mi)
% 0.23/1.33 % (30850)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30747 for (2999ds/18Mi)
% 0.23/1.33 % (30848)Instruction limit reached!
% 0.23/1.33 % (30848)------------------------------
% 0.23/1.33 % (30848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (30848)Termination reason: Unknown
% 0.23/1.33 % (30848)Termination phase: Saturation
% 0.23/1.33
% 0.23/1.33 % (30848)Memory used [KB]: 5500
% 0.23/1.33 % (30848)Time elapsed: 0.003 s
% 0.23/1.33 % (30848)Instructions burned: 2 (million)
% 0.23/1.33 % (30848)------------------------------
% 0.23/1.33 % (30848)------------------------------
% 0.23/1.33 % (30847)Instruction limit reached!
% 0.23/1.33 % (30847)------------------------------
% 0.23/1.33 % (30847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (30847)Termination reason: Unknown
% 0.23/1.33 % (30847)Termination phase: Saturation
% 0.23/1.33
% 0.23/1.33 % (30847)Memory used [KB]: 5500
% 0.23/1.33 % (30847)Time elapsed: 0.004 s
% 0.23/1.33 % (30847)Instructions burned: 3 (million)
% 0.23/1.33 % (30847)------------------------------
% 0.23/1.33 % (30847)------------------------------
% 0.23/1.34 % (30845)Instruction limit reached!
% 0.23/1.34 % (30845)------------------------------
% 0.23/1.34 % (30845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.34 % (30845)Termination reason: Unknown
% 0.23/1.34 % (30845)Termination phase: Saturation
% 0.23/1.34
% 0.23/1.34 % (30845)Memory used [KB]: 5500
% 0.23/1.34 % (30845)Time elapsed: 0.005 s
% 0.23/1.34 % (30845)Instructions burned: 5 (million)
% 0.23/1.34 % (30845)------------------------------
% 0.23/1.34 % (30845)------------------------------
% 0.23/1.34 % (30846)First to succeed.
% 0.23/1.34 % (30846)Refutation found. Thanks to Tanya!
% 0.23/1.34 % SZS status Theorem for DTF2THF_30747
% 0.23/1.34 % SZS output start Proof for DTF2THF_30747
% 0.23/1.34 thf(type_def_5, type, a: $tType).
% 0.23/1.34 thf(func_def_0, type, a: $tType).
% 0.23/1.34 thf(func_def_1, type, cE: a).
% 0.23/1.34 thf(func_def_2, type, cP: a > a > a).
% 0.23/1.34 thf(func_def_3, type, cJ: a > a).
% 0.23/1.34 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.23/1.34 thf(func_def_8, type, sK0: a).
% 0.23/1.34 thf(f55,plain,(
% 0.23/1.34 $false),
% 0.23/1.34 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 0.23/1.34 thf(f54,plain,(
% 0.23/1.34 (sK0 != sK0)),
% 0.23/1.34 inference(superposition,[status(thm)],[f12,f34])).
% 0.23/1.34 thf(f34,plain,(
% 0.23/1.34 ( ! [X0 : a] : (((cP @ X0 @ cE) = X0)) )),
% 0.23/1.34 inference(superposition,[status(thm)],[f23,f21])).
% 0.23/1.34 thf(f21,plain,(
% 0.23/1.34 ( ! [X0 : a] : (((cP @ (cJ @ (cJ @ X0)) @ cE) = X0)) )),
% 0.23/1.34 inference(superposition,[status(thm)],[f17,f13])).
% 0.23/1.34 thf(f13,plain,(
% 0.23/1.34 ( ! [X0 : a] : ((cE = (cP @ (cJ @ X0) @ X0))) )),
% 0.23/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.34 thf(f9,plain,(
% 0.23/1.34 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ((cP @ sK0 @ cE) != sK0) & ! [X2 : a,X3 : a,X4 : a] : ((cP @ X3 @ (cP @ X4 @ X2)) = (cP @ (cP @ X3 @ X4) @ X2)) & ! [X5 : a] : ((cP @ cE @ X5) = X5)),
% 0.23/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 0.23/1.34 thf(f8,plain,(
% 0.23/1.34 ? [X1 : a] : ((cP @ X1 @ cE) != X1) => ((cP @ sK0 @ cE) != sK0)),
% 0.23/1.34 introduced(definition,[],[choice_axiom])).
% 0.23/1.34 thf(f7,plain,(
% 0.23/1.34 ! [X0 : a] : (cE = (cP @ (cJ @ X0) @ X0)) & ? [X1 : a] : ((cP @ X1 @ cE) != X1) & ! [X2 : a,X3 : a,X4 : a] : ((cP @ X3 @ (cP @ X4 @ X2)) = (cP @ (cP @ X3 @ X4) @ X2)) & ! [X5 : a] : ((cP @ cE @ X5) = X5)),
% 0.23/1.34 inference(rectify,[status(thm)],[f6])).
% 0.23/1.34 thf(f6,plain,(
% 0.23/1.34 ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1)) & ? [X5 : a] : ((cP @ X5 @ cE) != X5) & ! [X2 : a,X4 : a,X3 : a] : ((cP @ X4 @ (cP @ X3 @ X2)) = (cP @ (cP @ X4 @ X3) @ X2)) & ! [X0 : a] : ((cP @ cE @ X0) = X0)),
% 0.23/1.34 inference(flattening,[status(thm)],[f5])).
% 0.23/1.34 thf(f5,plain,(
% 0.23/1.34 ? [X5 : a] : ((cP @ X5 @ cE) != X5) & (! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X2 : a,X4 : a,X3 : a] : ((cP @ X4 @ (cP @ X3 @ X2)) = (cP @ (cP @ X4 @ X3) @ X2)) & ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1)))),
% 0.23/1.34 inference(ennf_transformation,[status(thm)],[f4])).
% 0.23/1.34 thf(f4,plain,(
% 0.23/1.34 ~((! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X2 : a,X4 : a,X3 : a] : ((cP @ X4 @ (cP @ X3 @ X2)) = (cP @ (cP @ X4 @ X3) @ X2)) & ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1))) => ! [X5 : a] : ((cP @ X5 @ cE) = X5))),
% 0.23/1.34 inference(rectify,[status(thm)],[f2])).
% 0.23/1.34 thf(f2,negated_conjecture,(
% 0.23/1.34 ~((! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1)) & ! [X2 : a,X1 : a,X0 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2)))) => ! [X3 : a] : ((cP @ X3 @ cE) = X3))),
% 0.23/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/1.34 thf(f1,conjecture,(
% 0.23/1.34 (! [X0 : a] : ((cP @ cE @ X0) = X0) & ! [X1 : a] : (cE = (cP @ (cJ @ X1) @ X1)) & ! [X2 : a,X1 : a,X0 : a] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2)))) => ! [X3 : a] : ((cP @ X3 @ cE) = X3)),
% 0.23/1.34 file('/export/starexec/sandbox/tmp/tmp.1XBRPojJXg/DTF2THF_30747.p',cTHM17_pme)).
% 0.23/1.34 thf(f17,plain,(
% 0.23/1.34 ( ! [X0 : a,X1 : a] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = X1)) )),
% 0.23/1.34 inference(forward_demodulation,[status(thm)],[f15,f10])).
% 0.23/1.34 thf(f10,plain,(
% 0.23/1.34 ( ! [X5 : a] : (((cP @ cE @ X5) = X5)) )),
% 0.23/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.34 thf(f15,plain,(
% 0.23/1.34 ( ! [X0 : a,X1 : a] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = (cP @ cE @ X1))) )),
% 0.23/1.34 inference(superposition,[status(thm)],[f11,f13])).
% 0.23/1.34 thf(f11,plain,(
% 0.23/1.34 ( ! [X2 : a,X3 : a,X4 : a] : (((cP @ X3 @ (cP @ X4 @ X2)) = (cP @ (cP @ X3 @ X4) @ X2))) )),
% 0.23/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.34 thf(f23,plain,(
% 0.23/1.34 ( ! [X0 : a,X1 : a] : (((cP @ X0 @ X1) = (cP @ (cJ @ (cJ @ X0)) @ X1))) )),
% 0.23/1.34 inference(superposition,[status(thm)],[f17,f17])).
% 0.23/1.34 thf(f12,plain,(
% 0.23/1.34 ((cP @ sK0 @ cE) != sK0)),
% 0.23/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 0.23/1.34 % SZS output end Proof for DTF2THF_30747
% 0.23/1.34 % (30846)------------------------------
% 0.23/1.34 % (30846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.34 % (30846)Termination reason: Refutation
% 0.23/1.34
% 0.23/1.34 % (30846)Memory used [KB]: 5500
% 0.23/1.34 % (30846)Time elapsed: 0.008 s
% 0.23/1.34 % (30846)Instructions burned: 8 (million)
% 0.23/1.34 % (30846)------------------------------
% 0.23/1.34 % (30846)------------------------------
% 0.23/1.34 % (30843)Success in time 0.021 s
%------------------------------------------------------------------------------