%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU932^5 : 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 : n005.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 09:37:46 AM UTC 2026
% Result : Theorem 1.67s 1.45s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 76 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 189 ( 22 ~; 12 |; 31 &; 111 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 28 ^; 29 !; 30 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK0: $i > $i ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(func_def_9,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f24,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f23,f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( sK0 @ X1 )
!= X1 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i] :
( ( sK0 @ X1 )
!= X1 )
& ( ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) ) ) )
& ! [X4: $i] :
( ( ( sK1 @ X4 )
!= X4 )
| ( sK2 = X4 ) )
& ( sK2
= ( sK1 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i > $i] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= X1 )
& ? [X2: $i > $i] :
( ( ( ^ [Y0: $i] : ( X2 @ ( X0 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X0 @ ( X2 @ Y0 ) ) ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( X2 @ X4 )
!= X4 )
| ( X3 = X4 ) )
& ( ( X2 @ X3 )
= X3 ) ) ) )
=> ( ! [X1: $i] :
( ( sK0 @ X1 )
!= X1 )
& ? [X2: $i > $i] :
( ( ( ^ [Y0: $i] : ( sK0 @ ( X2 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X2 @ ( sK0 @ Y0 ) ) ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( X2 @ X4 )
!= X4 )
| ( X3 = X4 ) )
& ( ( X2 @ X3 )
= X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i > $i] :
( ( ( ^ [Y0: $i] : ( sK0 @ ( X2 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X2 @ ( sK0 @ Y0 ) ) ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( X2 @ X4 )
!= X4 )
| ( X3 = X4 ) )
& ( ( X2 @ X3 )
= X3 ) ) )
=> ( ( ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) ) ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( sK1 @ X4 )
!= X4 )
| ( X3 = X4 ) )
& ( ( sK1 @ X3 )
= X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: $i] :
( ! [X4: $i] :
( ( ( sK1 @ X4 )
!= X4 )
| ( X3 = X4 ) )
& ( ( sK1 @ X3 )
= X3 ) )
=> ( ! [X4: $i] :
( ( ( sK1 @ X4 )
!= X4 )
| ( sK2 = X4 ) )
& ( sK2
= ( sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i > $i] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= X1 )
& ? [X2: $i > $i] :
( ( ( ^ [Y0: $i] : ( X2 @ ( X0 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X0 @ ( X2 @ Y0 ) ) ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( ( X2 @ X4 )
!= X4 )
| ( X3 = X4 ) )
& ( ( X2 @ X3 )
= X3 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $i > $i] :
( ! [X4: $i] :
( ( X0 @ X4 )
!= X4 )
& ? [X1: $i > $i] :
( ( ( ^ [Y0: $i] : ( X0 @ ( X1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) )
& ? [X2: $i] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
!= X3 )
| ( X2 = X3 ) )
& ( ( X1 @ X2 )
= X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) )
& ( ( X1 @ X2 )
= X2 ) )
& ( ( ^ [Y0: $i] : ( X0 @ ( X1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) ) )
=> ? [X4: $i] :
( ( X0 @ X4 )
= X4 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) )
& ( ( X1 @ X2 )
= X2 ) )
& ( ( ^ [Y0: $i] : ( X0 @ ( X1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( X1 @ ( X0 @ Y0 ) ) ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
& ( ( ^ [X4: $i] : ( X0 @ ( X1 @ X4 ) ) )
= ( ^ [X5: $i] : ( X1 @ ( X0 @ X5 ) ) ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
& ( ( ^ [X2: $i] : ( X0 @ ( X1 @ X2 ) ) )
= ( ^ [X2: $i] : ( X1 @ ( X0 @ X2 ) ) ) ) )
=> ? [X4: $i] :
( ( X0 @ X4 )
= X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $i] :
( ? [X1: $i > $i] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
& ( ( ^ [X2: $i] : ( X0 @ ( X1 @ X2 ) ) )
= ( ^ [X2: $i] : ( X1 @ ( X0 @ X2 ) ) ) ) )
=> ? [X4: $i] :
( ( X0 @ X4 )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.OR1lzQUlsy/DTF2THF_7911.p',cTHM141_pme) ).
thf(f23,plain,
( sK2
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sK0 @ sK2 )
!= ( sK0 @ sK2 ) )
| ( sK2
= ( sK0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f20,f13]) ).
thf(f13,plain,
( sK2
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f20,plain,
! [X0: $i] :
( ( ( sK0 @ ( sK1 @ X0 ) )
!= ( sK0 @ X0 ) )
| ( sK2
= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f14,f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( sK1 @ ( sK0 @ X1 ) )
= ( sK0 @ ( sK1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: $i] : ( sK0 @ ( sK1 @ Y0 ) ) )
= ( ^ [Y0: $i] : ( sK1 @ ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f14,plain,
! [X4: $i] :
( ( ( sK1 @ X4 )
!= X4 )
| ( sK2 = X4 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU932^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.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 12:38:29 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : SEU932^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.49 % Domain : Set Theory (Functions)
% 0.30/0.49 % Problem : TPS problem THM141
% 0.30/0.49 % Version : Especial.
% 0.30/0.49 % English : If some function which commutes with f has a unique fixed point,
% 0.30/0.49 % then f has a fixed point.
% 0.30/0.49
% 0.30/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.49 % Source : [Bro09]
% 0.30/0.49 % Names : tps_0265 [Bro09]
% 0.30/0.49 % : THM141 [TPS]
% 0.30/0.49
% 0.30/0.49 % Status : Theorem
% 0.30/0.49 % Rating : 0.00 v9.0.0, 0.10 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, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.30/0.49 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.30/0.49 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 5 ( 5 avg)
% 0.30/0.49 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 7 @)
% 0.30/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.49 % Number of types : 1 ( 0 usr)
% 0.30/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.49 % Number of variables : 7 ( 2 ^; 2 !; 3 ?; 7 :)
% 0.30/0.49 % SPC : TH0_THM_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.49 % : Polymorphic definitions expanded.
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf(cTHM141_pme,conjecture,
% 0.30/0.49 ! [Xf: $i > $i] :
% 0.30/0.49 ( ? [Xg: $i > $i] :
% 0.30/0.49 ( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
% 0.30/0.49 = ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
% 0.30/0.49 & ? [Xx: $i] :
% 0.30/0.49 ( ( ( Xg @ Xx )
% 0.30/0.49 = Xx )
% 0.30/0.49 & ! [Xz: $i] :
% 0.30/0.49 ( ( ( Xg @ Xz )
% 0.30/0.49 = Xz )
% 0.30/0.49 => ( Xz = Xx ) ) ) )
% 0.30/0.49 => ? [Xy: $i] :
% 0.30/0.49 ( ( Xf @ Xy )
% 0.30/0.49 = Xy ) ) ).
% 0.30/0.49
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 ------------------------
% 1.67/1.41 ---- Embedded in THF ---
% 1.67/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.41 %%% Generated on Tue Feb 24 12:38:30 EST 2026
% 1.67/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.41 %%% Logic specification used:
% 1.67/1.41 %%% thf(spec, logic, $$dhol).
% 1.67/1.41
% 1.67/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OR1lzQUlsy/DTF2DTF7911.p
% See solution above
% 1.67/1.41 ------------------------
% 1.67/1.42 ---- Cleaned THF ---
% 1.67/1.42 thf(cTHM141_pme,conjecture,
% 1.67/1.42 ! [Xf: $i > $i] :
% 1.67/1.42 ( ? [Xg: $i > $i] :
% 1.67/1.42 ( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
% 1.67/1.42 = ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
% 1.67/1.42 & ? [Xx: $i] :
% 1.67/1.42 ( ( ( Xg @ Xx )
% 1.67/1.42 = Xx )
% 1.67/1.42 & ! [Xz: $i] :
% 1.67/1.42 ( ( ( Xg @ Xz )
% 1.67/1.42 = Xz )
% 1.67/1.42 => ( Xz = Xx ) ) ) )
% 1.67/1.42 => ? [Xy: $i] :
% 1.67/1.42 ( ( Xf @ Xy )
% 1.67/1.42 = Xy ) ) ).
% 1.67/1.42 ------------------------
% 1.67/1.44 % (8024)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_7911 for (3000ds/4Mi)
% 1.67/1.44 % (8023)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7911 for (3000ds/183Mi)
% 1.67/1.44 % (8026)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7911 for (3000ds/2Mi)
% 1.67/1.44 % (8027)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_7911 for (3000ds/2Mi)
% 1.67/1.44 % (8028)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_7911 for (3000ds/275Mi)
% 1.67/1.44 % (8025)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_7911 for (3000ds/27Mi)
% 1.67/1.44 % (8029)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7911 for (3000ds/18Mi)
% 1.67/1.44 % (8026)Instruction limit reached!
% 1.67/1.44 % (8026)------------------------------
% 1.67/1.44 % (8026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (8026)Termination reason: Unknown
% 1.67/1.44 % (8027)Instruction limit reached!
% 1.67/1.44 % (8027)------------------------------
% 1.67/1.44 % (8027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (8026)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (8026)Memory used [KB]: 5500
% 1.67/1.44 % (8026)Time elapsed: 0.003 s
% 1.67/1.44 % (8026)Instructions burned: 2 (million)
% 1.67/1.44 % (8026)------------------------------
% 1.67/1.44 % (8026)------------------------------
% 1.67/1.44 % (8027)Termination reason: Unknown
% 1.67/1.44 % (8027)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (8027)Memory used [KB]: 5500
% 1.67/1.44 % (8027)Time elapsed: 0.003 s
% 1.67/1.44 % (8027)Instructions burned: 3 (million)
% 1.67/1.44 % (8027)------------------------------
% 1.67/1.44 % (8027)------------------------------
% 1.67/1.44 % (8023)First to succeed.
% 1.67/1.45 % (8024)Also succeeded, but the first one will report.
% 1.67/1.45 % (8023)Refutation found. Thanks to Tanya!
% 1.67/1.45 % SZS status Theorem for DTF2THF_7911
% 1.67/1.45 % SZS output start Proof for DTF2THF_7911
% 1.67/1.45 thf(func_def_5, type, sK0: $i > $i).
% 1.67/1.45 thf(func_def_6, type, sK1: $i > $i).
% 1.67/1.45 thf(func_def_9, type, ph4: !>[X0: $tType]:(X0)).
% 1.67/1.45 thf(f24,plain,(
% 1.67/1.45 $false),
% 1.67/1.45 inference(subsumption_resolution,[status(thm)],[f23,f16])).
% 1.67/1.45 thf(f16,plain,(
% 1.67/1.45 ( ! [X1 : $i] : (((sK0 @ X1) != X1)) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.45 thf(f12,plain,(
% 1.67/1.45 ! [X1 : $i] : ((sK0 @ X1) != X1) & (((^[Y0 : $i]: (sK0 @ (sK1 @ Y0))) = (^[Y0 : $i]: (sK1 @ (sK0 @ Y0)))) & (! [X4 : $i] : (((sK1 @ X4) != X4) | (sK2 = X4)) & (sK2 = (sK1 @ sK2))))),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.67/1.45 thf(f9,plain,(
% 1.67/1.45 ? [X0 : $i > $i] : (! [X1 : $i] : ((X0 @ X1) != X1) & ? [X2 : $i > $i] : (((^[Y0 : $i]: (X2 @ (X0 @ Y0))) = (^[Y0 : $i]: (X0 @ (X2 @ Y0)))) & ? [X3 : $i] : (! [X4 : $i] : (((X2 @ X4) != X4) | (X3 = X4)) & ((X2 @ X3) = X3)))) => (! [X1 : $i] : ((sK0 @ X1) != X1) & ? [X2 : $i > $i] : (((^[Y0 : $i]: (sK0 @ (X2 @ Y0))) = (^[Y0 : $i]: (X2 @ (sK0 @ Y0)))) & ? [X3 : $i] : (! [X4 : $i] : (((X2 @ X4) != X4) | (X3 = X4)) & ((X2 @ X3) = X3))))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f10,plain,(
% 1.67/1.45 ? [X2 : $i > $i] : (((^[Y0 : $i]: (sK0 @ (X2 @ Y0))) = (^[Y0 : $i]: (X2 @ (sK0 @ Y0)))) & ? [X3 : $i] : (! [X4 : $i] : (((X2 @ X4) != X4) | (X3 = X4)) & ((X2 @ X3) = X3))) => (((^[Y0 : $i]: (sK0 @ (sK1 @ Y0))) = (^[Y0 : $i]: (sK1 @ (sK0 @ Y0)))) & ? [X3 : $i] : (! [X4 : $i] : (((sK1 @ X4) != X4) | (X3 = X4)) & ((sK1 @ X3) = X3)))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f11,plain,(
% 1.67/1.45 ? [X3 : $i] : (! [X4 : $i] : (((sK1 @ X4) != X4) | (X3 = X4)) & ((sK1 @ X3) = X3)) => (! [X4 : $i] : (((sK1 @ X4) != X4) | (sK2 = X4)) & (sK2 = (sK1 @ sK2)))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f8,plain,(
% 1.67/1.45 ? [X0 : $i > $i] : (! [X1 : $i] : ((X0 @ X1) != X1) & ? [X2 : $i > $i] : (((^[Y0 : $i]: (X2 @ (X0 @ Y0))) = (^[Y0 : $i]: (X0 @ (X2 @ Y0)))) & ? [X3 : $i] : (! [X4 : $i] : (((X2 @ X4) != X4) | (X3 = X4)) & ((X2 @ X3) = X3))))),
% 1.67/1.45 inference(rectify,[status(thm)],[f7])).
% 1.67/1.45 thf(f7,plain,(
% 1.67/1.45 ? [X0 : $i > $i] : (! [X4 : $i] : ((X0 @ X4) != X4) & ? [X1 : $i > $i] : (((^[Y0 : $i]: (X0 @ (X1 @ Y0))) = (^[Y0 : $i]: (X1 @ (X0 @ Y0)))) & ? [X2 : $i] : (! [X3 : $i] : (((X1 @ X3) != X3) | (X2 = X3)) & ((X1 @ X2) = X2))))),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f6])).
% 1.67/1.45 thf(f6,plain,(
% 1.67/1.45 ~! [X0 : $i > $i] : (? [X1 : $i > $i] : (? [X2 : $i] : (! [X3 : $i] : (((X1 @ X3) = X3) => (X2 = X3)) & ((X1 @ X2) = X2)) & ((^[Y0 : $i]: (X0 @ (X1 @ Y0))) = (^[Y0 : $i]: (X1 @ (X0 @ Y0))))) => ? [X4 : $i] : ((X0 @ X4) = X4))),
% 1.67/1.45 inference(rectify,[status(thm)],[f5])).
% 1.67/1.45 thf(f5,plain,(
% 1.67/1.45 ~! [X0 : $i > $i] : (? [X1 : $i > $i] : (? [X2 : $i] : (! [X3 : $i] : (((X1 @ X3) = X3) => (X2 = X3)) & ((X1 @ X2) = X2)) & ((^[Y0 : $i]: (X0 @ (X1 @ Y0))) = (^[Y0 : $i]: (X1 @ (X0 @ Y0))))) => ? [X6 : $i] : ((X0 @ X6) = X6))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.45 thf(f4,plain,(
% 1.67/1.45 ~! [X0 : $i > $i] : (? [X1 : $i > $i] : (? [X2 : $i] : (((X1 @ X2) = X2) & ! [X3 : $i] : (((X1 @ X3) = X3) => (X2 = X3))) & ((^[X4 : $i] : (X0 @ (X1 @ X4))) = (^[X5 : $i] : (X1 @ (X0 @ X5))))) => ? [X6 : $i] : ((X0 @ X6) = X6))),
% 1.67/1.45 inference(rectify,[status(thm)],[f2])).
% 1.67/1.45 thf(f2,negated_conjecture,(
% 1.67/1.45 ~! [X0 : $i > $i] : (? [X1 : $i > $i] : (? [X2 : $i] : (((X1 @ X2) = X2) & ! [X3 : $i] : (((X1 @ X3) = X3) => (X2 = X3))) & ((^[X2 : $i] : (X0 @ (X1 @ X2))) = (^[X2 : $i] : (X1 @ (X0 @ X2))))) => ? [X4 : $i] : ((X0 @ X4) = X4))),
% 1.67/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.45 thf(f1,conjecture,(
% 1.67/1.45 ! [X0 : $i > $i] : (? [X1 : $i > $i] : (? [X2 : $i] : (((X1 @ X2) = X2) & ! [X3 : $i] : (((X1 @ X3) = X3) => (X2 = X3))) & ((^[X2 : $i] : (X0 @ (X1 @ X2))) = (^[X2 : $i] : (X1 @ (X0 @ X2))))) => ? [X4 : $i] : ((X0 @ X4) = X4))),
% 1.67/1.45 file('/export/starexec/sandbox/tmp/tmp.OR1lzQUlsy/DTF2THF_7911.p',cTHM141_pme)).
% 1.67/1.45 thf(f23,plain,(
% 1.67/1.45 (sK2 = (sK0 @ sK2))),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.67/1.45 thf(f21,plain,(
% 1.67/1.45 ((sK0 @ sK2) != (sK0 @ sK2)) | (sK2 = (sK0 @ sK2))),
% 1.67/1.45 inference(superposition,[status(thm)],[f20,f13])).
% 1.67/1.45 thf(f13,plain,(
% 1.67/1.45 (sK2 = (sK1 @ sK2))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.45 thf(f20,plain,(
% 1.67/1.45 ( ! [X0 : $i] : (((sK0 @ (sK1 @ X0)) != (sK0 @ X0)) | (sK2 = (sK0 @ X0))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f14,f19])).
% 1.67/1.45 thf(f19,plain,(
% 1.67/1.45 ( ! [X1 : $i] : (((sK1 @ (sK0 @ X1)) = (sK0 @ (sK1 @ X1)))) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.67/1.45 thf(f18,plain,(
% 1.67/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (sK1 @ (sK0 @ Y0))) @ X1) = ((^[Y0 : $i]: (sK0 @ (sK1 @ Y0))) @ X1))) )),
% 1.67/1.45 inference(argument_congruence,[status(thm)],[f15])).
% 1.67/1.45 thf(f15,plain,(
% 1.67/1.45 ((^[Y0 : $i]: (sK0 @ (sK1 @ Y0))) = (^[Y0 : $i]: (sK1 @ (sK0 @ Y0))))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.45 thf(f14,plain,(
% 1.67/1.45 ( ! [X4 : $i] : (((sK1 @ X4) != X4) | (sK2 = X4)) )),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.45 % SZS output end Proof for DTF2THF_7911
% 1.67/1.45 % (8023)------------------------------
% 1.67/1.45 % (8023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (8023)Termination reason: Refutation
% 1.67/1.45
% 1.67/1.45 % (8023)Memory used [KB]: 5500
% 1.67/1.45 % (8023)Time elapsed: 0.004 s
% 1.67/1.45 % (8023)Instructions burned: 2 (million)
% 1.67/1.45 % (8023)------------------------------
% 1.67/1.45 % (8023)------------------------------
% 1.67/1.45 % (8022)Success in time 0.018 s
%------------------------------------------------------------------------------