%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV169^5 : 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 09:40:27 AM UTC 2026
% Result : Theorem 1.64s 1.32s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 59 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 206 ( 11 ~; 0 |; 32 &; 158 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 227 ( 206 ^; 15 !; 6 ?; 227 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: ( a > a > a ) > a ).
thf(func_def_8,type,
sK1: ( a > a > a ) > a ).
thf(func_def_10,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
sK4: a > a > a ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( sK0 @ sK4 )
!= ( sK0 @ sK4 ) ),
inference(superposition,[status(thm)],[f15,f22]) ).
thf(f22,plain,
! [X1: a > a > a] :
( ( sK1 @ X1 )
= ( sK0 @ X1 ) ),
inference(forward_demodulation,[status(thm)],[f21,f17]) ).
thf(f17,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK0 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a > a > a] :
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) )
@ X1 )
= ( sK0 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f10]) ).
thf(f10,plain,
( sK0
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK1 )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( sK0 != sK1 )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( sK0
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( X0 != X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) )
=> ( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK1 )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( sK0 != sK1 )
& ( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( sK0
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( X0 != X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( X0 != X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X1 )
& ( ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [X5: a,X6: a] : X6 ) ) ) )
& ( X1
= ( ^ [X7: a > a > a] :
( X7
@ ( X1
@ ^ [X8: a,X9: a] : X8 )
@ ( X1
@ ^ [X10: a,X11: a] : X11 ) ) ) )
& ( ( X1
@ ^ [X12: a,X13: a] : X13 )
= ( X0
@ ^ [X14: a,X15: a] : X15 ) )
& ( ( X0
@ ^ [X16: a,X17: a] : X16 )
= ( X1
@ ^ [X18: a,X19: a] : X18 ) ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( ( X1
@ ^ [X3: a,X4: a] : X4 )
= ( X0
@ ^ [X3: a,X4: a] : X4 ) )
& ( ( X0
@ ^ [X3: a,X4: a] : X3 )
= ( X1
@ ^ [X3: a,X4: a] : X3 ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > a ) > a,X1: ( a > a > a ) > a] :
( ( ( X0
= ( ^ [X2: a > a > a] :
( X2
@ ( X0
@ ^ [X3: a,X4: a] : X3 )
@ ( X0
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( ( X1
@ ^ [X3: a,X4: a] : X4 )
= ( X0
@ ^ [X3: a,X4: a] : X4 ) )
& ( ( X0
@ ^ [X3: a,X4: a] : X3 )
= ( X1
@ ^ [X3: a,X4: a] : X3 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.pQ5fUoLUDf/DTF2THF_17528.p',cTHM188_pme) ).
thf(f21,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(forward_demodulation,[status(thm)],[f20,f11]) ).
thf(f11,plain,
( ( sK0
@ ^ [Y0: a,Y1: a] : Y1 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f20,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(forward_demodulation,[status(thm)],[f19,f13]) ).
thf(f13,plain,
( ( sK0
@ ^ [Y0: a,Y1: a] : Y0 )
= ( sK1
@ ^ [Y0: a,Y1: a] : Y0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f19,plain,
! [X1: a > a > a] :
( ( X1
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) )
= ( sK1 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: a > a > a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK1
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK1 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f15,plain,
( ( sK1 @ sK4 )
!= ( sK0 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f12]) ).
thf(f12,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV169^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:41:14 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEV169^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPS problem from PAIRS-THMS
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_1021 [Bro09]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.46 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.20/0.46 % Number of connectives : 16 ( 0 ~; 0 |; 3 &; 12 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.20/0.46 % Number of types : 1 ( 1 usr)
% 0.20/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.46 % Number of variables : 20 ( 18 ^; 2 !; 0 ?; 20 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cTHM188_pme,conjecture,
% 0.20/0.46 ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
% 0.20/0.46 ( ( ( Xp
% 0.20/0.46 = ( ^ [Xg: a > a > a] :
% 0.20/0.46 ( Xg
% 0.20/0.46 @ ( Xp
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xx )
% 0.20/0.46 @ ( Xp
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 0.20/0.46 & ( Xq
% 0.20/0.46 = ( ^ [Xg: a > a > a] :
% 0.20/0.46 ( Xg
% 0.20/0.46 @ ( Xq
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xx )
% 0.20/0.46 @ ( Xq
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 0.20/0.46 & ( ( Xp
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xx )
% 0.20/0.46 = ( Xq
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xx ) )
% 0.20/0.46 & ( ( Xp
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xy )
% 0.20/0.46 = ( Xq
% 0.20/0.46 @ ^ [Xx: a,Xy: a] : Xy ) ) )
% 0.20/0.46 => ( Xp = Xq ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.44/1.30 ---- Embedded in THF ---
% 1.64/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.30 %%% Generated on Tue Feb 24 12:41:15 EST 2026
% 1.64/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.30 %%% Logic specification used:
% 1.64/1.30 %%% thf(spec, logic, $$dhol).
% 1.64/1.30
% 1.64/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pQ5fUoLUDf/DTF2DTF17528.p
% See solution above
% 1.64/1.30 ------------------------
% 1.64/1.30 ---- Cleaned THF ---
% 1.64/1.31 thf(a_type,type,
% 1.64/1.31 a: $tType ).
% 1.64/1.31
% 1.64/1.31 thf(cTHM188_pme,conjecture,
% 1.64/1.31 ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
% 1.64/1.31 ( ( ( Xp
% 1.64/1.31 = ( ^ [Xg: a > a > a] :
% 1.64/1.31 ( Xg
% 1.64/1.31 @ ( Xp
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xx )
% 1.64/1.31 @ ( Xp
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 1.64/1.31 & ( Xq
% 1.64/1.31 = ( ^ [Xg: a > a > a] :
% 1.64/1.31 ( Xg
% 1.64/1.31 @ ( Xq
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xx )
% 1.64/1.31 @ ( Xq
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 1.64/1.31 & ( ( Xp
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xx )
% 1.64/1.31 = ( Xq
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xx ) )
% 1.64/1.31 & ( ( Xp
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xy )
% 1.64/1.31 = ( Xq
% 1.64/1.31 @ ^ [Xx: a,Xy: a] : Xy ) ) )
% 1.64/1.31 => ( Xp = Xq ) ) ).
% 1.64/1.31 ------------------------
% 1.64/1.32 % (17859)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_17528 for (2999ds/2Mi)
% 1.64/1.32 % (17856)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_17528 for (2999ds/4Mi)
% 1.64/1.32 % (17859)Instruction limit reached!
% 1.64/1.32 % (17859)------------------------------
% 1.64/1.32 % (17859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (17859)Termination reason: Unknown
% 1.64/1.32 % (17859)Termination phase: Preprocessing 1
% 1.64/1.32
% 1.64/1.32 % (17859)Memory used [KB]: 895
% 1.64/1.32 % (17859)Time elapsed: 0.002 s
% 1.64/1.32 % (17859)Instructions burned: 2 (million)
% 1.64/1.32 % (17859)------------------------------
% 1.64/1.32 % (17859)------------------------------
% 1.64/1.32 % (17860)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_17528 for (2999ds/275Mi)
% 1.64/1.32 % (17860)First to succeed.
% 1.64/1.32 % (17856)Instruction limit reached!
% 1.64/1.32 % (17856)------------------------------
% 1.64/1.32 % (17856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (17856)Termination reason: Unknown
% 1.64/1.32 % (17856)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (17856)Memory used [KB]: 5500
% 1.64/1.32 % (17856)Time elapsed: 0.003 s
% 1.64/1.32 % (17856)Instructions burned: 5 (million)
% 1.64/1.32 % (17856)------------------------------
% 1.64/1.32 % (17856)------------------------------
% 1.64/1.32 % (17860)Refutation found. Thanks to Tanya!
% 1.64/1.32 % SZS status Theorem for DTF2THF_17528
% 1.64/1.32 % SZS output start Proof for DTF2THF_17528
% 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_7, type, sK0: (a > a > a) > a).
% 1.64/1.32 thf(func_def_8, type, sK1: (a > a > a) > a).
% 1.64/1.32 thf(func_def_10, type, ph3: !>[X0: $tType]:(X0)).
% 1.64/1.32 thf(func_def_11, type, sK4: a > a > a).
% 1.64/1.32 thf(f24,plain,(
% 1.64/1.32 $false),
% 1.64/1.32 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.64/1.32 thf(f23,plain,(
% 1.64/1.32 ((sK0 @ sK4) != (sK0 @ sK4))),
% 1.64/1.32 inference(superposition,[status(thm)],[f15,f22])).
% 1.64/1.32 thf(f22,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : (((sK1 @ X1) = (sK0 @ X1))) )),
% 1.64/1.32 inference(forward_demodulation,[status(thm)],[f21,f17])).
% 1.64/1.32 thf(f17,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : (((X1 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = (sK0 @ X1))) )),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.64/1.32 thf(f16,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : ((((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) @ X1) = (sK0 @ X1))) )),
% 1.64/1.32 inference(argument_congruence,[status(thm)],[f10])).
% 1.64/1.32 thf(f10,plain,(
% 1.64/1.32 (sK0 = (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f9,plain,(
% 1.64/1.32 ((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = sK1) & ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))) & (sK0 != sK1) & ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) & (sK0 = (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))))),
% 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 ? [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : (((^[Y0 : a > a > a]: (Y0 @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X1) & ((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))) & (X0 != X1) & ((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) & ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0)) => (((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = sK1) & ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))) & (sK0 != sK1) & ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) & (sK0 = (^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2)))))))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f7,plain,(
% 1.64/1.32 ? [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : (((^[Y0 : a > a > a]: (Y0 @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X1) & ((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))) & (X0 != X1) & ((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) & ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0))),
% 1.64/1.32 inference(flattening,[status(thm)],[f6])).
% 1.64/1.32 thf(f6,plain,(
% 1.64/1.32 ? [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : ((X0 != X1) & (((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))) & ((^[Y0 : a > a > a]: (Y0 @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X1) & ((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) & ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0)))),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.32 thf(f5,plain,(
% 1.64/1.32 ~! [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : ((((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))) & ((^[Y0 : a > a > a]: (Y0 @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X1) & ((X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) & ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0)) => (X0 = X1))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.32 thf(f4,plain,(
% 1.64/1.32 ~! [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : (((X0 = (^[X2 : a > a > a] : (X2 @ (X0 @ (^[X3 : a, X4 : a] : (X3))) @ (X0 @ (^[X5 : a, X6 : a] : (X6)))))) & (X1 = (^[X7 : a > a > a] : (X7 @ (X1 @ (^[X8 : a, X9 : a] : (X8))) @ (X1 @ (^[X10 : a, X11 : a] : (X11)))))) & ((X1 @ (^[X12 : a, X13 : a] : (X13))) = (X0 @ (^[X14 : a, X15 : a] : (X15)))) & ((X0 @ (^[X16 : a, X17 : a] : (X16))) = (X1 @ (^[X18 : a, X19 : a] : (X18))))) => (X0 = X1))),
% 1.64/1.32 inference(rectify,[status(thm)],[f2])).
% 1.64/1.32 thf(f2,negated_conjecture,(
% 1.64/1.32 ~! [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : (((X0 = (^[X2 : a > a > a] : (X2 @ (X0 @ (^[X3 : a, X4 : a] : (X3))) @ (X0 @ (^[X3 : a, X4 : a] : (X4)))))) & (X1 = (^[X2 : a > a > a] : (X2 @ (X1 @ (^[X3 : a, X4 : a] : (X3))) @ (X1 @ (^[X3 : a, X4 : a] : (X4)))))) & ((X1 @ (^[X3 : a, X4 : a] : (X4))) = (X0 @ (^[X3 : a, X4 : a] : (X4)))) & ((X0 @ (^[X3 : a, X4 : a] : (X3))) = (X1 @ (^[X3 : a, X4 : a] : (X3))))) => (X0 = X1))),
% 1.64/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.32 thf(f1,conjecture,(
% 1.64/1.32 ! [X0 : (a > a > a) > a,X1 : (a > a > a) > a] : (((X0 = (^[X2 : a > a > a] : (X2 @ (X0 @ (^[X3 : a, X4 : a] : (X3))) @ (X0 @ (^[X3 : a, X4 : a] : (X4)))))) & (X1 = (^[X2 : a > a > a] : (X2 @ (X1 @ (^[X3 : a, X4 : a] : (X3))) @ (X1 @ (^[X3 : a, X4 : a] : (X4)))))) & ((X1 @ (^[X3 : a, X4 : a] : (X4))) = (X0 @ (^[X3 : a, X4 : a] : (X4)))) & ((X0 @ (^[X3 : a, X4 : a] : (X3))) = (X1 @ (^[X3 : a, X4 : a] : (X3))))) => (X0 = X1))),
% 1.64/1.32 file('/export/starexec/sandbox/tmp/tmp.pQ5fUoLUDf/DTF2THF_17528.p',cTHM188_pme)).
% 1.64/1.32 thf(f21,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : (((X1 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = (sK1 @ X1))) )),
% 1.64/1.32 inference(forward_demodulation,[status(thm)],[f20,f11])).
% 1.64/1.32 thf(f11,plain,(
% 1.64/1.32 ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))) = (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f20,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : (((X1 @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = (sK1 @ X1))) )),
% 1.64/1.32 inference(forward_demodulation,[status(thm)],[f19,f13])).
% 1.64/1.32 thf(f13,plain,(
% 1.64/1.32 ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) = (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f19,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : (((X1 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))) = (sK1 @ X1))) )),
% 1.64/1.32 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.64/1.32 thf(f18,plain,(
% 1.64/1.32 ( ! [X1 : a > a > a] : (((sK1 @ X1) = ((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) @ X1))) )),
% 1.64/1.32 inference(argument_congruence,[status(thm)],[f14])).
% 1.64/1.32 thf(f14,plain,(
% 1.64/1.32 ((^[Y0 : a > a > a]: (Y0 @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK1 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = sK1)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 thf(f15,plain,(
% 1.64/1.32 ((sK1 @ sK4) != (sK0 @ sK4))),
% 1.64/1.32 inference(negative_extensionality,[status(thm)],[f12])).
% 1.64/1.32 thf(f12,plain,(
% 1.64/1.32 (sK0 != sK1)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.32 % SZS output end Proof for DTF2THF_17528
% 1.64/1.32 % (17860)------------------------------
% 1.64/1.32 % (17860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (17860)Termination reason: Refutation
% 1.64/1.32
% 1.64/1.32 % (17860)Memory used [KB]: 5500
% 1.64/1.32 % (17860)Time elapsed: 0.003 s
% 1.64/1.32 % (17860)Instructions burned: 2 (million)
% 1.64/1.32 % (17860)------------------------------
% 1.64/1.32 % (17860)------------------------------
% 1.64/1.32 % (17854)Success in time 0.013 s
%------------------------------------------------------------------------------