%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV224^5 : 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 : n020.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 09:40:36 AM UTC 2026
% Result : Theorem 1.31s 1.18s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 59 equ; 0 cnn)
% Maximal formula atoms : 2 ( 8 avg)
% Number of connectives : 381 ( 5 ~; 0 |; 18 &; 258 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 223 ( 223 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 5 usr; 5 con; 0-2 aty)
% ( 42 !!; 25 ??; 0 @@+; 0 @@-)
% Number of variables : 110 ( 84 ^; 20 !; 6 ?; 110 :)
% 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_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a ).
thf(func_def_21,type,
sK3: b > a > $o ).
thf(func_def_22,type,
sK4: b > $o ).
thf(func_def_23,type,
sK5: ( ( b > $o ) > ( b > $o ) > $o ) > b > $o ).
thf(f32,plain,
$false,
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: ( b > $o ) > ( b > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ X1 @ Y1 )
& ( ( sK3 @ Y1 )
= Y0 ) ) )
=> ( Y0 @ sK2 ) ) )
!= ( X1 @ sK4 @ ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: ( b > $o ) > ( b > $o ) > $o] :
( ( ( X1 @ sK4 @ ( sK5 @ X1 ) )
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ b
@ ^ [Y1: b] :
( ( sK5 @ X1 @ Y1 )
& ( ( sK3 @ Y1 )
= Y0 ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: ( b > $o ) > ( b > $o ) > $o] :
( ( ^ [Y0: b > $o] :
( ( X1 @ sK4 @ Y0 )
= ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
=> ( Y1 @ sK2 ) ) ) )
@ ( sK5 @ X1 ) )
= $false ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: ( b > $o ) > ( b > $o ) > $o] :
( ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( X1 @ sK4 @ Y0 )
= ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ b
@ ^ [Y2: b] :
( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 )
= Y1 ) ) )
=> ( Y1 @ sK2 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: ( b > $o ) > ( b > $o ) > $o] :
( ( ^ [Y0: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ sK4 @ Y1 )
= ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
=> ( Y2 @ sK2 ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ sK4 @ Y1 )
= ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
=> ( Y2 @ sK2 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( sK4
= ( ^ [Y0: b] : ( sK3 @ Y0 @ sK2 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y0: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y0 @ sK4 @ Y1 )
= ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ?? @ b
@ ^ [Y3: b] :
( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 )
= Y2 ) ) )
=> ( Y2 @ sK2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: b > $o] :
( ( Y0
= ( ^ [Y1: b] : ( sK3 @ Y1 @ sK2 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y1: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y1 @ Y0 @ Y2 )
= ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 )
= Y3 ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( b > $o )
@ ^ [Y0: b > $o] :
( ( Y0
= ( ^ [Y1: b] : ( sK3 @ Y1 @ sK2 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y1: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y1 @ Y0 @ Y2 )
= ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ?? @ b
@ ^ [Y4: b] :
( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 )
= Y3 ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: b > a > $o] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1
= ( ^ [Y2: b] : ( Y0 @ Y2 @ sK2 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y2: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y3: b > $o] :
( ( Y2 @ Y1 @ Y3 )
= ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ?? @ b
@ ^ [Y5: b] :
( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
=> ( Y4 @ sK2 ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( !! @ ( b > a > $o )
@ ^ [Y0: b > a > $o] :
( !! @ ( b > $o )
@ ^ [Y1: b > $o] :
( ( Y1
= ( ^ [Y2: b] : ( Y0 @ Y2 @ sK2 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y2: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y3: b > $o] :
( ( Y2 @ Y1 @ Y3 )
= ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ?? @ b
@ ^ [Y5: b] :
( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 )
= Y4 ) ) )
=> ( Y4 @ sK2 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( !! @ ( b > a > $o )
@ ^ [Y1: b > a > $o] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2
= ( ^ [Y3: b] : ( Y1 @ Y3 @ Y0 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y3: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y4: b > $o] :
( ( Y3 @ Y2 @ Y4 )
= ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ?? @ b
@ ^ [Y6: b] :
( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 )
= Y5 ) ) )
=> ( Y5 @ Y0 ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( b > a > $o )
@ ^ [Y1: b > a > $o] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2
= ( ^ [Y3: b] : ( Y1 @ Y3 @ Y0 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y3: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y4: b > $o] :
( ( Y3 @ Y2 @ Y4 )
= ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ?? @ b
@ ^ [Y6: b] :
( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 )
= Y5 ) ) )
=> ( Y5 @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( b > a > $o )
@ ^ [Y1: b > a > $o] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2
= ( ^ [Y3: b] : ( Y1 @ Y3 @ Y0 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y3: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y4: b > $o] :
( ( Y3 @ Y2 @ Y4 )
= ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ?? @ b
@ ^ [Y6: b] :
( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 )
= Y5 ) ) )
=> ( Y5 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( b > a > $o )
@ ^ [Y1: b > a > $o] :
( !! @ ( b > $o )
@ ^ [Y2: b > $o] :
( ( Y2
= ( ^ [Y3: b] : ( Y1 @ Y3 @ Y0 ) ) )
=> ( ?? @ ( ( b > $o ) > ( b > $o ) > $o )
@ ^ [Y3: ( b > $o ) > ( b > $o ) > $o] :
( !! @ ( b > $o )
@ ^ [Y4: b > $o] :
( ( Y3 @ Y2 @ Y4 )
= ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ?? @ b
@ ^ [Y6: b] :
( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 )
= Y5 ) ) )
=> ( Y5 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > $o,X1: b > a > $o,X2: a] :
( ( X0
= ( ^ [X3: b] : ( X1 @ X3 @ X2 ) ) )
=> ? [X4: ( b > $o ) > ( b > $o ) > $o] :
! [X5: b > $o] :
( ( X4 @ X0 @ X5 )
<=> ! [X6: a > $o] :
( ? [X7: b] :
( ( ( X1 @ X7 )
= X6 )
& ( X5 @ X7 ) )
=> ( X6 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: b > $o,X0: b > a > $o,X1: a] :
( ( X2
= ( ^ [X3: b] : ( X0 @ X3 @ X1 ) ) )
=> ? [X4: ( b > $o ) > ( b > $o ) > $o] :
! [X5: b > $o] :
( ( X4 @ X2 @ X5 )
<=> ! [X6: a > $o] :
( ? [X7: b] :
( ( ( X0 @ X7 )
= X6 )
& ( X5 @ X7 ) )
=> ( X6 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: b > $o,X0: b > a > $o,X1: a] :
( ( X2
= ( ^ [X3: b] : ( X0 @ X3 @ X1 ) ) )
=> ? [X4: ( b > $o ) > ( b > $o ) > $o] :
! [X5: b > $o] :
( ( X4 @ X2 @ X5 )
<=> ! [X6: a > $o] :
( ? [X7: b] :
( ( ( X0 @ X7 )
= X6 )
& ( X5 @ X7 ) )
=> ( X6 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nllwggPfFk/DTF2THF_15451.p',cTHM142_1_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV224^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n020.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:42:27 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEV224^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Set Theory (Sets of sets)
% 0.16/0.42 % Problem : TPS problem from FUNS-AND-SETS-OF-SETS-THMS
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0876 [Bro09]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.78 v9.1.0, 0.75 v9.0.0, 0.80 v8.2.0, 0.85 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 0.62 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.42 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.42 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 7 @)
% 0.16/0.42 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 13 ( 13 avg)
% 0.16/0.42 % Number of types : 3 ( 2 usr)
% 0.16/0.42 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.42 % Number of variables : 8 ( 1 ^; 5 !; 2 ?; 8 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(b_type,type,
% 0.16/0.42 b: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(a_type,type,
% 0.16/0.42 a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(cTHM142_1_pme,conjecture,
% 0.16/0.42 ! [Xa: b > a > $o,Xy: a,Xr: b > $o] :
% 0.16/0.42 ( ( Xr
% 0.16/0.42 = ( ^ [Xj: b] : ( Xa @ Xj @ Xy ) ) )
% 0.16/0.42 => ? [Xp: ( b > $o ) > ( b > $o ) > $o] :
% 0.16/0.42 ! [Xs: b > $o] :
% 0.16/0.42 ( ! [S: a > $o] :
% 0.16/0.42 ( ? [Xt: b] :
% 0.16/0.42 ( ( Xs @ Xt )
% 0.16/0.42 & ( S
% 0.16/0.42 = ( Xa @ Xt ) ) )
% 0.16/0.42 => ( S @ Xy ) )
% 0.16/0.42 <=> ( Xp @ Xr @ Xs ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.31/1.13 ---- Embedded in THF ---
% 1.31/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.31/1.13 %%% Generated on Tue Feb 24 12:42:27 EST 2026
% 1.31/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.31/1.13 %%% Logic specification used:
% 1.31/1.13 %%% thf(spec, logic, $$dhol).
% 1.31/1.13
% 1.31/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nllwggPfFk/DTF2DTF15451.p
% See solution above
% 1.31/1.13 ------------------------
% 1.31/1.13 ---- Cleaned THF ---
% 1.31/1.13 thf(b_type,type,
% 1.31/1.13 b: $tType ).
% 1.31/1.13
% 1.31/1.13 thf(a_type,type,
% 1.31/1.13 a: $tType ).
% 1.31/1.13
% 1.31/1.13 thf(cTHM142_1_pme,conjecture,
% 1.31/1.13 ! [Xa: b > a > $o,Xy: a,Xr: b > $o] :
% 1.31/1.13 ( ( Xr
% 1.31/1.13 = ( ^ [Xj: b] : ( Xa @ Xj @ Xy ) ) )
% 1.31/1.13 => ? [Xp: ( b > $o ) > ( b > $o ) > $o] :
% 1.31/1.13 ! [Xs: b > $o] :
% 1.31/1.13 ( ! [S: a > $o] :
% 1.31/1.13 ( ? [Xt: b] :
% 1.31/1.13 ( ( Xs @ Xt )
% 1.31/1.13 & ( S
% 1.31/1.13 = ( Xa @ Xt ) ) )
% 1.31/1.13 => ( S @ Xy ) )
% 1.31/1.13 <=> ( Xp @ Xr @ Xs ) ) ) ).
% 1.31/1.13 ------------------------
% 1.31/1.15 % (15553)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_15451 for (2999ds/4Mi)
% 1.31/1.15 % (15553)Instruction limit reached!
% 1.31/1.15 % (15553)------------------------------
% 1.31/1.15 % (15553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.15 % (15553)Termination reason: Unknown
% 1.31/1.15 % (15553)Termination phase: Saturation
% 1.31/1.15
% 1.31/1.15 % (15553)Memory used [KB]: 5500
% 1.31/1.15 % (15553)Time elapsed: 0.003 s
% 1.31/1.15 % (15553)Instructions burned: 4 (million)
% 1.31/1.15 % (15553)------------------------------
% 1.31/1.15 % (15553)------------------------------
% 1.31/1.15 % (15552)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/183Mi)
% 1.31/1.15 % (15555)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/2Mi)
% 1.31/1.15 % (15554)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_15451 for (2999ds/27Mi)
% 1.31/1.15 % (15557)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_15451 for (2999ds/275Mi)
% 1.31/1.15 % (15556)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_15451 for (2999ds/2Mi)
% 1.31/1.15 % (15558)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/18Mi)
% 1.31/1.16 % (15555)Instruction limit reached!
% 1.31/1.16 % (15555)------------------------------
% 1.31/1.16 % (15555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.16 % (15555)Termination reason: Unknown
% 1.31/1.16 % (15555)Termination phase: Saturation
% 1.31/1.16
% 1.31/1.16 % (15556)Instruction limit reached!
% 1.31/1.16 % (15556)------------------------------
% 1.31/1.16 % (15556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.16 % (15556)Termination reason: Unknown
% 1.31/1.16 % (15556)Termination phase: Saturation
% 1.31/1.16
% 1.31/1.16 % (15556)Memory used [KB]: 5500
% 1.31/1.16 % (15556)Time elapsed: 0.003 s
% 1.31/1.16 % (15556)Instructions burned: 3 (million)
% 1.31/1.16 % (15556)------------------------------
% 1.31/1.16 % (15556)------------------------------
% 1.31/1.16 % (15555)Memory used [KB]: 5500
% 1.31/1.16 % (15555)Time elapsed: 0.003 s
% 1.31/1.16 % (15555)Instructions burned: 3 (million)
% 1.31/1.16 % (15555)------------------------------
% 1.31/1.16 % (15555)------------------------------
% 1.31/1.16 % (15554)Refutation not found, incomplete strategy
% 1.31/1.16 % (15554)------------------------------
% 1.31/1.16 % (15554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.16 % (15554)Termination reason: Refutation not found, incomplete strategy
% 1.31/1.16
% 1.31/1.16
% 1.31/1.16 % (15554)Memory used [KB]: 5500
% 1.31/1.16 % (15554)Time elapsed: 0.003 s
% 1.31/1.16 % (15554)Instructions burned: 3 (million)
% 1.31/1.16 % (15554)------------------------------
% 1.31/1.16 % (15554)------------------------------
% 1.31/1.16 % (15559)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/3Mi)
% 1.31/1.16 % (15559)Instruction limit reached!
% 1.31/1.16 % (15559)------------------------------
% 1.31/1.16 % (15559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.16 % (15559)Termination reason: Unknown
% 1.31/1.16 % (15559)Termination phase: Saturation
% 1.31/1.16
% 1.31/1.16 % (15559)Memory used [KB]: 5500
% 1.31/1.16 % (15559)Time elapsed: 0.002 s
% 1.31/1.16 % (15559)Instructions burned: 3 (million)
% 1.31/1.16 % (15559)------------------------------
% 1.31/1.16 % (15559)------------------------------
% 1.31/1.16 % (15558)Instruction limit reached!
% 1.31/1.16 % (15558)------------------------------
% 1.31/1.16 % (15558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.16 % (15558)Termination reason: Unknown
% 1.31/1.16 % (15558)Termination phase: Saturation
% 1.31/1.16
% 1.31/1.16 % (15558)Memory used [KB]: 5628
% 1.31/1.16 % (15558)Time elapsed: 0.011 s
% 1.31/1.16 % (15558)Instructions burned: 19 (million)
% 1.31/1.16 % (15558)------------------------------
% 1.31/1.16 % (15558)------------------------------
% 1.31/1.17 % (15563)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/1041Mi)
% 1.31/1.17 % (15560)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/37Mi)
% 1.31/1.17 % (15561)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/15Mi)
% 1.31/1.17 % (15562)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/3Mi)
% 1.31/1.17 % (15562)Instruction limit reached!
% 1.31/1.17 % (15562)------------------------------
% 1.31/1.17 % (15562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.17 % (15562)Termination reason: Unknown
% 1.31/1.17 % (15562)Termination phase: Saturation
% 1.31/1.17
% 1.31/1.17 % (15562)Memory used [KB]: 5500
% 1.31/1.17 % (15562)Time elapsed: 0.003 s
% 1.31/1.17 % (15562)Instructions burned: 3 (million)
% 1.31/1.17 % (15562)------------------------------
% 1.31/1.17 % (15562)------------------------------
% 1.31/1.18 % (15564)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15451 for (2999ds/7Mi)
% 1.31/1.18 % (15561)Instruction limit reached!
% 1.31/1.18 % (15561)------------------------------
% 1.31/1.18 % (15561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.18 % (15561)Termination reason: Unknown
% 1.31/1.18 % (15561)Termination phase: Saturation
% 1.31/1.18
% 1.31/1.18 % (15561)Memory used [KB]: 5756
% 1.31/1.18 % (15561)Time elapsed: 0.010 s
% 1.31/1.18 % (15561)Instructions burned: 16 (million)
% 1.31/1.18 % (15561)------------------------------
% 1.31/1.18 % (15561)------------------------------
% 1.31/1.18 % (15560)First to succeed.
% 1.31/1.18 % (15564)Instruction limit reached!
% 1.31/1.18 % (15564)------------------------------
% 1.31/1.18 % (15564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.18 % (15564)Termination reason: Unknown
% 1.31/1.18 % (15564)Termination phase: Saturation
% 1.31/1.18
% 1.31/1.18 % (15564)Memory used [KB]: 1023
% 1.31/1.18 % (15564)Time elapsed: 0.005 s
% 1.31/1.18 % (15564)Instructions burned: 7 (million)
% 1.31/1.18 % (15564)------------------------------
% 1.31/1.18 % (15564)------------------------------
% 1.31/1.18 % (15560)Refutation found. Thanks to Tanya!
% 1.31/1.18 % SZS status Theorem for DTF2THF_15451
% 1.31/1.18 % SZS output start Proof for DTF2THF_15451
% 1.31/1.18 thf(type_def_5, type, b: $tType).
% 1.31/1.18 thf(type_def_6, type, a: $tType).
% 1.31/1.18 thf(func_def_0, type, b: $tType).
% 1.31/1.18 thf(func_def_1, type, a: $tType).
% 1.31/1.18 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.31/1.18 thf(func_def_20, type, sK2: a).
% 1.31/1.18 thf(func_def_21, type, sK3: b > a > $o).
% 1.31/1.18 thf(func_def_22, type, sK4: b > $o).
% 1.31/1.18 thf(func_def_23, type, sK5: ((b > $o) > (b > $o) > $o) > b > $o).
% 1.31/1.18 thf(f32,plain,(
% 1.31/1.18 $false),
% 1.31/1.18 inference(equality_resolution,[status(thm)],[f20])).
% 1.31/1.18 thf(f20,plain,(
% 1.31/1.18 ( ! [X1 : (b > $o) > (b > $o) > $o] : (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((?? @ b @ (^[Y1 : b]: ((sK5 @ X1 @ Y1) & ((sK3 @ Y1) = Y0)))) => (Y0 @ sK2)))) != (X1 @ sK4 @ (sK5 @ X1)))) )),
% 1.31/1.18 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.31/1.18 thf(f19,plain,(
% 1.31/1.18 ( ! [X1 : (b > $o) > (b > $o) > $o] : ((((X1 @ sK4 @ (sK5 @ X1)) = (!! @ (a > $o) @ (^[Y0 : a > $o]: ((?? @ b @ (^[Y1 : b]: ((sK5 @ X1 @ Y1) & ((sK3 @ Y1) = Y0)))) => (Y0 @ sK2))))) = $false)) )),
% 1.31/1.18 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.31/1.18 thf(f18,plain,(
% 1.31/1.18 ( ! [X1 : (b > $o) > (b > $o) > $o] : ((((^[Y0 : b > $o]: ((X1 @ sK4 @ Y0) = (!! @ (a > $o) @ (^[Y1 : a > $o]: ((?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((sK3 @ Y2) = Y1)))) => (Y1 @ sK2)))))) @ (sK5 @ X1)) = $false)) )),
% 1.31/1.18 inference(sigma_clausification,[status(thm)],[f17])).
% 1.31/1.18 thf(f17,plain,(
% 1.31/1.18 ( ! [X1 : (b > $o) > (b > $o) > $o] : (((!! @ (b > $o) @ (^[Y0 : b > $o]: ((X1 @ sK4 @ Y0) = (!! @ (a > $o) @ (^[Y1 : a > $o]: ((?? @ b @ (^[Y2 : b]: ((Y0 @ Y2) & ((sK3 @ Y2) = Y1)))) => (Y1 @ sK2))))))) = $false)) )),
% 1.31/1.18 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.31/1.18 thf(f16,plain,(
% 1.31/1.18 ( ! [X1 : (b > $o) > (b > $o) > $o] : ((((^[Y0 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 @ sK4 @ Y1) = (!! @ (a > $o) @ (^[Y2 : a > $o]: ((?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((sK3 @ Y3) = Y2)))) => (Y2 @ sK2)))))))) @ X1) = $false)) )),
% 1.31/1.18 inference(pi_clausification,[status(thm)],[f14])).
% 1.31/1.18 thf(f14,plain,(
% 1.31/1.18 ((?? @ ((b > $o) > (b > $o) > $o) @ (^[Y0 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 @ sK4 @ Y1) = (!! @ (a > $o) @ (^[Y2 : a > $o]: ((?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((sK3 @ Y3) = Y2)))) => (Y2 @ sK2))))))))) = $false)),
% 1.31/1.18 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.31/1.18 thf(f13,plain,(
% 1.31/1.18 (((sK4 = (^[Y0 : b]: (sK3 @ Y0 @ sK2))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y0 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((Y0 @ sK4 @ Y1) = (!! @ (a > $o) @ (^[Y2 : a > $o]: ((?? @ b @ (^[Y3 : b]: ((Y1 @ Y3) & ((sK3 @ Y3) = Y2)))) => (Y2 @ sK2)))))))))) = $false)),
% 1.31/1.18 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.31/1.18 thf(f12,plain,(
% 1.31/1.18 (((^[Y0 : b > $o]: ((Y0 = (^[Y1 : b]: (sK3 @ Y1 @ sK2))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y1 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y2 : b > $o]: ((Y1 @ Y0 @ Y2) = (!! @ (a > $o) @ (^[Y3 : a > $o]: ((?? @ b @ (^[Y4 : b]: ((Y2 @ Y4) & ((sK3 @ Y4) = Y3)))) => (Y3 @ sK2))))))))))) @ sK4) = $false)),
% 1.31/1.18 inference(sigma_clausification,[status(thm)],[f11])).
% 1.31/1.18 thf(f11,plain,(
% 1.31/1.18 ((!! @ (b > $o) @ (^[Y0 : b > $o]: ((Y0 = (^[Y1 : b]: (sK3 @ Y1 @ sK2))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y1 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y2 : b > $o]: ((Y1 @ Y0 @ Y2) = (!! @ (a > $o) @ (^[Y3 : a > $o]: ((?? @ b @ (^[Y4 : b]: ((Y2 @ Y4) & ((sK3 @ Y4) = Y3)))) => (Y3 @ sK2)))))))))))) = $false)),
% 1.31/1.18 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.31/1.18 thf(f10,plain,(
% 1.31/1.18 (((^[Y0 : b > a > $o]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 = (^[Y2 : b]: (Y0 @ Y2 @ sK2))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y2 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y3 : b > $o]: ((Y2 @ Y1 @ Y3) = (!! @ (a > $o) @ (^[Y4 : a > $o]: ((?? @ b @ (^[Y5 : b]: ((Y3 @ Y5) & ((Y0 @ Y5) = Y4)))) => (Y4 @ sK2))))))))))))) @ sK3) = $false)),
% 1.31/1.18 inference(sigma_clausification,[status(thm)],[f9])).
% 1.31/1.18 thf(f9,plain,(
% 1.31/1.18 ((!! @ (b > a > $o) @ (^[Y0 : b > a > $o]: (!! @ (b > $o) @ (^[Y1 : b > $o]: ((Y1 = (^[Y2 : b]: (Y0 @ Y2 @ sK2))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y2 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y3 : b > $o]: ((Y2 @ Y1 @ Y3) = (!! @ (a > $o) @ (^[Y4 : a > $o]: ((?? @ b @ (^[Y5 : b]: ((Y3 @ Y5) & ((Y0 @ Y5) = Y4)))) => (Y4 @ sK2)))))))))))))) = $false)),
% 1.31/1.18 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.31/1.18 thf(f8,plain,(
% 1.31/1.18 (((^[Y0 : a]: (!! @ (b > a > $o) @ (^[Y1 : b > a > $o]: (!! @ (b > $o) @ (^[Y2 : b > $o]: ((Y2 = (^[Y3 : b]: (Y1 @ Y3 @ Y0))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y3 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y4 : b > $o]: ((Y3 @ Y2 @ Y4) = (!! @ (a > $o) @ (^[Y5 : a > $o]: ((?? @ b @ (^[Y6 : b]: ((Y4 @ Y6) & ((Y1 @ Y6) = Y5)))) => (Y5 @ Y0))))))))))))))) @ sK2) = $false)),
% 1.31/1.18 inference(sigma_clausification,[status(thm)],[f7])).
% 1.31/1.18 thf(f7,plain,(
% 1.31/1.18 ((!! @ a @ (^[Y0 : a]: (!! @ (b > a > $o) @ (^[Y1 : b > a > $o]: (!! @ (b > $o) @ (^[Y2 : b > $o]: ((Y2 = (^[Y3 : b]: (Y1 @ Y3 @ Y0))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y3 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y4 : b > $o]: ((Y3 @ Y2 @ Y4) = (!! @ (a > $o) @ (^[Y5 : a > $o]: ((?? @ b @ (^[Y6 : b]: ((Y4 @ Y6) & ((Y1 @ Y6) = Y5)))) => (Y5 @ Y0)))))))))))))))) = $false)),
% 1.31/1.18 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.31/1.18 thf(f6,plain,(
% 1.31/1.18 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ (b > a > $o) @ (^[Y1 : b > a > $o]: (!! @ (b > $o) @ (^[Y2 : b > $o]: ((Y2 = (^[Y3 : b]: (Y1 @ Y3 @ Y0))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y3 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y4 : b > $o]: ((Y3 @ Y2 @ Y4) = (!! @ (a > $o) @ (^[Y5 : a > $o]: ((?? @ b @ (^[Y6 : b]: ((Y4 @ Y6) & ((Y1 @ Y6) = Y5)))) => (Y5 @ Y0))))))))))))))))))),
% 1.31/1.18 inference(cnf_transformation,[status(thm)],[f5])).
% 1.31/1.18 thf(f5,plain,(
% 1.31/1.18 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ (b > a > $o) @ (^[Y1 : b > a > $o]: (!! @ (b > $o) @ (^[Y2 : b > $o]: ((Y2 = (^[Y3 : b]: (Y1 @ Y3 @ Y0))) => (?? @ ((b > $o) > (b > $o) > $o) @ (^[Y3 : (b > $o) > (b > $o) > $o]: (!! @ (b > $o) @ (^[Y4 : b > $o]: ((Y3 @ Y2 @ Y4) = (!! @ (a > $o) @ (^[Y5 : a > $o]: ((?? @ b @ (^[Y6 : b]: ((Y4 @ Y6) & ((Y1 @ Y6) = Y5)))) => (Y5 @ Y0))))))))))))))))))),
% 1.31/1.18 inference(fool_elimination,[status(thm)],[f4])).
% 1.31/1.18 thf(f4,plain,(
% 1.31/1.18 ~! [X0 : b > $o,X1 : b > a > $o,X2 : a] : ((X0 = (^[X3 : b] : (X1 @ X3 @ X2))) => ? [X4 : (b > $o) > (b > $o) > $o] : ! [X5 : b > $o] : ((X4 @ X0 @ X5) <=> ! [X6 : a > $o] : (? [X7 : b] : (((X1 @ X7) = X6) & (X5 @ X7)) => (X6 @ X2))))),
% 1.31/1.18 inference(rectify,[status(thm)],[f2])).
% 1.31/1.18 thf(f2,negated_conjecture,(
% 1.31/1.18 ~! [X2 : b > $o,X0 : b > a > $o,X1 : a] : ((X2 = (^[X3 : b] : (X0 @ X3 @ X1))) => ? [X4 : (b > $o) > (b > $o) > $o] : ! [X5 : b > $o] : ((X4 @ X2 @ X5) <=> ! [X6 : a > $o] : (? [X7 : b] : (((X0 @ X7) = X6) & (X5 @ X7)) => (X6 @ X1))))),
% 1.31/1.18 inference(negated_conjecture,[status(cth)],[f1])).
% 1.31/1.18 thf(f1,conjecture,(
% 1.31/1.18 ! [X2 : b > $o,X0 : b > a > $o,X1 : a] : ((X2 = (^[X3 : b] : (X0 @ X3 @ X1))) => ? [X4 : (b > $o) > (b > $o) > $o] : ! [X5 : b > $o] : ((X4 @ X2 @ X5) <=> ! [X6 : a > $o] : (? [X7 : b] : (((X0 @ X7) = X6) & (X5 @ X7)) => (X6 @ X1))))),
% 1.31/1.18 file('/export/starexec/sandbox2/tmp/tmp.nllwggPfFk/DTF2THF_15451.p',cTHM142_1_pme)).
% 1.31/1.18 % SZS output end Proof for DTF2THF_15451
% 1.31/1.18 % (15560)------------------------------
% 1.31/1.18 % (15560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.18 % (15560)Termination reason: Refutation
% 1.31/1.18
% 1.31/1.18 % (15560)Memory used [KB]: 5884
% 1.31/1.18 % (15560)Time elapsed: 0.012 s
% 1.31/1.18 % (15560)Instructions burned: 21 (million)
% 1.31/1.18 % (15560)------------------------------
% 1.31/1.18 % (15560)------------------------------
% 1.31/1.18 % (15551)Success in time 0.042 s
%------------------------------------------------------------------------------