%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO361^5 : 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 : n022.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 09:54:02 AM UTC 2026
% Result : Theorem 1.26s 1.11s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 235 ( 82 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 245 ( 53 ~; 48 |; 12 &; 116 @)
% ( 8 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 67 ( 12 ^; 36 !; 19 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK2: $i > $i > $o ).
thf(func_def_6,type,
sK3: ( $i > $i > $o ) > $i ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f28,f32,f53,f61]) ).
thf(f61,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| spl4_1
| ~ spl4_2
| ~ spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f59,f31]) ).
thf(f31,plain,
( ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl4_4
<=> ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f59,plain,
( ( $true
!= ( sK2 @ sK0 @ sK0 ) )
| spl4_1
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f19,f22]) ).
thf(f22,plain,
( ( sK0 = sK1 )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl4_2
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f19,plain,
( ( ( sK2 @ sK0 @ sK1 )
!= $true )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl4_1
<=> ( ( sK2 @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f53,plain,
( spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| spl4_2
| ~ spl4_3 ),
inference(subsumption_resolution,[status(thm)],[f41,f23]) ).
thf(f23,plain,
( ( sK0 != sK1 )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f41,plain,
( ( sK0 = sK1 )
| ~ spl4_3 ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK1 = sK0 )
= $true )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( sK1 = sK0 )
= $true )
| ( $true != $true )
| ~ spl4_3 ),
inference(boolean_simplification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sK1 = sK0 )
= $true )
| ( $true
!= ( ( sK3
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ~ spl4_3 ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ sK0
@ sK1 )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ~ spl4_3 ),
inference(primitive_instantiation,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X4: $i > $i > $o] :
( ( ( X4 @ ( sK3 @ X4 ) @ ( sK3 @ X4 ) )
!= $true )
| ( $true
= ( X4 @ sK0 @ sK1 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl4_3
<=> ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ sK0 @ sK1 ) )
| ( ( X4 @ ( sK3 @ X4 ) @ ( sK3 @ X4 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f32,plain,
( spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f30]) ).
thf(f14,plain,
! [X3: $i] :
( ( ( sK2 @ X3 @ X3 )
= $true )
| ( sK0 != sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( sK0 != sK1 )
| ( ( ( sK2 @ sK0 @ sK1 )
!= $true )
& ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true ) ) )
& ( ( sK0 = sK1 )
| ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ sK0 @ sK1 ) )
| ( ( X4 @ ( sK3 @ X4 ) @ ( sK3 @ X4 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ( ( X0 != X1 )
| ? [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
!= $true )
& ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true ) ) )
& ( ( X0 = X1 )
| ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ X0 @ X1 ) )
| ? [X5: $i] :
( ( X4 @ X5 @ X5 )
!= $true ) ) ) )
=> ( ( ( sK0 != sK1 )
| ? [X2: $i > $i > $o] :
( ( ( X2 @ sK0 @ sK1 )
!= $true )
& ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true ) ) )
& ( ( sK0 = sK1 )
| ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ sK0 @ sK1 ) )
| ? [X5: $i] :
( ( X4 @ X5 @ X5 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i > $i > $o] :
( ( ( X2 @ sK0 @ sK1 )
!= $true )
& ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true ) )
=> ( ( ( sK2 @ sK0 @ sK1 )
!= $true )
& ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X4: $i > $i > $o] :
( ? [X5: $i] :
( ( X4 @ X5 @ X5 )
!= $true )
=> ( ( X4 @ ( sK3 @ X4 ) @ ( sK3 @ X4 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ( ( X0 != X1 )
| ? [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
!= $true )
& ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true ) ) )
& ( ( X0 = X1 )
| ! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ X0 @ X1 ) )
| ? [X5: $i] :
( ( X4 @ X5 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $i,X1: $i] :
( ( ( X0 != X1 )
| ? [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
!= $true )
& ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true ) ) )
& ( ( X0 = X1 )
| ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true ) )
<~> ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
<=> ! [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
=> ( ( X2 @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) )
<=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) )
<=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.4PFJDIXbDi/DTF2THF_1112.p',cTHM47) ).
thf(f28,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f21,f26]) ).
thf(f13,plain,
! [X4: $i > $i > $o] :
( ( $true
= ( X4 @ sK0 @ sK1 ) )
| ( ( X4 @ ( sK3 @ X4 ) @ ( sK3 @ X4 ) )
!= $true )
| ( sK0 = sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f24,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f21,f17]) ).
thf(f15,plain,
( ( ( sK2 @ sK0 @ sK1 )
!= $true )
| ( sK0 != sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO361^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n022.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 14:28:36 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SYO361^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Syntactic
% 0.16/0.41 % Problem : TPS problem THM47
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English : Shows equivalence of two definitions of =.
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0406 [Bro09]
% 0.16/0.41 % : THM47 [TPS]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.16/0.41 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.16/0.41 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 1 ( 1 avg)
% 0.16/0.41 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.16/0.41 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 9 ( 9 avg)
% 0.16/0.41 % Number of types : 2 ( 0 usr)
% 0.16/0.41 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.41 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(cTHM47,conjecture,
% 0.16/0.41 ! [X: $i,Y: $i] :
% 0.16/0.41 ( ( X = Y )
% 0.16/0.41 <=> ! [R: $i > $i > $o] :
% 0.16/0.41 ( ! [Z: $i] : ( R @ Z @ Z )
% 0.16/0.41 => ( R @ X @ Y ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.08/1.08 ---- Embedded in THF ---
% 1.08/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.08/1.08 %%% Generated on Tue Feb 24 14:28:36 EST 2026
% 1.08/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.08/1.08 %%% Logic specification used:
% 1.08/1.08 %%% thf(spec, logic, $$dhol).
% 1.08/1.08
% 1.08/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4PFJDIXbDi/DTF2DTF1112.p
% See solution above
% 1.08/1.08 ------------------------
% 1.08/1.09 ---- Cleaned THF ---
% 1.08/1.09 thf(cTHM47,conjecture,
% 1.08/1.09 ! [X: $i,Y: $i] :
% 1.08/1.09 ( ( X = Y )
% 1.08/1.09 <=> ! [R: $i > $i > $o] :
% 1.08/1.09 ( ! [Z: $i] : ( R @ Z @ Z )
% 1.08/1.09 => ( R @ X @ Y ) ) ) ).
% 1.08/1.09 ------------------------
% 1.08/1.11 % (1218)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_1112 for (3000ds/2Mi)
% 1.08/1.11 % (1214)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1112 for (3000ds/183Mi)
% 1.08/1.11 % (1216)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_1112 for (3000ds/27Mi)
% 1.08/1.11 % (1217)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1112 for (3000ds/2Mi)
% 1.08/1.11 % (1215)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_1112 for (3000ds/4Mi)
% 1.08/1.11 % (1220)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1112 for (3000ds/18Mi)
% 1.08/1.11 % (1219)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_1112 for (3000ds/275Mi)
% 1.08/1.11 % (1217)Instruction limit reached!
% 1.08/1.11 % (1217)------------------------------
% 1.08/1.11 % (1217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.08/1.11 % (1217)Termination reason: Unknown
% 1.08/1.11 % (1217)Termination phase: Saturation
% 1.08/1.11
% 1.08/1.11 % (1217)Memory used [KB]: 5500
% 1.08/1.11 % (1217)Time elapsed: 0.003 s
% 1.08/1.11 % (1217)Instructions burned: 2 (million)
% 1.08/1.11 % (1217)------------------------------
% 1.08/1.11 % (1217)------------------------------
% 1.08/1.11 % (1218)Instruction limit reached!
% 1.08/1.11 % (1218)------------------------------
% 1.08/1.11 % (1218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.08/1.11 % (1218)Termination reason: Unknown
% 1.08/1.11 % (1218)Termination phase: Saturation
% 1.08/1.11
% 1.08/1.11 % (1218)Memory used [KB]: 5500
% 1.08/1.11 % (1218)Time elapsed: 0.003 s
% 1.08/1.11 % (1218)Instructions burned: 2 (million)
% 1.08/1.11 % (1218)------------------------------
% 1.08/1.11 % (1218)------------------------------
% 1.08/1.11 % (1216)Refutation not found, incomplete strategy
% 1.08/1.11 % (1216)------------------------------
% 1.08/1.11 % (1216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.08/1.11 % (1219)First to succeed.
% 1.08/1.11 % (1216)Termination reason: Refutation not found, incomplete strategy
% 1.08/1.11
% 1.08/1.11
% 1.08/1.11 % (1216)Memory used [KB]: 5500
% 1.08/1.11 % (1216)Time elapsed: 0.003 s
% 1.08/1.11 % (1216)Instructions burned: 2 (million)
% 1.08/1.11 % (1216)------------------------------
% 1.08/1.11 % (1216)------------------------------
% 1.26/1.11 % (1215)Instruction limit reached!
% 1.26/1.11 % (1215)------------------------------
% 1.26/1.11 % (1215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.11 % (1215)Termination reason: Unknown
% 1.26/1.11 % (1215)Termination phase: Saturation
% 1.26/1.11
% 1.26/1.11 % (1215)Memory used [KB]: 5500
% 1.26/1.11 % (1215)Time elapsed: 0.005 s
% 1.26/1.11 % (1215)Instructions burned: 5 (million)
% 1.26/1.11 % (1215)------------------------------
% 1.26/1.11 % (1215)------------------------------
% 1.26/1.11 % (1220)Also succeeded, but the first one will report.
% 1.26/1.11 % (1219)Refutation found. Thanks to Tanya!
% 1.26/1.11 % SZS status Theorem for DTF2THF_1112
% 1.26/1.11 % SZS output start Proof for DTF2THF_1112
% 1.26/1.11 thf(func_def_5, type, sK2: $i > $i > $o).
% 1.26/1.11 thf(func_def_6, type, sK3: ($i > $i > $o) > $i).
% 1.26/1.11 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.26/1.11 thf(f62,plain,(
% 1.26/1.11 $false),
% 1.26/1.11 inference(avatar_sat_refutation,[status(thm)],[f24,f28,f32,f53,f61])).
% 1.26/1.11 thf(f61,plain,(
% 1.26/1.11 spl4_1 | ~spl4_2 | ~spl4_4),
% 1.26/1.11 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.26/1.11 thf(f60,plain,(
% 1.26/1.11 $false | (spl4_1 | ~spl4_2 | ~spl4_4)),
% 1.26/1.11 inference(subsumption_resolution,[status(thm)],[f59,f31])).
% 1.26/1.11 thf(f31,plain,(
% 1.26/1.11 ( ! [X3 : $i] : (((sK2 @ X3 @ X3) = $true)) ) | ~spl4_4),
% 1.26/1.11 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.26/1.11 thf(f30,definition,(
% 1.26/1.11 spl4_4 <=> ! [X3 : $i] : ((sK2 @ X3 @ X3) = $true)),
% 1.26/1.11 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.26/1.11 thf(f59,plain,(
% 1.26/1.11 ($true != (sK2 @ sK0 @ sK0)) | (spl4_1 | ~spl4_2)),
% 1.26/1.11 inference(superposition,[status(thm)],[f19,f22])).
% 1.26/1.11 thf(f22,plain,(
% 1.26/1.11 (sK0 = sK1) | ~spl4_2),
% 1.26/1.11 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.26/1.11 thf(f21,definition,(
% 1.26/1.11 spl4_2 <=> (sK0 = sK1)),
% 1.26/1.11 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.26/1.11 thf(f19,plain,(
% 1.26/1.11 ((sK2 @ sK0 @ sK1) != $true) | spl4_1),
% 1.26/1.11 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.26/1.11 thf(f17,definition,(
% 1.26/1.11 spl4_1 <=> ((sK2 @ sK0 @ sK1) = $true)),
% 1.26/1.11 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.26/1.11 thf(f53,plain,(
% 1.26/1.11 spl4_2 | ~spl4_3),
% 1.26/1.11 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.26/1.11 thf(f52,plain,(
% 1.26/1.11 $false | (spl4_2 | ~spl4_3)),
% 1.26/1.11 inference(subsumption_resolution,[status(thm)],[f41,f23])).
% 1.26/1.11 thf(f23,plain,(
% 1.26/1.11 (sK0 != sK1) | spl4_2),
% 1.26/1.11 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.26/1.11 thf(f41,plain,(
% 1.26/1.11 (sK0 = sK1) | ~spl4_3),
% 1.26/1.11 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.26/1.11 thf(f40,plain,(
% 1.26/1.11 ((sK1 = sK0) = $true) | ~spl4_3),
% 1.26/1.11 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.26/1.11 thf(f39,plain,(
% 1.26/1.11 ((sK1 = sK0) = $true) | ($true != $true) | ~spl4_3),
% 1.26/1.11 inference(boolean_simplification,[status(thm)],[f38])).
% 1.26/1.11 thf(f38,plain,(
% 1.26/1.11 ((sK1 = sK0) = $true) | ($true != ((sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | ~spl4_3),
% 1.26/1.11 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.26/1.11 thf(f33,plain,(
% 1.26/1.11 (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ sK0 @ sK1) = $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) != $true) | ~spl4_3),
% 1.26/1.11 inference(primitive_instantiation,[status(thm)],[f27])).
% 1.26/1.11 thf(f27,plain,(
% 1.26/1.11 ( ! [X4 : $i > $i > $o] : (((X4 @ (sK3 @ X4) @ (sK3 @ X4)) != $true) | ($true = (X4 @ sK0 @ sK1))) ) | ~spl4_3),
% 1.26/1.11 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.26/1.11 thf(f26,definition,(
% 1.26/1.11 spl4_3 <=> ! [X4 : $i > $i > $o] : (($true = (X4 @ sK0 @ sK1)) | ((X4 @ (sK3 @ X4) @ (sK3 @ X4)) != $true))),
% 1.26/1.11 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.26/1.11 thf(f32,plain,(
% 1.26/1.11 spl4_4 | ~spl4_2),
% 1.26/1.11 inference(avatar_split_clause,[status(thm)],[f14,f21,f30])).
% 1.26/1.11 thf(f14,plain,(
% 1.26/1.11 ( ! [X3 : $i] : (((sK2 @ X3 @ X3) = $true) | (sK0 != sK1)) )),
% 1.26/1.11 inference(cnf_transformation,[status(thm)],[f12])).
% 1.26/1.11 thf(f12,plain,(
% 1.26/1.11 ((sK0 != sK1) | (((sK2 @ sK0 @ sK1) != $true) & ! [X3 : $i] : ((sK2 @ X3 @ X3) = $true))) & ((sK0 = sK1) | ! [X4 : $i > $i > $o] : (($true = (X4 @ sK0 @ sK1)) | ((X4 @ (sK3 @ X4) @ (sK3 @ X4)) != $true)))),
% 1.26/1.11 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f11,f10,f9])).
% 1.26/1.11 thf(f9,plain,(
% 1.26/1.11 ? [X0 : $i,X1 : $i] : (((X0 != X1) | ? [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) != $true) & ! [X3 : $i] : ((X2 @ X3 @ X3) = $true))) & ((X0 = X1) | ! [X4 : $i > $i > $o] : (($true = (X4 @ X0 @ X1)) | ? [X5 : $i] : ((X4 @ X5 @ X5) != $true)))) => (((sK0 != sK1) | ? [X2 : $i > $i > $o] : (((X2 @ sK0 @ sK1) != $true) & ! [X3 : $i] : ((X2 @ X3 @ X3) = $true))) & ((sK0 = sK1) | ! [X4 : $i > $i > $o] : (($true = (X4 @ sK0 @ sK1)) | ? [X5 : $i] : ((X4 @ X5 @ X5) != $true))))),
% 1.26/1.11 introduced(definition,[],[choice_axiom])).
% 1.26/1.11 thf(f10,plain,(
% 1.26/1.11 ? [X2 : $i > $i > $o] : (((X2 @ sK0 @ sK1) != $true) & ! [X3 : $i] : ((X2 @ X3 @ X3) = $true)) => (((sK2 @ sK0 @ sK1) != $true) & ! [X3 : $i] : ((sK2 @ X3 @ X3) = $true))),
% 1.26/1.11 introduced(definition,[],[choice_axiom])).
% 1.26/1.11 thf(f11,plain,(
% 1.26/1.11 ! [X4 : $i > $i > $o] : (? [X5 : $i] : ((X4 @ X5 @ X5) != $true) => ((X4 @ (sK3 @ X4) @ (sK3 @ X4)) != $true))),
% 1.26/1.11 introduced(definition,[],[choice_axiom])).
% 1.26/1.11 thf(f8,plain,(
% 1.26/1.11 ? [X0 : $i,X1 : $i] : (((X0 != X1) | ? [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) != $true) & ! [X3 : $i] : ((X2 @ X3 @ X3) = $true))) & ((X0 = X1) | ! [X4 : $i > $i > $o] : (($true = (X4 @ X0 @ X1)) | ? [X5 : $i] : ((X4 @ X5 @ X5) != $true))))),
% 1.26/1.11 inference(rectify,[status(thm)],[f7])).
% 1.26/1.11 thf(f7,plain,(
% 1.26/1.11 ? [X0 : $i,X1 : $i] : (((X0 != X1) | ? [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) != $true) & ! [X3 : $i] : ((X2 @ X3 @ X3) = $true))) & ((X0 = X1) | ! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | ? [X3 : $i] : ((X2 @ X3 @ X3) != $true))))),
% 1.26/1.11 inference(nnf_transformation,[status(thm)],[f6])).
% 1.26/1.11 thf(f6,plain,(
% 1.26/1.11 ? [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | ? [X3 : $i] : ((X2 @ X3 @ X3) != $true)) <~> (X0 = X1))),
% 1.26/1.11 inference(ennf_transformation,[status(thm)],[f5])).
% 1.26/1.11 thf(f5,plain,(
% 1.26/1.11 ~! [X0 : $i,X1 : $i] : ((X0 = X1) <=> ! [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) => ((X2 @ X0 @ X1) = $true)))),
% 1.26/1.11 inference(fool_elimination,[status(thm)],[f4])).
% 1.26/1.11 thf(f4,plain,(
% 1.26/1.11 ~! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) <=> (X0 = X1))),
% 1.26/1.11 inference(rectify,[status(thm)],[f2])).
% 1.26/1.11 thf(f2,negated_conjecture,(
% 1.26/1.11 ~! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) <=> (X0 = X1))),
% 1.26/1.11 inference(negated_conjecture,[status(cth)],[f1])).
% 1.26/1.11 thf(f1,conjecture,(
% 1.26/1.11 ! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) <=> (X0 = X1))),
% 1.26/1.11 file('/export/starexec/sandbox/tmp/tmp.4PFJDIXbDi/DTF2THF_1112.p',cTHM47)).
% 1.26/1.11 thf(f28,plain,(
% 1.26/1.11 spl4_3 | spl4_2),
% 1.26/1.11 inference(avatar_split_clause,[status(thm)],[f13,f21,f26])).
% 1.26/1.11 thf(f13,plain,(
% 1.26/1.11 ( ! [X4 : $i > $i > $o] : (($true = (X4 @ sK0 @ sK1)) | ((X4 @ (sK3 @ X4) @ (sK3 @ X4)) != $true) | (sK0 = sK1)) )),
% 1.26/1.11 inference(cnf_transformation,[status(thm)],[f12])).
% 1.26/1.11 thf(f24,plain,(
% 1.26/1.11 ~spl4_1 | ~spl4_2),
% 1.26/1.11 inference(avatar_split_clause,[status(thm)],[f15,f21,f17])).
% 1.26/1.11 thf(f15,plain,(
% 1.26/1.11 ((sK2 @ sK0 @ sK1) != $true) | (sK0 != sK1)),
% 1.26/1.11 inference(cnf_transformation,[status(thm)],[f12])).
% 1.26/1.11 % SZS output end Proof for DTF2THF_1112
% 1.26/1.11 % (1219)------------------------------
% 1.26/1.11 % (1219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.11 % (1219)Termination reason: Refutation
% 1.26/1.11
% 1.26/1.11 % (1219)Memory used [KB]: 5500
% 1.26/1.11 % (1219)Time elapsed: 0.004 s
% 1.26/1.11 % (1219)Instructions burned: 2 (million)
% 1.26/1.11 % (1219)------------------------------
% 1.26/1.11 % (1219)------------------------------
% 1.26/1.11 % (1213)Success in time 0.017 s
%------------------------------------------------------------------------------