%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV220^5 : 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 : n016.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 09:40:35 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 211 ( 96 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 256 ( 23 ~; 11 |; 54 &; 139 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 5 con; 0-2 aty)
% ( 0 !!; 13 ??; 0 @@+; 0 @@-)
% Number of variables : 84 ( 29 ^; 24 !; 31 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
f: b > a ).
thf(func_def_3,type,
w: ( b > $o ) > $o ).
thf(func_def_13,type,
sK0: a ).
thf(func_def_14,type,
sK1: a > $o ).
thf(func_def_15,type,
sK2: b > $o ).
thf(func_def_16,type,
sK3: b ).
thf(func_def_19,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
$true = $false,
inference(superposition,[status(thm)],[f26,f25]) ).
thf(f25,plain,
( ( sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true != $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f13,f16]) ).
thf(f16,plain,
( ( w @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( sK1 @ sK0 )
!= $true )
& ( ( w @ sK2 )
= $true )
& ( sK1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( sK0
= ( f @ sK3 ) )
& ! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ sK3 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ? [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
& ? [X2: b > $o] :
( ( ( w @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X1 ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ X3 )
= $true ) ) ) )
=> ( ? [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
& ? [X2: b > $o] :
( ( ( w @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X1 ) ) )
& ? [X3: b] :
( ( sK0
= ( f @ X3 ) )
& ! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ X3 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
& ? [X2: b > $o] :
( ( ( w @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X1 ) ) )
=> ( ( ( sK1 @ sK0 )
!= $true )
& ? [X2: b > $o] :
( ( ( w @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: b > $o] :
( ( ( w @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= sK1 ) )
=> ( ( ( w @ sK2 )
= $true )
& ( sK1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: b] :
( ( sK0
= ( f @ X3 ) )
& ! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ X3 )
= $true ) ) )
=> ( ( sK0
= ( f @ sK3 ) )
& ! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ sK3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a] :
( ? [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
& ? [X2: b > $o] :
( ( ( w @ X2 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X1 ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ? [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
& ? [X4: b > $o] :
( ( ( w @ X4 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X3 ) ) )
& ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ! [X2: b > $o] :
( ( ( w @ X2 )
!= $true )
| ( ( X2 @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ! [X2: b > $o] :
( ( ( w @ X2 )
= $true )
=> ( ( X2 @ X1 )
= $true ) ) )
=> ! [X3: a > $o] :
( ? [X4: b > $o] :
( ( ( w @ X4 )
= $true )
& ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X3 ) )
=> ( ( X3 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) )
& ( ( f @ X1 )
= X0 ) )
=> ! [X3: a > $o] :
( ? [X4: b > $o] :
( ( X3
= ( ^ [X5: a] :
? [X6: b] :
( ( ( f @ X6 )
= X5 )
& ( X4 @ X6 ) ) ) )
& ( w @ X4 ) )
=> ( X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) )
& ( ( f @ X1 )
= X0 ) )
=> ! [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X3: a] :
? [X4: b] :
( ( ( f @ X4 )
= X3 )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
=> ( X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) )
& ( ( f @ X1 )
= X0 ) )
=> ! [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X3: a] :
? [X4: b] :
( ( ( f @ X4 )
= X3 )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
=> ( X2 @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rvpiYTmVgg/DTF2THF_30994.p',cX5205_pme) ).
thf(f13,plain,
! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( ( X4 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f26,plain,
( ( sK2 @ sK3 )
= $false ),
inference(equality_resolution,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: b] :
( ( ( f @ X1 )
!= ( f @ sK3 ) )
| ( ( sK2 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: b] :
( ( ( ( f @ X1 )
= ( f @ sK3 ) )
= $false )
| ( ( sK2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: b] :
( $false
= ( ( sK2 @ X1 )
& ( ( f @ X1 )
= ( f @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: b] :
( $false
= ( ^ [Y0: b] :
( ( sK2 @ Y0 )
& ( ( f @ Y0 )
= ( f @ sK3 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ?? @ b
@ ^ [Y0: b] :
( ( sK2 @ Y0 )
& ( ( f @ Y0 )
= ( f @ sK3 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ ( f @ sK3 ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f15,f14]) ).
thf(f14,plain,
( sK0
= ( f @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
( sK1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f17,plain,
( ( sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV220^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % 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 12:42:36 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEV220^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory (Sets of sets)
% 0.19/0.46 % Problem : TPS problem X5205
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0322 [Bro09]
% 0.19/0.46 % : THM86 [TPS]
% 0.19/0.46 % : X5205 [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.19/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 4 ( 5 avg)
% 0.19/0.46 % Number of connectives : 13 ( 0 ~; 0 |; 3 &; 7 @)
% 0.19/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.19/0.46 % Number of types : 3 ( 2 usr)
% 0.19/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.46 % Number of variables : 7 ( 1 ^; 3 !; 3 ?; 7 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(b_type,type,
% 0.19/0.46 b: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(f,type,
% 0.19/0.46 f: b > a ).
% 0.19/0.46
% 0.19/0.46 thf(w,type,
% 0.19/0.46 w: ( b > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cX5205_pme,conjecture,
% 0.19/0.46 ! [Xx: a] :
% 0.19/0.46 ( ? [Xt: b] :
% 0.19/0.46 ( ! [S: b > $o] :
% 0.19/0.46 ( ( w @ S )
% 0.19/0.46 => ( S @ Xt ) )
% 0.19/0.46 & ( Xx
% 0.19/0.46 = ( f @ Xt ) ) )
% 0.19/0.46 => ! [S: a > $o] :
% 0.19/0.46 ( ? [Xt: b > $o] :
% 0.19/0.46 ( ( w @ Xt )
% 0.19/0.46 & ( S
% 0.19/0.46 = ( ^ [Xz: a] :
% 0.19/0.46 ? [Xt0: b] :
% 0.19/0.46 ( ( Xt @ Xt0 )
% 0.19/0.46 & ( Xz
% 0.19/0.46 = ( f @ Xt0 ) ) ) ) ) )
% 0.19/0.46 => ( S @ Xx ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 12:42:37 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rvpiYTmVgg/DTF2DTF30994.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(b_type,type,
% 1.46/1.28 b: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(a_type,type,
% 1.46/1.28 a: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(f,type,
% 1.46/1.28 f: b > a ).
% 1.46/1.28
% 1.46/1.28 thf(w,type,
% 1.46/1.28 w: ( b > $o ) > $o ).
% 1.46/1.28
% 1.46/1.28 thf(cX5205_pme,conjecture,
% 1.46/1.28 ! [Xx: a] :
% 1.46/1.28 ( ? [Xt: b] :
% 1.46/1.28 ( ! [S: b > $o] :
% 1.46/1.28 ( ( w @ S )
% 1.46/1.28 => ( S @ Xt ) )
% 1.46/1.28 & ( Xx
% 1.46/1.28 = ( f @ Xt ) ) )
% 1.46/1.28 => ! [S: a > $o] :
% 1.46/1.28 ( ? [Xt: b > $o] :
% 1.46/1.28 ( ( w @ Xt )
% 1.46/1.28 & ( S
% 1.46/1.28 = ( ^ [Xz: a] :
% 1.46/1.28 ? [Xt0: b] :
% 1.46/1.28 ( ( Xt @ Xt0 )
% 1.46/1.28 & ( Xz
% 1.46/1.28 = ( f @ Xt0 ) ) ) ) ) )
% 1.46/1.28 => ( S @ Xx ) ) ) ).
% 1.46/1.28 ------------------------
% 1.61/1.30 % (31136)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30994 for (2999ds/183Mi)
% 1.61/1.30 % (31140)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_30994 for (2999ds/2Mi)
% 1.61/1.30 % (31137)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_30994 for (2999ds/4Mi)
% 1.61/1.30 % (31140)Instruction limit reached!
% 1.61/1.30 % (31140)------------------------------
% 1.61/1.30 % (31140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (31140)Termination reason: Unknown
% 1.61/1.30 % (31140)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (31140)Memory used [KB]: 5500
% 1.61/1.30 % (31140)Time elapsed: 0.002 s
% 1.61/1.30 % (31140)Instructions burned: 2 (million)
% 1.61/1.30 % (31140)------------------------------
% 1.61/1.30 % (31140)------------------------------
% 1.61/1.30 % (31136)First to succeed.
% 1.61/1.30 % (31137)Also succeeded, but the first one will report.
% 1.61/1.30 % (31136)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_30994
% 1.61/1.30 % SZS output start Proof for DTF2THF_30994
% 1.61/1.30 thf(type_def_5, type, b: $tType).
% 1.61/1.30 thf(type_def_6, type, a: $tType).
% 1.61/1.30 thf(func_def_0, type, b: $tType).
% 1.61/1.30 thf(func_def_1, type, a: $tType).
% 1.61/1.30 thf(func_def_2, type, f: b > a).
% 1.61/1.30 thf(func_def_3, type, w: (b > $o) > $o).
% 1.61/1.30 thf(func_def_13, type, sK0: a).
% 1.61/1.30 thf(func_def_14, type, sK1: a > $o).
% 1.61/1.30 thf(func_def_15, type, sK2: b > $o).
% 1.61/1.30 thf(func_def_16, type, sK3: b).
% 1.61/1.30 thf(func_def_19, type, ph5: !>[X0: $tType]:(X0)).
% 1.61/1.30 thf(f29,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.61/1.30 thf(f27,plain,(
% 1.61/1.30 ($true = $false)),
% 1.61/1.30 inference(superposition,[status(thm)],[f26,f25])).
% 1.61/1.30 thf(f25,plain,(
% 1.61/1.30 ((sK2 @ sK3) = $true)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ($true != $true) | ((sK2 @ sK3) = $true)),
% 1.61/1.30 inference(superposition,[status(thm)],[f13,f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 ((w @ sK2) = $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 (((sK1 @ sK0) != $true) & (((w @ sK2) = $true) & (sK1 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK2 @ Y1) & ((f @ Y1) = Y0)))))))) & ((sK0 = (f @ sK3)) & ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ sK3) = $true)))),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8])).
% 1.61/1.30 thf(f8,plain,(
% 1.61/1.30 ? [X0 : a] : (? [X1 : a > $o] : (((X1 @ X0) != $true) & ? [X2 : b > $o] : (((w @ X2) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X2 @ Y1) & ((f @ Y1) = Y0))))) = X1))) & ? [X3 : b] : (((f @ X3) = X0) & ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ X3) = $true)))) => (? [X1 : a > $o] : (((X1 @ sK0) != $true) & ? [X2 : b > $o] : (((w @ X2) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X2 @ Y1) & ((f @ Y1) = Y0))))) = X1))) & ? [X3 : b] : ((sK0 = (f @ X3)) & ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ X3) = $true))))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ? [X1 : a > $o] : (((X1 @ sK0) != $true) & ? [X2 : b > $o] : (((w @ X2) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X2 @ Y1) & ((f @ Y1) = Y0))))) = X1))) => (((sK1 @ sK0) != $true) & ? [X2 : b > $o] : (((w @ X2) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X2 @ Y1) & ((f @ Y1) = Y0))))) = sK1)))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ? [X2 : b > $o] : (((w @ X2) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X2 @ Y1) & ((f @ Y1) = Y0))))) = sK1)) => (((w @ sK2) = $true) & (sK1 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK2 @ Y1) & ((f @ Y1) = Y0)))))))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ? [X3 : b] : ((sK0 = (f @ X3)) & ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ X3) = $true))) => ((sK0 = (f @ sK3)) & ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ sK3) = $true)))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f7,plain,(
% 1.61/1.30 ? [X0 : a] : (? [X1 : a > $o] : (((X1 @ X0) != $true) & ? [X2 : b > $o] : (((w @ X2) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X2 @ Y1) & ((f @ Y1) = Y0))))) = X1))) & ? [X3 : b] : (((f @ X3) = X0) & ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ X3) = $true))))),
% 1.61/1.30 inference(rectify,[status(thm)],[f6])).
% 1.61/1.30 thf(f6,plain,(
% 1.61/1.30 ? [X0 : a] : (? [X3 : a > $o] : (((X3 @ X0) != $true) & ? [X4 : b > $o] : (((w @ X4) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X4 @ Y1) & ((f @ Y1) = Y0))))) = X3))) & ? [X1 : b] : (((f @ X1) = X0) & ! [X2 : b > $o] : (((w @ X2) != $true) | ((X2 @ X1) = $true))))),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,plain,(
% 1.61/1.30 ~! [X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & ! [X2 : b > $o] : (((w @ X2) = $true) => ((X2 @ X1) = $true))) => ! [X3 : a > $o] : (? [X4 : b > $o] : (((w @ X4) = $true) & ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((X4 @ Y1) & ((f @ Y1) = Y0))))) = X3)) => ((X3 @ X0) = $true)))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.30 thf(f4,plain,(
% 1.61/1.30 ~! [X0 : a] : (? [X1 : b] : (! [X2 : b > $o] : ((w @ X2) => (X2 @ X1)) & ((f @ X1) = X0)) => ! [X3 : a > $o] : (? [X4 : b > $o] : ((X3 = (^[X5 : a] : (? [X6 : b] : (((f @ X6) = X5) & (X4 @ X6))))) & (w @ X4)) => (X3 @ X0)))),
% 1.61/1.30 inference(rectify,[status(thm)],[f2])).
% 1.61/1.30 thf(f2,negated_conjecture,(
% 1.61/1.30 ~! [X0 : a] : (? [X1 : b] : (! [X2 : b > $o] : ((w @ X2) => (X2 @ X1)) & ((f @ X1) = X0)) => ! [X2 : a > $o] : (? [X1 : b > $o] : ((X2 = (^[X3 : a] : (? [X4 : b] : (((f @ X4) = X3) & (X1 @ X4))))) & (w @ X1)) => (X2 @ X0)))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.30 thf(f1,conjecture,(
% 1.61/1.30 ! [X0 : a] : (? [X1 : b] : (! [X2 : b > $o] : ((w @ X2) => (X2 @ X1)) & ((f @ X1) = X0)) => ! [X2 : a > $o] : (? [X1 : b > $o] : ((X2 = (^[X3 : a] : (? [X4 : b] : (((f @ X4) = X3) & (X1 @ X4))))) & (w @ X1)) => (X2 @ X0)))),
% 1.61/1.30 file('/export/starexec/sandbox2/tmp/tmp.rvpiYTmVgg/DTF2THF_30994.p',cX5205_pme)).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ( ! [X4 : b > $o] : (((w @ X4) != $true) | ((X4 @ sK3) = $true)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f26,plain,(
% 1.61/1.30 ((sK2 @ sK3) = $false)),
% 1.61/1.30 inference(equality_resolution,[status(thm)],[f23])).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 ( ! [X1 : b] : (((f @ X1) != (f @ sK3)) | ((sK2 @ X1) = $false)) )),
% 1.61/1.30 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.61/1.30 thf(f22,plain,(
% 1.61/1.30 ( ! [X1 : b] : ((((f @ X1) = (f @ sK3)) = $false) | ((sK2 @ X1) = $false)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.61/1.30 thf(f21,plain,(
% 1.61/1.30 ( ! [X1 : b] : (($false = ((sK2 @ X1) & ((f @ X1) = (f @ sK3))))) )),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.61/1.30 thf(f20,plain,(
% 1.61/1.30 ( ! [X1 : b] : (($false = ((^[Y0 : b]: ((sK2 @ Y0) & ((f @ Y0) = (f @ sK3)))) @ X1))) )),
% 1.61/1.30 inference(pi_clausification,[status(thm)],[f19])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ((?? @ b @ (^[Y0 : b]: ((sK2 @ Y0) & ((f @ Y0) = (f @ sK3))))) != $true)),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.61/1.30 thf(f18,plain,(
% 1.61/1.30 ($true != ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK2 @ Y1) & ((f @ Y1) = Y0))))) @ (f @ sK3)))),
% 1.61/1.30 inference(definition_unfolding,[status(thm)],[f17,f15,f14])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 (sK0 = (f @ sK3))),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f15,plain,(
% 1.61/1.30 (sK1 = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((sK2 @ Y1) & ((f @ Y1) = Y0))))))),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ((sK1 @ sK0) != $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 % SZS output end Proof for DTF2THF_30994
% 1.61/1.30 % (31136)------------------------------
% 1.61/1.30 % (31136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (31136)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (31136)Memory used [KB]: 5500
% 1.61/1.30 % (31136)Time elapsed: 0.003 s
% 1.61/1.30 % (31136)Instructions burned: 2 (million)
% 1.61/1.30 % (31136)------------------------------
% 1.61/1.30 % (31136)------------------------------
% 1.61/1.30 % (31135)Success in time 0.003 s
%------------------------------------------------------------------------------