%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU864^5 : 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 : n028.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 09:37:37 AM UTC 2026
% Result : Theorem 1.55s 1.38s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 149 ( 75 equ; 2 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 143 ( 25 ~; 28 |; 14 &; 63 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 37 ^; 25 !; 3 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
t: a ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: ( a > $o ) > $o ).
thf(func_def_12,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
$true != $true,
inference(superposition,[status(thm)],[f14,f19]) ).
thf(f19,plain,
( $true
= ( sK0 @ ( (=) @ t ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) ),
inference(boolean_simplification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( sK0
@ ^ [Y0: a] :
( ( t = Y0 )
| $false ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( sK0
@ ^ [Y0: a] :
( ( t = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( sK0
@ ^ [Y0: a] :
( ( t = Y0 )
| ( ^ [Y1: a] : $false
@ Y0 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f11]) ).
thf(f11,plain,
( $true
= ( sK0
@ ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( $true
!= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ( $true
= ( sK0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( t != X2 )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
!= ( sK0 @ X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: ( a > $o ) > $o] :
( ( $true
!= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( t != X2 )
| ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
!= ( X0 @ X1 ) ) ) )
=> ( ( $true
!= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ( $true
= ( sK0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( t != X2 )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
!= ( sK0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: ( a > $o ) > $o] :
( ( $true
!= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( t != X2 )
| ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
!= ( X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > $o ) > $o] :
( ( $true
!= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( t != X2 )
| ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) )
| ( $true
!= ( X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( $true
= ( X0
@ ^ [Y0: a] : $false ) )
& ! [X1: a > $o] :
( ( $true
= ( X0 @ X1 ) )
=> ! [X2: a] :
( ( t = X2 )
=> ( $true
= ( X0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) ) ) ) )
=> ( $true
= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( X0
@ ^ [X3: a] :
( ( X1 @ X3 )
| ( X2 = X3 ) ) ) ) )
& ( X0
@ ^ [X4: a] : $false ) )
=> ( X0
@ ^ [X5: a] : ( t = X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X0
@ ^ [X4: a] :
( ( X2 @ X4 )
| ( X3 = X4 ) ) ) ) )
& ( X0
@ ^ [X1: a] : $false ) )
=> ( X0
@ ^ [X1: a] : ( t = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X0
@ ^ [X4: a] :
( ( X2 @ X4 )
| ( X3 = X4 ) ) ) ) )
& ( X0
@ ^ [X1: a] : $false ) )
=> ( X0
@ ^ [X1: a] : ( t = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FiyDZaDE4P/DTF2THF_6578.p',cDOMLEMMA1_pme) ).
thf(f13,plain,
! [X1: a > $o] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( t = Y0 )
| ( X1 @ Y0 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f10]) ).
thf(f10,plain,
! [X2: a,X1: a > $o] :
( ( t != X2 )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X2 = Y0 )
| ( X1 @ Y0 ) ) ) )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f14,plain,
( $true
!= ( sK0 @ ( (=) @ t ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
!= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU864^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n028.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:36:26 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.40 ---- Original DTF file ---
% 0.19/0.40 thf(spec,logic,$$dhol).
% 0.19/0.40 %------------------------------------------------------------------------------
% 0.19/0.40 % File : SEU864^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.40 % Domain : Set Theory (Finite sets)
% 0.19/0.40 % Problem : TPS problem from FINITE-SET-THMS
% 0.19/0.40 % Version : Especial.
% 0.19/0.40 % English :
% 0.19/0.40
% 0.19/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.40 % Source : [Bro09]
% 0.19/0.40 % Names : tps_0863 [Bro09]
% 0.19/0.40
% 0.19/0.40 % Status : Theorem
% 0.19/0.40 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 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, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.19/0.40 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.40 % Number of atoms : 4 ( 3 equ; 0 cnn)
% 0.19/0.40 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.40 % Number of connectives : 10 ( 0 ~; 1 |; 1 &; 5 @)
% 0.19/0.40 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.40 % Maximal formula depth : 12 ( 12 avg)
% 0.19/0.40 % Number of types : 2 ( 1 usr)
% 0.19/0.40 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.40 % Number of symbols : 3 ( 1 usr; 2 con; 0-2 aty)
% 0.19/0.40 % Number of variables : 6 ( 3 ^; 3 !; 0 ?; 6 :)
% 0.19/0.40 % SPC : TH0_THM_EQU_NAR
% 0.19/0.40
% 0.19/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.40 %------------------------------------------------------------------------------
% 0.19/0.40 thf(a_type,type,
% 0.19/0.40 a: $tType ).
% 0.19/0.40
% 0.19/0.40 thf(t,type,
% 0.19/0.40 t: a ).
% 0.19/0.40
% 0.19/0.40 thf(cDOMLEMMA1_pme,conjecture,
% 0.19/0.40 ! [X: ( a > $o ) > $o] :
% 0.19/0.40 ( ( ( X
% 0.19/0.40 @ ^ [Xy: a] : $false )
% 0.19/0.40 & ! [Xx: a > $o] :
% 0.19/0.40 ( ( X @ Xx )
% 0.19/0.40 => ! [Xt_0: a] :
% 0.19/0.40 ( ( t = Xt_0 )
% 0.19/0.40 => ( X
% 0.19/0.40 @ ^ [Xz: a] :
% 0.19/0.40 ( ( Xx @ Xz )
% 0.19/0.40 | ( Xt_0 = Xz ) ) ) ) ) )
% 0.19/0.40 => ( X
% 0.19/0.40 @ ^ [Xy: a] : ( t = Xy ) ) ) ).
% 0.19/0.40
% 0.19/0.40 %------------------------------------------------------------------------------
% 0.19/0.40 ------------------------
% 1.55/1.34 ---- Embedded in THF ---
% 1.55/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.34 %%% Generated on Tue Feb 24 12:36:27 EST 2026
% 1.55/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.34 %%% Logic specification used:
% 1.55/1.34 %%% thf(spec, logic, $$dhol).
% 1.55/1.34
% 1.55/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FiyDZaDE4P/DTF2DTF6578.p
% See solution above
% 1.55/1.34 ------------------------
% 1.55/1.35 ---- Cleaned THF ---
% 1.55/1.36 thf(a_type,type,
% 1.55/1.36 a: $tType ).
% 1.55/1.36
% 1.55/1.36 thf(t,type,
% 1.55/1.36 t: a ).
% 1.55/1.36
% 1.55/1.36 thf(cDOMLEMMA1_pme,conjecture,
% 1.55/1.36 ! [X: ( a > $o ) > $o] :
% 1.55/1.36 ( ( ( X
% 1.55/1.36 @ ^ [Xy: a] : $false )
% 1.55/1.36 & ! [Xx: a > $o] :
% 1.55/1.36 ( ( X @ Xx )
% 1.55/1.36 => ! [Xt_0: a] :
% 1.55/1.36 ( ( t = Xt_0 )
% 1.55/1.36 => ( X
% 1.55/1.36 @ ^ [Xz: a] :
% 1.55/1.36 ( ( Xx @ Xz )
% 1.55/1.36 | ( Xt_0 = Xz ) ) ) ) ) )
% 1.55/1.36 => ( X
% 1.55/1.36 @ ^ [Xy: a] : ( t = Xy ) ) ) ).
% 1.55/1.36 ------------------------
% 1.55/1.37 % (6676)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_6578 for (3000ds/4Mi)
% 1.55/1.37 % (6678)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6578 for (3000ds/2Mi)
% 1.55/1.37 % (6680)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_6578 for (3000ds/275Mi)
% 1.55/1.37 % (6679)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_6578 for (3000ds/2Mi)
% 1.55/1.37 % (6681)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6578 for (3000ds/18Mi)
% 1.55/1.37 % (6677)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_6578 for (3000ds/27Mi)
% 1.55/1.37 % (6675)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6578 for (3000ds/183Mi)
% 1.55/1.38 % (6679)Instruction limit reached!
% 1.55/1.38 % (6679)------------------------------
% 1.55/1.38 % (6679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.38 % (6679)Termination reason: Unknown
% 1.55/1.38 % (6679)Termination phase: Saturation
% 1.55/1.38
% 1.55/1.38 % (6679)Memory used [KB]: 895
% 1.55/1.38 % (6679)Time elapsed: 0.003 s
% 1.55/1.38 % (6679)Instructions burned: 2 (million)
% 1.55/1.38 % (6679)------------------------------
% 1.55/1.38 % (6679)------------------------------
% 1.55/1.38 % (6680)Refutation not found, incomplete strategy
% 1.55/1.38 % (6680)------------------------------
% 1.55/1.38 % (6680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.38 % (6678)Instruction limit reached!
% 1.55/1.38 % (6678)------------------------------
% 1.55/1.38 % (6678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.38 % (6678)Termination reason: Unknown
% 1.55/1.38 % (6678)Termination phase: Saturation
% 1.55/1.38
% 1.55/1.38 % (6678)Memory used [KB]: 5500
% 1.55/1.38 % (6678)Time elapsed: 0.004 s
% 1.55/1.38 % (6678)Instructions burned: 2 (million)
% 1.55/1.38 % (6678)------------------------------
% 1.55/1.38 % (6678)------------------------------
% 1.55/1.38 % (6680)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.38
% 1.55/1.38
% 1.55/1.38 % (6680)Memory used [KB]: 5500
% 1.55/1.38 % (6680)Time elapsed: 0.003 s
% 1.55/1.38 % (6680)Instructions burned: 2 (million)
% 1.55/1.38 % (6680)------------------------------
% 1.55/1.38 % (6680)------------------------------
% 1.55/1.38 % (6677)First to succeed.
% 1.55/1.38 % (6681)Also succeeded, but the first one will report.
% 1.55/1.38 % (6677)Refutation found. Thanks to Tanya!
% 1.55/1.38 % SZS status Theorem for DTF2THF_6578
% 1.55/1.38 % SZS output start Proof for DTF2THF_6578
% 1.55/1.38 thf(type_def_5, type, a: $tType).
% 1.55/1.38 thf(func_def_0, type, a: $tType).
% 1.55/1.38 thf(func_def_1, type, t: a).
% 1.55/1.38 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.55/1.38 thf(func_def_10, type, sK0: (a > $o) > $o).
% 1.55/1.38 thf(func_def_12, type, ph2: !>[X0: $tType]:(X0)).
% 1.55/1.38 thf(f25,plain,(
% 1.55/1.38 $false),
% 1.55/1.38 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.55/1.38 thf(f20,plain,(
% 1.55/1.38 ($true != $true)),
% 1.55/1.38 inference(superposition,[status(thm)],[f14,f19])).
% 1.55/1.38 thf(f19,plain,(
% 1.55/1.38 ($true = (sK0 @ (= @ t)))),
% 1.55/1.38 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.55/1.38 thf(f18,plain,(
% 1.55/1.38 ($true = (sK0 @ (^[Y0 : a]: (t = Y0))))),
% 1.55/1.38 inference(boolean_simplification,[status(thm)],[f17])).
% 1.55/1.38 thf(f17,plain,(
% 1.55/1.38 ($true = (sK0 @ (^[Y0 : a]: ((t = Y0) | $false))))),
% 1.55/1.38 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.55/1.38 thf(f16,plain,(
% 1.55/1.38 ($true = (sK0 @ (^[Y0 : a]: ((t = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))),
% 1.55/1.38 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.55/1.38 thf(f15,plain,(
% 1.55/1.38 ($true = (sK0 @ (^[Y0 : a]: ((t = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))) | ($true != $true)),
% 1.55/1.38 inference(superposition,[status(thm)],[f13,f11])).
% 1.55/1.38 thf(f11,plain,(
% 1.55/1.38 ($true = (sK0 @ (^[Y0 : a]: ($false))))),
% 1.55/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.38 thf(f9,plain,(
% 1.55/1.38 ($true != (sK0 @ (^[Y0 : a]: (t = Y0)))) & ($true = (sK0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o] : (! [X2 : a] : ((t != X2) | ($true = (sK0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) | ($true != (sK0 @ X1)))),
% 1.55/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.55/1.38 thf(f8,plain,(
% 1.55/1.38 ? [X0 : (a > $o) > $o] : (($true != (X0 @ (^[Y0 : a]: (t = Y0)))) & ($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o] : (! [X2 : a] : ((t != X2) | ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) | ($true != (X0 @ X1)))) => (($true != (sK0 @ (^[Y0 : a]: (t = Y0)))) & ($true = (sK0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o] : (! [X2 : a] : ((t != X2) | ($true = (sK0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) | ($true != (sK0 @ X1))))),
% 1.55/1.38 introduced(definition,[],[choice_axiom])).
% 1.55/1.38 thf(f7,plain,(
% 1.55/1.38 ? [X0 : (a > $o) > $o] : (($true != (X0 @ (^[Y0 : a]: (t = Y0)))) & ($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o] : (! [X2 : a] : ((t != X2) | ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) | ($true != (X0 @ X1))))),
% 1.55/1.38 inference(flattening,[status(thm)],[f6])).
% 1.55/1.38 thf(f6,plain,(
% 1.55/1.38 ? [X0 : (a > $o) > $o] : (($true != (X0 @ (^[Y0 : a]: (t = Y0)))) & (($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o] : (! [X2 : a] : ((t != X2) | ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))) | ($true != (X0 @ X1)))))),
% 1.55/1.38 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.38 thf(f5,plain,(
% 1.55/1.38 ~! [X0 : (a > $o) > $o] : ((($true = (X0 @ (^[Y0 : a]: ($false)))) & ! [X1 : a > $o] : (($true = (X0 @ X1)) => ! [X2 : a] : ((t = X2) => ($true = (X0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0)))))))) => ($true = (X0 @ (^[Y0 : a]: (t = Y0)))))),
% 1.55/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.38 thf(f4,plain,(
% 1.55/1.38 ~! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : ((X0 @ X1) => ! [X2 : a] : ((t = X2) => (X0 @ (^[X3 : a] : ((X1 @ X3) | (X2 = X3)))))) & (X0 @ (^[X4 : a] : ($false)))) => (X0 @ (^[X5 : a] : ((t = X5)))))),
% 1.55/1.38 inference(rectify,[status(thm)],[f2])).
% 1.55/1.38 thf(f2,negated_conjecture,(
% 1.55/1.38 ~! [X0 : (a > $o) > $o] : ((! [X2 : a > $o] : ((X0 @ X2) => ! [X3 : a] : ((t = X3) => (X0 @ (^[X4 : a] : ((X2 @ X4) | (X3 = X4)))))) & (X0 @ (^[X1 : a] : ($false)))) => (X0 @ (^[X1 : a] : ((t = X1)))))),
% 1.55/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.38 thf(f1,conjecture,(
% 1.55/1.38 ! [X0 : (a > $o) > $o] : ((! [X2 : a > $o] : ((X0 @ X2) => ! [X3 : a] : ((t = X3) => (X0 @ (^[X4 : a] : ((X2 @ X4) | (X3 = X4)))))) & (X0 @ (^[X1 : a] : ($false)))) => (X0 @ (^[X1 : a] : ((t = X1)))))),
% 1.55/1.38 file('/export/starexec/sandbox/tmp/tmp.FiyDZaDE4P/DTF2THF_6578.p',cDOMLEMMA1_pme)).
% 1.55/1.38 thf(f13,plain,(
% 1.55/1.38 ( ! [X1 : a > $o] : (($true != (sK0 @ X1)) | ($true = (sK0 @ (^[Y0 : a]: ((t = Y0) | (X1 @ Y0)))))) )),
% 1.55/1.38 inference(equality_resolution,[status(thm)],[f10])).
% 1.55/1.38 thf(f10,plain,(
% 1.55/1.38 ( ! [X2 : a,X1 : a > $o] : ((t != X2) | ($true = (sK0 @ (^[Y0 : a]: ((X2 = Y0) | (X1 @ Y0))))) | ($true != (sK0 @ X1))) )),
% 1.55/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.38 thf(f14,plain,(
% 1.55/1.38 ($true != (sK0 @ (= @ t)))),
% 1.55/1.38 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.55/1.38 thf(f12,plain,(
% 1.55/1.38 ($true != (sK0 @ (^[Y0 : a]: (t = Y0))))),
% 1.55/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.38 % SZS output end Proof for DTF2THF_6578
% 1.55/1.38 % (6677)------------------------------
% 1.55/1.38 % (6677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.38 % (6677)Termination reason: Refutation
% 1.55/1.38
% 1.55/1.38 % (6677)Memory used [KB]: 5500
% 1.55/1.38 % (6677)Time elapsed: 0.004 s
% 1.55/1.38 % (6677)Instructions burned: 2 (million)
% 1.55/1.38 % (6677)------------------------------
% 1.55/1.38 % (6677)------------------------------
% 1.55/1.38 % (6674)Success in time 0.017 s
%------------------------------------------------------------------------------