%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO265^5 : 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 09:53:48 AM UTC 2026
% Result : Theorem 1.53s 1.36s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 168 ( 109 equ; 1 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 133 ( 36 ~; 40 |; 16 &; 28 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 8 usr; 11 con; 0-2 aty)
% ( 0 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 42 ( 31 ^; 8 !; 3 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
x: a ).
thf(func_def_12,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_14,type,
sK3: a ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f39,f43,f46,f52]) ).
thf(f52,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f48,f32]) ).
thf(f32,plain,
( ( x != sK2 )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_2
<=> ( x = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f48,plain,
( ( x = sK2 )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f29,f38]) ).
thf(f38,plain,
( ( sK2 = sK3 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_3
<=> ( sK2 = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f29,plain,
( ( x = sK3 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_1
<=> ( x = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f46,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f44,f33]) ).
thf(f33,plain,
( ( x = sK2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f44,plain,
( ( x != sK2 )
| ~ spl0_4 ),
inference(equality_resolution,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X1: a] :
( ( sK2 != X1 )
| ( x != X1 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl0_4
<=> ! [X1: a] :
( ( sK2 != X1 )
| ( x != X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f43,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f41,f31]) ).
thf(f18,plain,
! [X1: a] :
( ( x != sK2 )
| ( sK2 != X1 )
| ( x != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: a] :
( ( ( x = sK2 )
= $false )
| ( x != X1 )
| ( sK2 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a] :
( ( sK2 != X1 )
| ( ( x = X1 )
= $false )
| ( ( x = sK2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: a] :
( ( ( sK2 = X1 )
= $false )
| ( ( x = X1 )
= $false )
| ( ( x = sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a] :
( ( ( ( sK2 = X1 )
& ( x = X1 ) )
= $false )
| ( ( x = sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: a] :
( ( ( x = sK2 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK2 = Y0 )
& ( x = Y0 ) )
@ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK2 = Y0 )
& ( x = Y0 ) ) )
= $false )
| ( ( x = sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ?? @ a
@ ^ [Y0: a] :
( ( sK2 = Y0 )
& ( x = Y0 ) ) )
!= ( x = sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) )
@ sK2 )
!= ( x = sK2 ) ),
inference(negative_extensionality,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( (=) @ x ) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ a
@ ^ [Y1: a] :
( ( Y0 = Y1 )
& ( x = Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 )
@ x ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
!= ( ^ [X2: a] :
? [X3: a] :
( ( x = X3 )
& ( X2 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
!= ( ^ [X2: a] :
? [X1: a] :
( ( x = X1 )
& ( X1 = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 )
@ x )
= ( ^ [X2: a] :
? [X1: a] :
( ( x = X1 )
& ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6gdwPv4fGW/DTF2THF_21170.p',cX5210) ).
thf(f39,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f31,f36]) ).
thf(f24,plain,
( ( sK2 = sK3 )
| ( x = sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK2 = sK3 )
= $true )
| ( x = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ( sK2 = sK3 )
& ( x = sK3 ) )
= $true )
| ( x = sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( x = sK2 )
| ( $true
= ( ^ [Y0: a] :
( ( sK2 = Y0 )
& ( x = Y0 ) )
@ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK2 = Y0 )
& ( x = Y0 ) ) )
= $true )
| ( x = sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( x = sK2 )
= $true )
| ( ( ?? @ a
@ ^ [Y0: a] :
( ( sK2 = Y0 )
& ( x = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f31,f27]) ).
thf(f25,plain,
( ( x = sK3 )
| ( x = sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( x = sK2 )
| ( ( x = sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO265^5 : 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 14:27:11 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SYO265^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Syntactic
% 0.17/0.40 % Problem : TPS problem X5210
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0178 [Bro09]
% 0.17/0.40 % : X5210 [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.22 v7.2.0, 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 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.17/0.40 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 1 ( 4 avg)
% 0.17/0.40 % Number of connectives : 2 ( 0 ~; 0 |; 1 &; 1 @)
% 0.17/0.40 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 1 ( 1 avg)
% 0.17/0.40 % Number of types : 1 ( 1 usr)
% 0.17/0.40 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 2 ( 1 usr; 1 con; 0-2 aty)
% 0.17/0.40 % Number of variables : 4 ( 3 ^; 0 !; 1 ?; 4 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(a_type,type,
% 0.17/0.40 a: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(x,type,
% 0.17/0.40 x: a ).
% 0.17/0.40
% 0.17/0.40 thf(cX5210,conjecture,
% 0.17/0.40 ( ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 0.17/0.40 @ x )
% 0.17/0.40 = ( ^ [Xz: a] :
% 0.17/0.40 ? [Xy: a] :
% 0.17/0.40 ( ( Xy = x )
% 0.17/0.40 & ( Xz = Xy ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.53/1.33 ---- Embedded in THF ---
% 1.53/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.33 %%% Generated on Tue Feb 24 14:27:12 EST 2026
% 1.53/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.33 %%% Logic specification used:
% 1.53/1.33 %%% thf(spec, logic, $$dhol).
% 1.53/1.33
% 1.53/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6gdwPv4fGW/DTF2DTF21170.p
% See solution above
% 1.53/1.33 ------------------------
% 1.53/1.34 ---- Cleaned THF ---
% 1.53/1.34 thf(a_type,type,
% 1.53/1.34 a: $tType ).
% 1.53/1.34
% 1.53/1.34 thf(x,type,
% 1.53/1.34 x: a ).
% 1.53/1.34
% 1.53/1.34 thf(cX5210,conjecture,
% 1.53/1.34 ( ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
% 1.53/1.34 @ x )
% 1.53/1.34 = ( ^ [Xz: a] :
% 1.53/1.34 ? [Xy: a] :
% 1.53/1.34 ( ( Xy = x )
% 1.53/1.34 & ( Xz = Xy ) ) ) ) ).
% 1.53/1.34 ------------------------
% 1.53/1.36 % (21271)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_21170 for (3000ds/2Mi)
% 1.53/1.36 % (21269)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_21170 for (3000ds/27Mi)
% 1.53/1.36 % (21268)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_21170 for (3000ds/4Mi)
% 1.53/1.36 % (21272)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_21170 for (3000ds/275Mi)
% 1.53/1.36 % (21267)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21170 for (3000ds/183Mi)
% 1.53/1.36 % (21273)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21170 for (3000ds/18Mi)
% 1.53/1.36 % (21270)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21170 for (3000ds/2Mi)
% 1.53/1.36 % (21271)Instruction limit reached!
% 1.53/1.36 % (21271)------------------------------
% 1.53/1.36 % (21271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (21271)Termination reason: Unknown
% 1.53/1.36 % (21271)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (21271)Memory used [KB]: 5373
% 1.53/1.36 % (21271)Time elapsed: 0.003 s
% 1.53/1.36 % (21271)Instructions burned: 2 (million)
% 1.53/1.36 % (21271)------------------------------
% 1.53/1.36 % (21271)------------------------------
% 1.53/1.36 % (21270)Instruction limit reached!
% 1.53/1.36 % (21270)------------------------------
% 1.53/1.36 % (21270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (21270)Termination reason: Unknown
% 1.53/1.36 % (21272)First to succeed.
% 1.53/1.36 % (21270)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (21270)Memory used [KB]: 5500
% 1.53/1.36 % (21270)Time elapsed: 0.004 s
% 1.53/1.36 % (21270)Instructions burned: 3 (million)
% 1.53/1.36 % (21270)------------------------------
% 1.53/1.36 % (21270)------------------------------
% 1.53/1.36 % (21268)Instruction limit reached!
% 1.53/1.36 % (21268)------------------------------
% 1.53/1.36 % (21268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (21268)Termination reason: Unknown
% 1.53/1.36 % (21268)Termination phase: Saturation
% 1.53/1.36
% 1.53/1.36 % (21268)Memory used [KB]: 5500
% 1.53/1.36 % (21268)Time elapsed: 0.005 s
% 1.53/1.36 % (21268)Instructions burned: 4 (million)
% 1.53/1.36 % (21268)------------------------------
% 1.53/1.36 % (21268)------------------------------
% 1.53/1.36 % (21273)Also succeeded, but the first one will report.
% 1.53/1.36 % (21267)Also succeeded, but the first one will report.
% 1.53/1.36 % (21272)Refutation found. Thanks to Tanya!
% 1.53/1.36 % SZS status Theorem for DTF2THF_21170
% 1.53/1.36 % SZS output start Proof for DTF2THF_21170
% 1.53/1.36 thf(type_def_5, type, a: $tType).
% 1.53/1.36 thf(func_def_0, type, a: $tType).
% 1.53/1.36 thf(func_def_1, type, x: a).
% 1.53/1.36 thf(func_def_12, type, ph1: !>[X0: $tType]:(X0)).
% 1.53/1.36 thf(func_def_13, type, sK2: a).
% 1.53/1.36 thf(func_def_14, type, sK3: a).
% 1.53/1.36 thf(f53,plain,(
% 1.53/1.36 $false),
% 1.53/1.36 inference(avatar_sat_refutation,[status(thm)],[f34,f39,f43,f46,f52])).
% 1.53/1.36 thf(f52,plain,(
% 1.53/1.36 ~spl0_1 | spl0_2 | ~spl0_3),
% 1.53/1.36 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.53/1.36 thf(f51,plain,(
% 1.53/1.36 $false | (~spl0_1 | spl0_2 | ~spl0_3)),
% 1.53/1.36 inference(subsumption_resolution,[status(thm)],[f48,f32])).
% 1.53/1.36 thf(f32,plain,(
% 1.53/1.36 (x != sK2) | spl0_2),
% 1.53/1.36 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.53/1.36 thf(f31,definition,(
% 1.53/1.36 spl0_2 <=> (x = sK2)),
% 1.53/1.36 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.53/1.36 thf(f48,plain,(
% 1.53/1.36 (x = sK2) | (~spl0_1 | ~spl0_3)),
% 1.53/1.36 inference(superposition,[status(thm)],[f29,f38])).
% 1.53/1.36 thf(f38,plain,(
% 1.53/1.36 (sK2 = sK3) | ~spl0_3),
% 1.53/1.36 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.53/1.36 thf(f36,definition,(
% 1.53/1.36 spl0_3 <=> (sK2 = sK3)),
% 1.53/1.36 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.53/1.36 thf(f29,plain,(
% 1.53/1.36 (x = sK3) | ~spl0_1),
% 1.53/1.36 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.53/1.36 thf(f27,definition,(
% 1.53/1.36 spl0_1 <=> (x = sK3)),
% 1.53/1.36 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.53/1.36 thf(f46,plain,(
% 1.53/1.36 ~spl0_2 | ~spl0_4),
% 1.53/1.36 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.53/1.36 thf(f45,plain,(
% 1.53/1.36 $false | (~spl0_2 | ~spl0_4)),
% 1.53/1.36 inference(subsumption_resolution,[status(thm)],[f44,f33])).
% 1.53/1.36 thf(f33,plain,(
% 1.53/1.36 (x = sK2) | ~spl0_2),
% 1.53/1.36 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.53/1.36 thf(f44,plain,(
% 1.53/1.36 (x != sK2) | ~spl0_4),
% 1.53/1.36 inference(equality_resolution,[status(thm)],[f42])).
% 1.53/1.36 thf(f42,plain,(
% 1.53/1.36 ( ! [X1 : a] : ((sK2 != X1) | (x != X1)) ) | ~spl0_4),
% 1.53/1.36 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.53/1.36 thf(f41,definition,(
% 1.53/1.36 spl0_4 <=> ! [X1 : a] : ((sK2 != X1) | (x != X1))),
% 1.53/1.36 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.53/1.36 thf(f43,plain,(
% 1.53/1.36 ~spl0_2 | spl0_4),
% 1.53/1.36 inference(avatar_split_clause,[status(thm)],[f18,f41,f31])).
% 1.53/1.36 thf(f18,plain,(
% 1.53/1.36 ( ! [X1 : a] : ((x != sK2) | (sK2 != X1) | (x != X1)) )),
% 1.53/1.36 inference(equality_proxy_clausification,[status(thm)],[f17])).
% 1.53/1.36 thf(f17,plain,(
% 1.53/1.36 ( ! [X1 : a] : (((x = sK2) = $false) | (x != X1) | (sK2 != X1)) )),
% 1.53/1.36 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.53/1.36 thf(f16,plain,(
% 1.53/1.36 ( ! [X1 : a] : ((sK2 != X1) | ((x = X1) = $false) | ((x = sK2) = $false)) )),
% 1.53/1.36 inference(equality_proxy_clausification,[status(thm)],[f15])).
% 1.53/1.36 thf(f15,plain,(
% 1.53/1.36 ( ! [X1 : a] : (((sK2 = X1) = $false) | ((x = X1) = $false) | ((x = sK2) = $false)) )),
% 1.53/1.36 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.53/1.36 thf(f14,plain,(
% 1.53/1.36 ( ! [X1 : a] : ((((sK2 = X1) & (x = X1)) = $false) | ((x = sK2) = $false)) )),
% 1.53/1.36 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.53/1.36 thf(f13,plain,(
% 1.53/1.36 ( ! [X1 : a] : (((x = sK2) = $false) | (((^[Y0 : a]: ((sK2 = Y0) & (x = Y0))) @ X1) = $false)) )),
% 1.53/1.36 inference(pi_clausification,[status(thm)],[f12])).
% 1.53/1.36 thf(f12,plain,(
% 1.53/1.36 ((?? @ a @ (^[Y0 : a]: ((sK2 = Y0) & (x = Y0)))) = $false) | ((x = sK2) = $false)),
% 1.53/1.36 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.53/1.36 thf(f10,plain,(
% 1.53/1.36 ((?? @ a @ (^[Y0 : a]: ((sK2 = Y0) & (x = Y0)))) != (x = sK2))),
% 1.53/1.36 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.53/1.36 thf(f9,plain,(
% 1.53/1.36 (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((Y0 = Y1) & (x = Y1))))) @ sK2) != (x = sK2))),
% 1.53/1.36 inference(negative_extensionality,[status(thm)],[f8])).
% 1.53/1.36 thf(f8,plain,(
% 1.53/1.36 ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((Y0 = Y1) & (x = Y1))))) != (= @ x))),
% 1.53/1.36 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.53/1.36 thf(f7,plain,(
% 1.53/1.36 ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((Y0 = Y1) & (x = Y1))))) != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ x))),
% 1.53/1.36 inference(cnf_transformation,[status(thm)],[f6])).
% 1.53/1.36 thf(f6,plain,(
% 1.53/1.36 ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((Y0 = Y1) & (x = Y1))))) != ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ x))),
% 1.53/1.36 inference(flattening,[status(thm)],[f5])).
% 1.53/1.36 thf(f5,plain,(
% 1.53/1.36 ~((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((Y0 = Y1) & (x = Y1))))) = ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ x))),
% 1.53/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.36 thf(f4,plain,(
% 1.53/1.36 ~(((^[X0 : a, X1 : a] : ((X0 = X1))) @ x) = (^[X2 : a] : (? [X3 : a] : ((x = X3) & (X2 = X3)))))),
% 1.53/1.36 inference(rectify,[status(thm)],[f2])).
% 1.53/1.36 thf(f2,negated_conjecture,(
% 1.53/1.36 ~(((^[X0 : a, X1 : a] : ((X0 = X1))) @ x) = (^[X2 : a] : (? [X1 : a] : ((x = X1) & (X1 = X2)))))),
% 1.53/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.36 thf(f1,conjecture,(
% 1.53/1.36 (((^[X0 : a, X1 : a] : ((X0 = X1))) @ x) = (^[X2 : a] : (? [X1 : a] : ((x = X1) & (X1 = X2)))))),
% 1.53/1.36 file('/export/starexec/sandbox/tmp/tmp.6gdwPv4fGW/DTF2THF_21170.p',cX5210)).
% 1.53/1.36 thf(f39,plain,(
% 1.53/1.36 spl0_3 | spl0_2),
% 1.53/1.36 inference(avatar_split_clause,[status(thm)],[f24,f31,f36])).
% 1.53/1.36 thf(f24,plain,(
% 1.53/1.36 (sK2 = sK3) | (x = sK2)),
% 1.53/1.36 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.53/1.36 thf(f23,plain,(
% 1.53/1.36 ((sK2 = sK3) = $true) | (x = sK2)),
% 1.53/1.36 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.53/1.36 thf(f21,plain,(
% 1.53/1.36 (((sK2 = sK3) & (x = sK3)) = $true) | (x = sK2)),
% 1.53/1.36 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.53/1.36 thf(f20,plain,(
% 1.53/1.36 (x = sK2) | ($true = ((^[Y0 : a]: ((sK2 = Y0) & (x = Y0))) @ sK3))),
% 1.53/1.36 inference(sigma_clausification,[status(thm)],[f19])).
% 1.53/1.36 thf(f19,plain,(
% 1.53/1.36 ((?? @ a @ (^[Y0 : a]: ((sK2 = Y0) & (x = Y0)))) = $true) | (x = sK2)),
% 1.53/1.36 inference(equality_proxy_clausification,[status(thm)],[f11])).
% 1.53/1.36 thf(f11,plain,(
% 1.53/1.36 ((x = sK2) = $true) | ((?? @ a @ (^[Y0 : a]: ((sK2 = Y0) & (x = Y0)))) = $true)),
% 1.53/1.36 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.53/1.36 thf(f34,plain,(
% 1.53/1.36 spl0_1 | spl0_2),
% 1.53/1.36 inference(avatar_split_clause,[status(thm)],[f25,f31,f27])).
% 1.53/1.36 thf(f25,plain,(
% 1.53/1.36 (x = sK3) | (x = sK2)),
% 1.53/1.36 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.53/1.36 thf(f22,plain,(
% 1.53/1.36 (x = sK2) | ((x = sK3) = $true)),
% 1.53/1.36 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.53/1.36 % SZS output end Proof for DTF2THF_21170
% 1.53/1.36 % (21272)------------------------------
% 1.53/1.36 % (21272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.36 % (21272)Termination reason: Refutation
% 1.53/1.36
% 1.53/1.36 % (21272)Memory used [KB]: 5500
% 1.53/1.36 % (21272)Time elapsed: 0.004 s
% 1.53/1.36 % (21272)Instructions burned: 2 (million)
% 1.53/1.36 % (21272)------------------------------
% 1.53/1.36 % (21272)------------------------------
% 1.53/1.36 % (21266)Success in time 0.017 s
%------------------------------------------------------------------------------