%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO271^5 : 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 09:53:49 AM UTC 2026
% Result : Theorem 1.64s 1.34s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 123 ( 92 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 298 ( 67 ~; 16 |; 8 &; 192 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 39 ^; 26 !; 10 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cJ: ( b > $o ) > b ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_11,type,
sK0: b > a ).
thf(func_def_12,type,
sK1: b > a ).
thf(func_def_14,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK4: b ).
thf(f41,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f37,f40]) ).
thf(f40,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sK0 @ sK4 )
!= ( sK0 @ sK4 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f13,f22]) ).
thf(f22,plain,
( ! [X1: b] :
( ( sK0 @ X1 )
= ( sK1 @ X1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl2_1
<=> ! [X1: b] :
( ( sK0 @ X1 )
= ( sK1 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f13,plain,
( ( sK0 @ sK4 )
!= ( sK1 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f11]) ).
thf(f11,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) )
& ( sK0 != sK1 )
& ! [X2: b > $o] :
( ! [X3: b] :
( ( X2 @ X3 )
!= $true )
| ( ( X2 @ ( cJ @ X2 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: b > a,X1: b > a] :
( ( ( X0
@ ( cJ
@ ^ [Y0: b] :
( ( X1 @ Y0 )
!= ( X0 @ Y0 ) ) ) )
= ( X1
@ ( cJ
@ ^ [Y0: b] :
( ( X1 @ Y0 )
!= ( X0 @ Y0 ) ) ) ) )
& ( X0 != X1 ) )
=> ( ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) )
& ( sK0 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ? [X0: b > a,X1: b > a] :
( ( ( X0
@ ( cJ
@ ^ [Y0: b] :
( ( X1 @ Y0 )
!= ( X0 @ Y0 ) ) ) )
= ( X1
@ ( cJ
@ ^ [Y0: b] :
( ( X1 @ Y0 )
!= ( X0 @ Y0 ) ) ) ) )
& ( X0 != X1 ) )
& ! [X2: b > $o] :
( ! [X3: b] :
( ( X2 @ X3 )
!= $true )
| ( ( X2 @ ( cJ @ X2 ) )
= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X2: b > a,X3: b > a] :
( ( ( X2
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) )
= ( X3
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) ) )
& ( X2 != X3 ) )
& ! [X0: b > $o] :
( ! [X1: b] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( cJ @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: b > $o] :
( ? [X1: b] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( cJ @ X0 ) )
= $true ) )
=> ! [X2: b > a,X3: b > a] :
( ( ( X2
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) )
= ( X3
@ ( cJ
@ ^ [Y0: b] :
( ( X3 @ Y0 )
!= ( X2 @ Y0 ) ) ) ) )
=> ( X2 = X3 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: b > $o] :
( ? [X1: b] : ( X0 @ X1 )
=> ( X0 @ ( cJ @ X0 ) ) )
=> ! [X2: b > a,X3: b > a] :
( ( ( X3
@ ( cJ
@ ^ [X4: b] :
( ( X3 @ X4 )
!= ( X2 @ X4 ) ) ) )
= ( X2
@ ( cJ
@ ^ [X5: b] :
( ( X3 @ X5 )
!= ( X2 @ X5 ) ) ) ) )
=> ( X2 = X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b > $o] :
( ? [X1: b] : ( X0 @ X1 )
=> ( X0 @ ( cJ @ X0 ) ) )
=> ! [X2: b > a,X3: b > a] :
( ( ( X3
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) )
= ( X2
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) ) )
=> ( X2 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: b > $o] :
( ? [X1: b] : ( X0 @ X1 )
=> ( X0 @ ( cJ @ X0 ) ) )
=> ! [X2: b > a,X3: b > a] :
( ( ( X3
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) )
= ( X2
@ ( cJ
@ ^ [X1: b] :
( ( X2 @ X1 )
!= ( X3 @ X1 ) ) ) ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0gVmaUapdO/DTF2THF_22487.p',cX5500) ).
thf(f37,plain,
( ~ spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f34,f21,f24]) ).
thf(f24,definition,
( spl2_2
<=> ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f34,plain,
! [X1: b] :
( ( ( sK0 @ X1 )
= ( sK1 @ X1 ) )
| ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
!= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: b] :
( ( ( ( sK1 @ X1 )
= ( sK0 @ X1 ) )
= $true )
| ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
!= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: b] :
( ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
!= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK1 @ X1 )
!= ( sK0 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: b] :
( ( $false
= ( ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
= ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( sK1 @ X1 )
!= ( sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: b] :
( ( $true
= ( ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
!= ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( sK1 @ X1 )
!= ( sK0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: b] :
( ( ( ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) )
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) )
@ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f35]) ).
thf(f35,plain,
( $false
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
!= ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) )
| spl2_2 ),
inference(superposition,[status(thm)],[f26,f12]) ).
thf(f12,plain,
( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f26,plain,
( ( ( sK0
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) )
!= ( sK1
@ ( cJ
@ ^ [Y0: b] :
( ( sK1 @ Y0 )
!= ( sK0 @ Y0 ) ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO271^5 : 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
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:27:27 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
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO271^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : TPS problem X5500
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0321 [Bro09]
% 0.18/0.45 % : X5500 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.45 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 2 ( 4 avg)
% 0.18/0.45 % Number of connectives : 16 ( 2 ~; 0 |; 0 &; 11 @)
% 0.18/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.18/0.45 % Number of types : 3 ( 2 usr)
% 0.18/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.18/0.45 % Number of variables : 6 ( 2 ^; 3 !; 1 ?; 6 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(b_type,type,
% 0.18/0.45 b: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(cJ,type,
% 0.18/0.45 cJ: ( b > $o ) > b ).
% 0.18/0.45
% 0.18/0.45 thf(cX5500,conjecture,
% 0.18/0.45 ( ! [P: b > $o] :
% 0.18/0.45 ( ? [Xx: b] : ( P @ Xx )
% 0.18/0.45 => ( P @ ( cJ @ P ) ) )
% 0.18/0.45 => ! [Xf: b > a,Xg: b > a] :
% 0.18/0.45 ( ( ( Xf
% 0.18/0.45 @ ( cJ
% 0.18/0.45 @ ^ [Xx: b] :
% 0.18/0.45 ( ( Xf @ Xx )
% 0.18/0.45 != ( Xg @ Xx ) ) ) )
% 0.18/0.45 = ( Xg
% 0.18/0.45 @ ( cJ
% 0.18/0.45 @ ^ [Xx: b] :
% 0.18/0.45 ( ( Xf @ Xx )
% 0.18/0.45 != ( Xg @ Xx ) ) ) ) )
% 0.18/0.45 => ( Xf = Xg ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.64/1.31 ---- Embedded in THF ---
% 1.64/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.31 %%% Generated on Tue Feb 24 14:27:27 EST 2026
% 1.64/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.31 %%% Logic specification used:
% 1.64/1.31 %%% thf(spec, logic, $$dhol).
% 1.64/1.31
% 1.64/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0gVmaUapdO/DTF2DTF22487.p
% See solution above
% 1.64/1.31 ------------------------
% 1.64/1.32 ---- Cleaned THF ---
% 1.64/1.32 thf(b_type,type,
% 1.64/1.32 b: $tType ).
% 1.64/1.32
% 1.64/1.32 thf(a_type,type,
% 1.64/1.32 a: $tType ).
% 1.64/1.32
% 1.64/1.32 thf(cJ,type,
% 1.64/1.32 cJ: ( b > $o ) > b ).
% 1.64/1.32
% 1.64/1.32 thf(cX5500,conjecture,
% 1.64/1.32 ( ! [P: b > $o] :
% 1.64/1.32 ( ? [Xx: b] : ( P @ Xx )
% 1.64/1.32 => ( P @ ( cJ @ P ) ) )
% 1.64/1.32 => ! [Xf: b > a,Xg: b > a] :
% 1.64/1.32 ( ( ( Xf
% 1.64/1.32 @ ( cJ
% 1.64/1.32 @ ^ [Xx: b] :
% 1.64/1.32 ( ( Xf @ Xx )
% 1.64/1.32 != ( Xg @ Xx ) ) ) )
% 1.64/1.32 = ( Xg
% 1.64/1.32 @ ( cJ
% 1.64/1.32 @ ^ [Xx: b] :
% 1.64/1.32 ( ( Xf @ Xx )
% 1.64/1.32 != ( Xg @ Xx ) ) ) ) )
% 1.64/1.32 => ( Xf = Xg ) ) ) ).
% 1.64/1.32 ------------------------
% 1.64/1.33 % (22681)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22487 for (3000ds/18Mi)
% 1.64/1.33 % (22679)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_22487 for (3000ds/2Mi)
% 1.64/1.33 % (22677)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_22487 for (3000ds/27Mi)
% 1.64/1.34 % (22679)Instruction limit reached!
% 1.64/1.34 % (22679)------------------------------
% 1.64/1.34 % (22679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (22679)Termination reason: Unknown
% 1.64/1.34 % (22679)Termination phase: Saturation
% 1.64/1.34
% 1.64/1.34 % (22679)Memory used [KB]: 5500
% 1.64/1.34 % (22679)Time elapsed: 0.003 s
% 1.64/1.34 % (22679)Instructions burned: 4 (million)
% 1.64/1.34 % (22679)------------------------------
% 1.64/1.34 % (22679)------------------------------
% 1.64/1.34 % (22677)First to succeed.
% 1.64/1.34 % (22677)Refutation found. Thanks to Tanya!
% 1.64/1.34 % SZS status Theorem for DTF2THF_22487
% 1.64/1.34 % SZS output start Proof for DTF2THF_22487
% 1.64/1.34 thf(type_def_5, type, b: $tType).
% 1.64/1.34 thf(type_def_7, type, a: $tType).
% 1.64/1.34 thf(func_def_0, type, b: $tType).
% 1.64/1.34 thf(func_def_1, type, a: $tType).
% 1.64/1.34 thf(func_def_2, type, cJ: (b > $o) > b).
% 1.64/1.34 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.34 thf(func_def_11, type, sK0: b > a).
% 1.64/1.34 thf(func_def_12, type, sK1: b > a).
% 1.64/1.34 thf(func_def_14, type, ph3: !>[X0: $tType]:(X0)).
% 1.64/1.34 thf(func_def_15, type, sK4: b).
% 1.64/1.34 thf(f41,plain,(
% 1.64/1.34 $false),
% 1.64/1.34 inference(avatar_sat_refutation,[status(thm)],[f36,f37,f40])).
% 1.64/1.34 thf(f40,plain,(
% 1.64/1.34 ~spl2_1),
% 1.64/1.34 inference(avatar_contradiction_clause,[status(thm)],[f39])).
% 1.64/1.34 thf(f39,plain,(
% 1.64/1.34 $false | ~spl2_1),
% 1.64/1.34 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.64/1.34 thf(f38,plain,(
% 1.64/1.34 ((sK0 @ sK4) != (sK0 @ sK4)) | ~spl2_1),
% 1.64/1.34 inference(superposition,[status(thm)],[f13,f22])).
% 1.64/1.34 thf(f22,plain,(
% 1.64/1.34 ( ! [X1 : b] : (((sK0 @ X1) = (sK1 @ X1))) ) | ~spl2_1),
% 1.64/1.34 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.64/1.34 thf(f21,definition,(
% 1.64/1.34 spl2_1 <=> ! [X1 : b] : ((sK0 @ X1) = (sK1 @ X1))),
% 1.64/1.34 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.64/1.34 thf(f13,plain,(
% 1.64/1.34 ((sK0 @ sK4) != (sK1 @ sK4))),
% 1.64/1.34 inference(negative_extensionality,[status(thm)],[f11])).
% 1.64/1.34 thf(f11,plain,(
% 1.64/1.34 (sK0 != sK1)),
% 1.64/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.34 thf(f9,plain,(
% 1.64/1.34 (((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0))))))) & (sK0 != sK1)) & ! [X2 : b > $o] : (! [X3 : b] : ((X2 @ X3) != $true) | ((X2 @ (cJ @ X2)) = $true))),
% 1.64/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.64/1.34 thf(f8,plain,(
% 1.64/1.34 ? [X0 : b > a,X1 : b > a] : (((X0 @ (cJ @ (^[Y0 : b]: (~ ((X1 @ Y0) = (X0 @ Y0)))))) = (X1 @ (cJ @ (^[Y0 : b]: (~ ((X1 @ Y0) = (X0 @ Y0))))))) & (X0 != X1)) => (((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0))))))) & (sK0 != sK1))),
% 1.64/1.34 introduced(definition,[],[choice_axiom])).
% 1.64/1.34 thf(f7,plain,(
% 1.64/1.34 ? [X0 : b > a,X1 : b > a] : (((X0 @ (cJ @ (^[Y0 : b]: (~ ((X1 @ Y0) = (X0 @ Y0)))))) = (X1 @ (cJ @ (^[Y0 : b]: (~ ((X1 @ Y0) = (X0 @ Y0))))))) & (X0 != X1)) & ! [X2 : b > $o] : (! [X3 : b] : ((X2 @ X3) != $true) | ((X2 @ (cJ @ X2)) = $true))),
% 1.64/1.34 inference(rectify,[status(thm)],[f6])).
% 1.64/1.34 thf(f6,plain,(
% 1.64/1.34 ? [X2 : b > a,X3 : b > a] : (((X2 @ (cJ @ (^[Y0 : b]: (~ ((X3 @ Y0) = (X2 @ Y0)))))) = (X3 @ (cJ @ (^[Y0 : b]: (~ ((X3 @ Y0) = (X2 @ Y0))))))) & (X2 != X3)) & ! [X0 : b > $o] : (! [X1 : b] : ((X0 @ X1) != $true) | ((X0 @ (cJ @ X0)) = $true))),
% 1.64/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.34 thf(f5,plain,(
% 1.64/1.34 ~(! [X0 : b > $o] : (? [X1 : b] : ((X0 @ X1) = $true) => ((X0 @ (cJ @ X0)) = $true)) => ! [X2 : b > a,X3 : b > a] : (((X2 @ (cJ @ (^[Y0 : b]: (~ ((X3 @ Y0) = (X2 @ Y0)))))) = (X3 @ (cJ @ (^[Y0 : b]: (~ ((X3 @ Y0) = (X2 @ Y0))))))) => (X2 = X3)))),
% 1.64/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.34 thf(f4,plain,(
% 1.64/1.34 ~(! [X0 : b > $o] : (? [X1 : b] : (X0 @ X1) => (X0 @ (cJ @ X0))) => ! [X2 : b > a,X3 : b > a] : (((X3 @ (cJ @ (^[X4 : b] : (((X3 @ X4) != (X2 @ X4)))))) = (X2 @ (cJ @ (^[X5 : b] : (((X3 @ X5) != (X2 @ X5))))))) => (X2 = X3)))),
% 1.64/1.34 inference(rectify,[status(thm)],[f2])).
% 1.64/1.34 thf(f2,negated_conjecture,(
% 1.64/1.34 ~(! [X0 : b > $o] : (? [X1 : b] : (X0 @ X1) => (X0 @ (cJ @ X0))) => ! [X2 : b > a,X3 : b > a] : (((X3 @ (cJ @ (^[X1 : b] : (((X2 @ X1) != (X3 @ X1)))))) = (X2 @ (cJ @ (^[X1 : b] : (((X2 @ X1) != (X3 @ X1))))))) => (X2 = X3)))),
% 1.64/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.34 thf(f1,conjecture,(
% 1.64/1.34 ! [X0 : b > $o] : (? [X1 : b] : (X0 @ X1) => (X0 @ (cJ @ X0))) => ! [X2 : b > a,X3 : b > a] : (((X3 @ (cJ @ (^[X1 : b] : (((X2 @ X1) != (X3 @ X1)))))) = (X2 @ (cJ @ (^[X1 : b] : (((X2 @ X1) != (X3 @ X1))))))) => (X2 = X3))),
% 1.64/1.34 file('/export/starexec/sandbox/tmp/tmp.0gVmaUapdO/DTF2THF_22487.p',cX5500)).
% 1.64/1.34 thf(f37,plain,(
% 1.64/1.34 ~spl2_2 | spl2_1),
% 1.64/1.34 inference(avatar_split_clause,[status(thm)],[f34,f21,f24])).
% 1.64/1.34 thf(f24,definition,(
% 1.64/1.34 spl2_2 <=> ((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))))),
% 1.64/1.34 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.64/1.34 thf(f34,plain,(
% 1.64/1.34 ( ! [X1 : b] : (((sK0 @ X1) = (sK1 @ X1)) | ((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) != (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))))) )),
% 1.64/1.34 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.64/1.34 thf(f33,plain,(
% 1.64/1.34 ( ! [X1 : b] : ((((sK1 @ X1) = (sK0 @ X1)) = $true) | ((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) != (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))))) )),
% 1.64/1.34 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.64/1.34 thf(f32,plain,(
% 1.64/1.34 ( ! [X1 : b] : (((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) != (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0))))))) | ($false = (~ ((sK1 @ X1) = (sK0 @ X1))))) )),
% 1.64/1.34 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.64/1.34 thf(f31,plain,(
% 1.64/1.34 ( ! [X1 : b] : (($false = ((sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = (sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))))) | ($false = (~ ((sK1 @ X1) = (sK0 @ X1))))) )),
% 1.64/1.34 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.64/1.34 thf(f30,plain,(
% 1.64/1.34 ( ! [X1 : b] : (($true = (~ ((sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = (sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0))))))))) | ($false = (~ ((sK1 @ X1) = (sK0 @ X1))))) )),
% 1.64/1.34 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.64/1.34 thf(f28,plain,(
% 1.64/1.34 ( ! [X1 : b] : ((((^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))) @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = $true) | ($false = ((^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))) @ X1))) )),
% 1.64/1.34 introduced(definition,[],[choice_axiom])).
% 1.64/1.34 thf(f36,plain,(
% 1.64/1.34 spl2_2),
% 1.64/1.34 inference(avatar_contradiction_clause,[status(thm)],[f35])).
% 1.64/1.34 thf(f35,plain,(
% 1.64/1.34 $false | spl2_2),
% 1.64/1.34 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.64/1.34 thf(f29,plain,(
% 1.64/1.34 ((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) != (sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0))))))) | spl2_2),
% 1.64/1.34 inference(superposition,[status(thm)],[f26,f12])).
% 1.64/1.34 thf(f12,plain,(
% 1.64/1.34 ((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) = (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))))),
% 1.64/1.34 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.34 thf(f26,plain,(
% 1.64/1.34 ((sK0 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0)))))) != (sK1 @ (cJ @ (^[Y0 : b]: (~ ((sK1 @ Y0) = (sK0 @ Y0))))))) | spl2_2),
% 1.64/1.34 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.64/1.34 % SZS output end Proof for DTF2THF_22487
% 1.64/1.34 % (22677)------------------------------
% 1.64/1.34 % (22677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (22677)Termination reason: Refutation
% 1.64/1.34
% 1.64/1.34 % (22677)Memory used [KB]: 5500
% 1.64/1.34 % (22677)Time elapsed: 0.003 s
% 1.64/1.34 % (22677)Instructions burned: 2 (million)
% 1.64/1.34 % (22677)------------------------------
% 1.64/1.34 % (22677)------------------------------
% 1.64/1.34 % (22674)Success in time 0.002 s
%------------------------------------------------------------------------------