%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO222^5 : 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 : n021.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 09:53:42 AM UTC 2026
% Result : Theorem 1.68s 1.34s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 3 unt; 0 typ; 3 def)
% Number of atoms : 190 ( 77 equ; 2 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 247 ( 56 ~; 43 |; 22 &; 110 @)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 71 ( 2 ^; 57 !; 12 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_6,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_9,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f165,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f23,f28,f39,f164]) ).
thf(f164,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f163]) ).
thf(f163,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(equality_resolution,[status(thm)],[f160]) ).
thf(f160,plain,
( ! [X0: $i] :
( ( f @ a )
!= X0 )
| ~ spl1_1
| ~ spl1_3 ),
inference(equality_resolution,[status(thm)],[f122]) ).
thf(f122,plain,
( ! [X0: $i,X1: $i] :
( ( ( f @ a )
!= X0 )
| ( X0 != X1 ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( f @ a )
!= X0 )
| ( $true != $true ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f87,f27]) ).
thf(f27,plain,
( ( ( cP @ a )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl1_3
<=> ( ( cP @ a )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f87,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( ( f @ X1 )
!= X0 )
| ( X0 != X2 ) )
| ~ spl1_1 ),
inference(equality_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( X0 = X2 ) )
| ( ( f @ X1 )
!= X0 )
| ( ( cP @ X1 )
!= $true ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f14,f54]) ).
thf(f54,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ ( (=) @ X0 ) )
= X1 )
| ( ( f @ X1 )
!= X0 ) )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f19,f44]) ).
thf(f44,plain,
! [X0: $i] :
( ( f @ ( sK0 @ ( (=) @ X0 ) ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) )
| ( $true
!= ( X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ( ( ( cP @ a )
= $true )
& ! [X1: $i] :
( $true
!= ( X0 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
!= ( f @ X3 ) )
| ( X2 = X3 ) ) )
| ( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X4: $i] :
( ( $true
!= ( cP @ X4 ) )
& ( $true
= ( X0 @ ( f @ X4 ) ) ) )
=> ( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ( ( ( cP @ a )
= $true )
& ! [X1: $i] :
( $true
!= ( X0 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
!= ( f @ X3 ) )
| ( X2 = X3 ) ) )
| ? [X4: $i] :
( ( $true
!= ( cP @ X4 ) )
& ( $true
= ( X0 @ ( f @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ( ( ( cP @ a )
= $true )
& ! [X4: $i] :
( $true
!= ( X0 @ X4 ) )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
!= ( f @ X3 ) )
| ( X2 = X3 ) ) )
| ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ ( f @ X1 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ( ! [X4: $i] :
( $true
!= ( X0 @ X4 ) )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
!= ( f @ X3 ) )
| ( X2 = X3 ) )
& ( ( cP @ a )
= $true ) )
| ? [X1: $i] :
( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ ( f @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
( ( ( ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
= ( f @ X3 ) )
=> ( X2 = X3 ) )
& ( ( cP @ a )
= $true ) )
=> ? [X4: $i] :
( $true
= ( X0 @ X4 ) ) )
& ! [X1: $i] :
( ( ( X0 @ ( f @ X1 ) )
= $true )
=> ( ( cP @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ ( f @ X1 ) )
=> ( cP @ X1 ) )
& ( ( ( cP @ a )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
= ( f @ X3 ) )
=> ( X2 = X3 ) ) )
=> ? [X4: $i] : ( X0 @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ ( f @ X1 ) )
=> ( cP @ X1 ) )
& ( ( ( cP @ a )
& ! [X2: $i,X1: $i] :
( ( ( f @ X1 )
= ( f @ X2 ) )
=> ( X1 = X2 ) ) )
=> ? [X3: $i] : ( X0 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ ( f @ X1 ) )
=> ( cP @ X1 ) )
& ( ( ( cP @ a )
& ! [X2: $i,X1: $i] :
( ( ( f @ X1 )
= ( f @ X2 ) )
=> ( X1 = X2 ) ) )
=> ? [X3: $i] : ( X0 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UzONONChnO/DTF2THF_3582.p',cTHM115A) ).
thf(f19,plain,
( ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
!= ( f @ X3 ) )
| ( X2 = X3 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl1_1
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( f @ X2 )
!= ( f @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f14,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
!= ( X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f39,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true
= ( ^ [Y0: $i] : $false
@ ( f
@ ( sK0
@ ^ [Y0: $i] : $false ) ) ) )
| ~ spl1_2 ),
inference(primitive_instantiation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl1_2
<=> ! [X0: $i > $o] :
( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f28,plain,
( spl1_2
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f15,f25,f21]) ).
thf(f15,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) )
| ( ( cP @ a )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f23,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f11,f21,f18]) ).
thf(f11,plain,
! [X2: $i,X3: $i,X0: $i > $o] :
( ( X2 = X3 )
| ( ( f @ X2 )
!= ( f @ X3 ) )
| ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO222^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:26:24 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO222^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem THM115A
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : Sunil's example.
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0352 [Bro09]
% 0.28/0.46 % : THM115 [TPS]
% 0.28/0.46 % : THM115A [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.28/0.46 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.28/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 2 &; 7 @)
% 0.28/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(f,type,
% 0.28/0.46 f: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(a,type,
% 0.28/0.46 a: $i ).
% 0.28/0.46
% 0.28/0.46 thf(cP,type,
% 0.28/0.46 cP: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM115A,conjecture,
% 0.28/0.46 ? [A: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( A @ ( f @ Xx ) )
% 0.28/0.46 => ( cP @ Xx ) )
% 0.28/0.46 & ( ( ( cP @ a )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( ( f @ Xx )
% 0.28/0.46 = ( f @ Xy ) )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 => ? [Xz: $i] : ( A @ Xz ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.68/1.30 ---- Embedded in THF ---
% 1.68/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.31 %%% Generated on Tue Feb 24 14:26:24 EST 2026
% 1.68/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.31 %%% Logic specification used:
% 1.68/1.31 %%% thf(spec, logic, $$dhol).
% 1.68/1.31
% 1.68/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.UzONONChnO/DTF2DTF3582.p
% See solution above
% 1.68/1.31 ------------------------
% 1.68/1.31 ---- Cleaned THF ---
% 1.68/1.32 thf(f,type,
% 1.68/1.32 f: $i > $i ).
% 1.68/1.32
% 1.68/1.32 thf(a,type,
% 1.68/1.32 a: $i ).
% 1.68/1.32
% 1.68/1.32 thf(cP,type,
% 1.68/1.32 cP: $i > $o ).
% 1.68/1.32
% 1.68/1.32 thf(cTHM115A,conjecture,
% 1.68/1.32 ? [A: $i > $o] :
% 1.68/1.32 ( ! [Xx: $i] :
% 1.68/1.32 ( ( A @ ( f @ Xx ) )
% 1.68/1.32 => ( cP @ Xx ) )
% 1.68/1.32 & ( ( ( cP @ a )
% 1.68/1.32 & ! [Xx: $i,Xy: $i] :
% 1.68/1.32 ( ( ( f @ Xx )
% 1.68/1.32 = ( f @ Xy ) )
% 1.68/1.32 => ( Xx = Xy ) ) )
% 1.68/1.32 => ? [Xz: $i] : ( A @ Xz ) ) ) ).
% 1.68/1.32 ------------------------
% 1.68/1.33 % (3779)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_3582 for (2999ds/2Mi)
% 1.68/1.33 % (3779)Instruction limit reached!
% 1.68/1.33 % (3779)------------------------------
% 1.68/1.33 % (3779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (3779)Termination reason: Unknown
% 1.68/1.33 % (3779)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (3779)Memory used [KB]: 5500
% 1.68/1.33 % (3779)Time elapsed: 0.003 s
% 1.68/1.33 % (3779)Instructions burned: 2 (million)
% 1.68/1.33 % (3779)------------------------------
% 1.68/1.33 % (3779)------------------------------
% 1.68/1.33 % (3777)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_3582 for (2999ds/27Mi)
% 1.68/1.33 % (3780)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_3582 for (2999ds/275Mi)
% 1.68/1.33 % (3777)Refutation not found, incomplete strategy
% 1.68/1.33 % (3777)------------------------------
% 1.68/1.33 % (3777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (3777)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.33
% 1.68/1.33
% 1.68/1.33 % (3777)Memory used [KB]: 5500
% 1.68/1.33 % (3777)Time elapsed: 0.004 s
% 1.68/1.33 % (3777)Instructions burned: 2 (million)
% 1.68/1.33 % (3777)------------------------------
% 1.68/1.33 % (3777)------------------------------
% 1.68/1.34 % (3775)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3582 for (2999ds/183Mi)
% 1.68/1.34 % (3780)First to succeed.
% 1.68/1.34 % (3780)Refutation found. Thanks to Tanya!
% 1.68/1.34 % SZS status Theorem for DTF2THF_3582
% 1.68/1.34 % SZS output start Proof for DTF2THF_3582
% 1.68/1.34 thf(func_def_0, type, f: $i > $i).
% 1.68/1.34 thf(func_def_2, type, cP: $i > $o).
% 1.68/1.34 thf(func_def_6, type, sK0: ($i > $o) > $i).
% 1.68/1.34 thf(func_def_9, type, ph2: !>[X0: $tType]:(X0)).
% 1.68/1.34 thf(f165,plain,(
% 1.68/1.34 $false),
% 1.68/1.34 inference(avatar_sat_refutation,[status(thm)],[f23,f28,f39,f164])).
% 1.68/1.34 thf(f164,plain,(
% 1.68/1.34 ~spl1_1 | ~spl1_3),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f163])).
% 1.68/1.34 thf(f163,plain,(
% 1.68/1.34 $false | (~spl1_1 | ~spl1_3)),
% 1.68/1.34 inference(equality_resolution,[status(thm)],[f160])).
% 1.68/1.34 thf(f160,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (((f @ a) != X0)) ) | (~spl1_1 | ~spl1_3)),
% 1.68/1.34 inference(equality_resolution,[status(thm)],[f122])).
% 1.68/1.34 thf(f122,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (((f @ a) != X0) | (X0 != X1)) ) | (~spl1_1 | ~spl1_3)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.68/1.34 thf(f117,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((f @ a) != X0) | ($true != $true)) ) | (~spl1_1 | ~spl1_3)),
% 1.68/1.34 inference(superposition,[status(thm)],[f87,f27])).
% 1.68/1.34 thf(f27,plain,(
% 1.68/1.34 ((cP @ a) = $true) | ~spl1_3),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.68/1.34 thf(f25,definition,(
% 1.68/1.34 spl1_3 <=> ((cP @ a) = $true)),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.68/1.34 thf(f87,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP @ X1) != $true) | ((f @ X1) != X0) | (X0 != X2)) ) | ~spl1_1),
% 1.68/1.34 inference(equality_proxy_clausification,[status(thm)],[f82])).
% 1.68/1.34 thf(f82,plain,(
% 1.68/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (X0 = X2)) | ((f @ X1) != X0) | ((cP @ X1) != $true)) ) | ~spl1_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f14,f54])).
% 1.68/1.34 thf(f54,plain,(
% 1.68/1.34 ( ! [X0 : $i,X1 : $i] : (((sK0 @ (= @ X0)) = X1) | ((f @ X1) != X0)) ) | ~spl1_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f19,f44])).
% 1.68/1.34 thf(f44,plain,(
% 1.68/1.34 ( ! [X0 : $i] : (((f @ (sK0 @ (= @ X0))) = X0)) )),
% 1.68/1.34 inference(leibniz_equality_elimination,[status(thm)],[f13])).
% 1.68/1.34 thf(f13,plain,(
% 1.68/1.34 ( ! [X0 : $i > $o,X1 : $i] : (($true = (X0 @ (f @ (sK0 @ X0)))) | ($true != (X0 @ X1))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.68/1.34 thf(f10,plain,(
% 1.68/1.34 ! [X0 : $i > $o] : ((((cP @ a) = $true) & ! [X1 : $i] : ($true != (X0 @ X1)) & ! [X2 : $i,X3 : $i] : (((f @ X2) != (f @ X3)) | (X2 = X3))) | (($true != (cP @ (sK0 @ X0))) & ($true = (X0 @ (f @ (sK0 @ X0))))))),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.68/1.34 thf(f9,plain,(
% 1.68/1.34 ! [X0 : $i > $o] : (? [X4 : $i] : (($true != (cP @ X4)) & ($true = (X0 @ (f @ X4)))) => (($true != (cP @ (sK0 @ X0))) & ($true = (X0 @ (f @ (sK0 @ X0))))))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f8,plain,(
% 1.68/1.34 ! [X0 : $i > $o] : ((((cP @ a) = $true) & ! [X1 : $i] : ($true != (X0 @ X1)) & ! [X2 : $i,X3 : $i] : (((f @ X2) != (f @ X3)) | (X2 = X3))) | ? [X4 : $i] : (($true != (cP @ X4)) & ($true = (X0 @ (f @ X4)))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f7])).
% 1.68/1.34 thf(f7,plain,(
% 1.68/1.34 ! [X0 : $i > $o] : ((((cP @ a) = $true) & ! [X4 : $i] : ($true != (X0 @ X4)) & ! [X2 : $i,X3 : $i] : (((f @ X2) != (f @ X3)) | (X2 = X3))) | ? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ (f @ X1)) = $true)))),
% 1.68/1.34 inference(flattening,[status(thm)],[f6])).
% 1.68/1.34 thf(f6,plain,(
% 1.68/1.34 ! [X0 : $i > $o] : ((! [X4 : $i] : ($true != (X0 @ X4)) & (! [X2 : $i,X3 : $i] : (((f @ X2) != (f @ X3)) | (X2 = X3)) & ((cP @ a) = $true))) | ? [X1 : $i] : (((cP @ X1) != $true) & ((X0 @ (f @ X1)) = $true)))),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.34 thf(f5,plain,(
% 1.68/1.34 ~? [X0 : $i > $o] : (((! [X2 : $i,X3 : $i] : (((f @ X2) = (f @ X3)) => (X2 = X3)) & ((cP @ a) = $true)) => ? [X4 : $i] : ($true = (X0 @ X4))) & ! [X1 : $i] : (((X0 @ (f @ X1)) = $true) => ((cP @ X1) = $true)))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.34 thf(f4,plain,(
% 1.68/1.34 ~? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)) & (((cP @ a) & ! [X2 : $i,X3 : $i] : (((f @ X2) = (f @ X3)) => (X2 = X3))) => ? [X4 : $i] : (X0 @ X4)))),
% 1.68/1.34 inference(rectify,[status(thm)],[f2])).
% 1.68/1.34 thf(f2,negated_conjecture,(
% 1.68/1.34 ~? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)) & (((cP @ a) & ! [X2 : $i,X1 : $i] : (((f @ X1) = (f @ X2)) => (X1 = X2))) => ? [X3 : $i] : (X0 @ X3)))),
% 1.68/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.34 thf(f1,conjecture,(
% 1.68/1.34 ? [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)) & (((cP @ a) & ! [X2 : $i,X1 : $i] : (((f @ X1) = (f @ X2)) => (X1 = X2))) => ? [X3 : $i] : (X0 @ X3)))),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.UzONONChnO/DTF2THF_3582.p',cTHM115A)).
% 1.68/1.34 thf(f19,plain,(
% 1.68/1.34 ( ! [X2 : $i,X3 : $i] : (((f @ X2) != (f @ X3)) | (X2 = X3)) ) | ~spl1_1),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.68/1.34 thf(f18,definition,(
% 1.68/1.34 spl1_1 <=> ! [X2 : $i,X3 : $i] : ((X2 = X3) | ((f @ X2) != (f @ X3)))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.68/1.34 thf(f14,plain,(
% 1.68/1.34 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cP @ (sK0 @ X0))) | ($true != (X0 @ X1))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.68/1.34 thf(f39,plain,(
% 1.68/1.34 ~spl1_2),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.68/1.34 thf(f38,plain,(
% 1.68/1.34 $false | ~spl1_2),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.68/1.34 thf(f37,plain,(
% 1.68/1.34 ($false = $true) | ~spl1_2),
% 1.68/1.34 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.68/1.34 thf(f35,plain,(
% 1.68/1.34 ($true = ((^[Y0 : $i]: ($false)) @ (f @ (sK0 @ (^[Y0 : $i]: ($false)))))) | ~spl1_2),
% 1.68/1.34 inference(primitive_instantiation,[status(thm)],[f22])).
% 1.68/1.34 thf(f22,plain,(
% 1.68/1.34 ( ! [X0 : $i > $o] : (($true = (X0 @ (f @ (sK0 @ X0))))) ) | ~spl1_2),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.68/1.34 thf(f21,definition,(
% 1.68/1.34 spl1_2 <=> ! [X0 : $i > $o] : ($true = (X0 @ (f @ (sK0 @ X0))))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.68/1.34 thf(f28,plain,(
% 1.68/1.34 spl1_2 | spl1_3),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f15,f25,f21])).
% 1.68/1.34 thf(f15,plain,(
% 1.68/1.34 ( ! [X0 : $i > $o] : (($true = (X0 @ (f @ (sK0 @ X0)))) | ((cP @ a) = $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.68/1.34 thf(f23,plain,(
% 1.68/1.34 spl1_1 | spl1_2),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f11,f21,f18])).
% 1.68/1.34 thf(f11,plain,(
% 1.68/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i > $o] : ((X2 = X3) | ((f @ X2) != (f @ X3)) | ($true = (X0 @ (f @ (sK0 @ X0))))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.68/1.34 % SZS output end Proof for DTF2THF_3582
% 1.68/1.34 % (3780)------------------------------
% 1.68/1.34 % (3780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (3780)Termination reason: Refutation
% 1.68/1.34
% 1.68/1.34 % (3780)Memory used [KB]: 5628
% 1.68/1.34 % (3780)Time elapsed: 0.010 s
% 1.68/1.34 % (3780)Instructions burned: 11 (million)
% 1.68/1.34 % (3780)------------------------------
% 1.68/1.34 % (3780)------------------------------
% 1.68/1.34 % (3772)Success in time 0.02 s
%------------------------------------------------------------------------------