%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU886^5 : 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 : n026.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 09:37:40 AM UTC 2026
% Result : Theorem 1.79s 1.52s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 185 ( 78 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 224 ( 49 ~; 32 |; 39 &; 96 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 22 !; 20 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
f: b > a ).
thf(func_def_3,type,
y: b > $o ).
thf(func_def_4,type,
x: b > $o ).
thf(func_def_8,type,
sK0: a ).
thf(func_def_9,type,
sK1: b ).
thf(f29,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f25,f28]) ).
thf(f28,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f26,f12]) ).
thf(f12,plain,
( $true
= ( x @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( x @ X1 )
!= $true ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= sK0 )
| ( $true
!= ( y @ X2 ) ) ) )
& ( sK0
= ( f @ sK1 ) )
& ( $true
= ( x @ sK1 ) )
& ( $true
= ( y @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ( ! [X1: b] :
( ( ( f @ X1 )
!= X0 )
| ( ( x @ X1 )
!= $true ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= X0 )
| ( $true
!= ( y @ X2 ) ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( $true
= ( x @ X3 ) )
& ( $true
= ( y @ X3 ) ) ) )
=> ( ( ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( x @ X1 )
!= $true ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= sK0 )
| ( $true
!= ( y @ X2 ) ) ) )
& ? [X3: b] :
( ( sK0
= ( f @ X3 ) )
& ( $true
= ( x @ X3 ) )
& ( $true
= ( y @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: b] :
( ( sK0
= ( f @ X3 ) )
& ( $true
= ( x @ X3 ) )
& ( $true
= ( y @ X3 ) ) )
=> ( ( sK0
= ( f @ sK1 ) )
& ( $true
= ( x @ sK1 ) )
& ( $true
= ( y @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a] :
( ( ! [X1: b] :
( ( ( f @ X1 )
!= X0 )
| ( ( x @ X1 )
!= $true ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= X0 )
| ( $true
!= ( y @ X2 ) ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( $true
= ( x @ X3 ) )
& ( $true
= ( y @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ( ! [X3: b] :
( ( ( f @ X3 )
!= X0 )
| ( $true
!= ( x @ X3 ) ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= X0 )
| ( $true
!= ( y @ X2 ) ) ) )
& ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( ( x @ X1 )
= $true )
& ( ( y @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( ( x @ X1 )
= $true )
& ( ( y @ X1 )
= $true ) )
=> ( ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( $true
= ( x @ X3 ) ) )
& ? [X2: b] :
( ( $true
= ( y @ X2 ) )
& ( ( f @ X2 )
= X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( y @ X2 ) )
& ? [X3: b] :
( ( x @ X3 )
& ( ( f @ X3 )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( y @ X1 ) )
& ? [X1: b] :
( ( x @ X1 )
& ( ( f @ X1 )
= X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( y @ X1 ) )
& ? [X1: b] :
( ( x @ X1 )
& ( ( f @ X1 )
= X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cJzMCRdcCj/DTF2THF_2761.p',cX5203_pme) ).
thf(f26,plain,
( ( $true
!= ( x @ sK1 ) )
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: b] :
( ( ( f @ X1 )
!= ( f @ sK1 ) )
| ( ( x @ X1 )
!= $true ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl2_1
<=> ! [X1: b] :
( ( ( x @ X1 )
!= $true )
| ( ( f @ X1 )
!= ( f @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f25,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f23,f11]) ).
thf(f11,plain,
( $true
= ( y @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f23,plain,
( ( $true
!= ( y @ sK1 ) )
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X2: b] :
( ( ( f @ X2 )
!= ( f @ sK1 ) )
| ( $true
!= ( y @ X2 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl2_2
<=> ! [X2: b] :
( ( $true
!= ( y @ X2 ) )
| ( ( f @ X2 )
!= ( f @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f22,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f20,f17]) ).
thf(f15,plain,
! [X2: b,X1: b] :
( ( ( x @ X1 )
!= $true )
| ( ( f @ X1 )
!= ( f @ sK1 ) )
| ( $true
!= ( y @ X2 ) )
| ( ( f @ X2 )
!= ( f @ sK1 ) ) ),
inference(definition_unfolding,[status(thm)],[f14,f13,f13]) ).
thf(f13,plain,
( sK0
= ( f @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f14,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( x @ X1 )
!= $true )
| ( ( f @ X2 )
!= sK0 )
| ( $true
!= ( y @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU886^5 : 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
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:36:25 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SEU886^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.48 % Domain : Set Theory
% 0.19/0.48 % Problem : TPS problem X5203
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Bro09]
% 0.19/0.48 % Names : tps_0249 [Bro09]
% 0.19/0.48 % : X5203 [TPS]
% 0.19/0.48 % : THM11 [TPS]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.19/0.48 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.19/0.48 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 7 ( 7 avg)
% 0.19/0.48 % Number of connectives : 13 ( 0 ~; 0 |; 5 &; 7 @)
% 0.19/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.48 % Number of types : 3 ( 2 usr)
% 0.19/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.19/0.48 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.48 % : Polymorphic definitions expanded.
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(b_type,type,
% 0.19/0.48 b: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(a_type,type,
% 0.19/0.48 a: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(f,type,
% 0.19/0.48 f: b > a ).
% 0.19/0.48
% 0.19/0.48 thf(y,type,
% 0.19/0.48 y: b > $o ).
% 0.19/0.48
% 0.19/0.48 thf(x,type,
% 0.19/0.48 x: b > $o ).
% 0.19/0.48
% 0.19/0.48 thf(cX5203_pme,conjecture,
% 0.19/0.48 ! [Xx0: a] :
% 0.19/0.48 ( ? [Xt: b] :
% 0.19/0.48 ( ( x @ Xt )
% 0.19/0.48 & ( y @ Xt )
% 0.19/0.48 & ( Xx0
% 0.19/0.48 = ( f @ Xt ) ) )
% 0.19/0.48 => ( ? [Xt: b] :
% 0.19/0.48 ( ( x @ Xt )
% 0.19/0.48 & ( Xx0
% 0.19/0.48 = ( f @ Xt ) ) )
% 0.19/0.48 & ? [Xt: b] :
% 0.19/0.48 ( ( y @ Xt )
% 0.19/0.48 & ( Xx0
% 0.19/0.48 = ( f @ Xt ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.61/1.48 ---- Embedded in THF ---
% 1.61/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.48 %%% Generated on Tue Feb 24 12:36:26 EST 2026
% 1.61/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.48 %%% Logic specification used:
% 1.61/1.48 %%% thf(spec, logic, $$dhol).
% 1.61/1.48
% 1.61/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cJzMCRdcCj/DTF2DTF2761.p
% See solution above
% 1.61/1.48 ------------------------
% 1.61/1.49 ---- Cleaned THF ---
% 1.61/1.49 thf(b_type,type,
% 1.61/1.49 b: $tType ).
% 1.61/1.49
% 1.61/1.49 thf(a_type,type,
% 1.61/1.49 a: $tType ).
% 1.61/1.49
% 1.61/1.49 thf(f,type,
% 1.61/1.49 f: b > a ).
% 1.61/1.49
% 1.61/1.49 thf(y,type,
% 1.61/1.49 y: b > $o ).
% 1.61/1.49
% 1.61/1.49 thf(x,type,
% 1.61/1.49 x: b > $o ).
% 1.61/1.49
% 1.61/1.49 thf(cX5203_pme,conjecture,
% 1.61/1.49 ! [Xx0: a] :
% 1.61/1.49 ( ? [Xt: b] :
% 1.61/1.49 ( ( x @ Xt )
% 1.61/1.49 & ( y @ Xt )
% 1.61/1.49 & ( Xx0
% 1.61/1.49 = ( f @ Xt ) ) )
% 1.61/1.49 => ( ? [Xt: b] :
% 1.61/1.49 ( ( x @ Xt )
% 1.61/1.49 & ( Xx0
% 1.61/1.49 = ( f @ Xt ) ) )
% 1.61/1.49 & ? [Xt: b] :
% 1.61/1.49 ( ( y @ Xt )
% 1.61/1.49 & ( Xx0
% 1.61/1.49 = ( f @ Xt ) ) ) ) ) ).
% 1.61/1.49 ------------------------
% 1.79/1.51 % (2863)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_2761 for (2999ds/275Mi)
% 1.79/1.51 % (2860)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_2761 for (2999ds/27Mi)
% 1.79/1.51 % (2859)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_2761 for (2999ds/4Mi)
% 1.79/1.51 % (2861)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2761 for (2999ds/2Mi)
% 1.79/1.51 % (2864)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2761 for (2999ds/18Mi)
% 1.79/1.51 % (2858)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2761 for (2999ds/183Mi)
% 1.79/1.51 % (2861)Instruction limit reached!
% 1.79/1.51 % (2861)------------------------------
% 1.79/1.51 % (2861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.51 % (2863)First to succeed.
% 1.79/1.51 % (2861)Termination reason: Unknown
% 1.79/1.51 % (2861)Termination phase: Saturation
% 1.79/1.51
% 1.79/1.51 % (2861)Memory used [KB]: 5500
% 1.79/1.51 % (2861)Time elapsed: 0.004 s
% 1.79/1.51 % (2861)Instructions burned: 2 (million)
% 1.79/1.51 % (2861)------------------------------
% 1.79/1.51 % (2861)------------------------------
% 1.79/1.51 % (2864)Also succeeded, but the first one will report.
% 1.79/1.51 % (2862)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_2761 for (2999ds/2Mi)
% 1.79/1.52 % (2858)Also succeeded, but the first one will report.
% 1.79/1.52 % (2863)Refutation found. Thanks to Tanya!
% 1.79/1.52 % SZS status Theorem for DTF2THF_2761
% 1.79/1.52 % SZS output start Proof for DTF2THF_2761
% 1.79/1.52 thf(type_def_5, type, b: $tType).
% 1.79/1.52 thf(type_def_6, type, a: $tType).
% 1.79/1.52 thf(func_def_0, type, b: $tType).
% 1.79/1.52 thf(func_def_1, type, a: $tType).
% 1.79/1.52 thf(func_def_2, type, f: b > a).
% 1.79/1.52 thf(func_def_3, type, y: b > $o).
% 1.79/1.52 thf(func_def_4, type, x: b > $o).
% 1.79/1.52 thf(func_def_8, type, sK0: a).
% 1.79/1.52 thf(func_def_9, type, sK1: b).
% 1.79/1.52 thf(f29,plain,(
% 1.79/1.52 $false),
% 1.79/1.52 inference(avatar_sat_refutation,[status(thm)],[f22,f25,f28])).
% 1.79/1.52 thf(f28,plain,(
% 1.79/1.52 ~spl2_1),
% 1.79/1.52 inference(avatar_contradiction_clause,[status(thm)],[f27])).
% 1.79/1.52 thf(f27,plain,(
% 1.79/1.52 $false | ~spl2_1),
% 1.79/1.52 inference(subsumption_resolution,[status(thm)],[f26,f12])).
% 1.79/1.52 thf(f12,plain,(
% 1.79/1.52 ($true = (x @ sK1))),
% 1.79/1.52 inference(cnf_transformation,[status(thm)],[f10])).
% 1.79/1.52 thf(f10,plain,(
% 1.79/1.52 (! [X1 : b] : (((f @ X1) != sK0) | ((x @ X1) != $true)) | ! [X2 : b] : (((f @ X2) != sK0) | ($true != (y @ X2)))) & ((sK0 = (f @ sK1)) & ($true = (x @ sK1)) & ($true = (y @ sK1)))),
% 1.79/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.79/1.52 thf(f8,plain,(
% 1.79/1.52 ? [X0 : a] : ((! [X1 : b] : (((f @ X1) != X0) | ((x @ X1) != $true)) | ! [X2 : b] : (((f @ X2) != X0) | ($true != (y @ X2)))) & ? [X3 : b] : (((f @ X3) = X0) & ($true = (x @ X3)) & ($true = (y @ X3)))) => ((! [X1 : b] : (((f @ X1) != sK0) | ((x @ X1) != $true)) | ! [X2 : b] : (((f @ X2) != sK0) | ($true != (y @ X2)))) & ? [X3 : b] : ((sK0 = (f @ X3)) & ($true = (x @ X3)) & ($true = (y @ X3))))),
% 1.79/1.52 introduced(definition,[],[choice_axiom])).
% 1.79/1.52 thf(f9,plain,(
% 1.79/1.52 ? [X3 : b] : ((sK0 = (f @ X3)) & ($true = (x @ X3)) & ($true = (y @ X3))) => ((sK0 = (f @ sK1)) & ($true = (x @ sK1)) & ($true = (y @ sK1)))),
% 1.79/1.52 introduced(definition,[],[choice_axiom])).
% 1.79/1.52 thf(f7,plain,(
% 1.79/1.52 ? [X0 : a] : ((! [X1 : b] : (((f @ X1) != X0) | ((x @ X1) != $true)) | ! [X2 : b] : (((f @ X2) != X0) | ($true != (y @ X2)))) & ? [X3 : b] : (((f @ X3) = X0) & ($true = (x @ X3)) & ($true = (y @ X3))))),
% 1.79/1.52 inference(rectify,[status(thm)],[f6])).
% 1.79/1.52 thf(f6,plain,(
% 1.79/1.52 ? [X0 : a] : ((! [X3 : b] : (((f @ X3) != X0) | ($true != (x @ X3))) | ! [X2 : b] : (((f @ X2) != X0) | ($true != (y @ X2)))) & ? [X1 : b] : (((f @ X1) = X0) & ((x @ X1) = $true) & ((y @ X1) = $true)))),
% 1.79/1.52 inference(ennf_transformation,[status(thm)],[f5])).
% 1.79/1.52 thf(f5,plain,(
% 1.79/1.52 ~! [X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & ((x @ X1) = $true) & ((y @ X1) = $true)) => (? [X3 : b] : (((f @ X3) = X0) & ($true = (x @ X3))) & ? [X2 : b] : (($true = (y @ X2)) & ((f @ X2) = X0))))),
% 1.79/1.52 inference(fool_elimination,[status(thm)],[f4])).
% 1.79/1.52 thf(f4,plain,(
% 1.79/1.52 ~! [X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & (y @ X1) & (x @ X1)) => (? [X2 : b] : (((f @ X2) = X0) & (y @ X2)) & ? [X3 : b] : ((x @ X3) & ((f @ X3) = X0))))),
% 1.79/1.52 inference(rectify,[status(thm)],[f2])).
% 1.79/1.52 thf(f2,negated_conjecture,(
% 1.79/1.52 ~! [X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & (y @ X1) & (x @ X1)) => (? [X1 : b] : (((f @ X1) = X0) & (y @ X1)) & ? [X1 : b] : ((x @ X1) & ((f @ X1) = X0))))),
% 1.79/1.52 inference(negated_conjecture,[status(cth)],[f1])).
% 1.79/1.52 thf(f1,conjecture,(
% 1.79/1.52 ! [X0 : a] : (? [X1 : b] : (((f @ X1) = X0) & (y @ X1) & (x @ X1)) => (? [X1 : b] : (((f @ X1) = X0) & (y @ X1)) & ? [X1 : b] : ((x @ X1) & ((f @ X1) = X0))))),
% 1.79/1.52 file('/export/starexec/sandbox/tmp/tmp.cJzMCRdcCj/DTF2THF_2761.p',cX5203_pme)).
% 1.79/1.52 thf(f26,plain,(
% 1.79/1.52 ($true != (x @ sK1)) | ~spl2_1),
% 1.79/1.52 inference(equality_resolution,[status(thm)],[f18])).
% 1.79/1.52 thf(f18,plain,(
% 1.79/1.52 ( ! [X1 : b] : (((f @ X1) != (f @ sK1)) | ((x @ X1) != $true)) ) | ~spl2_1),
% 1.79/1.52 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.79/1.52 thf(f17,definition,(
% 1.79/1.52 spl2_1 <=> ! [X1 : b] : (((x @ X1) != $true) | ((f @ X1) != (f @ sK1)))),
% 1.79/1.52 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.79/1.52 thf(f25,plain,(
% 1.79/1.52 ~spl2_2),
% 1.79/1.52 inference(avatar_contradiction_clause,[status(thm)],[f24])).
% 1.79/1.52 thf(f24,plain,(
% 1.79/1.52 $false | ~spl2_2),
% 1.79/1.52 inference(subsumption_resolution,[status(thm)],[f23,f11])).
% 1.79/1.52 thf(f11,plain,(
% 1.79/1.52 ($true = (y @ sK1))),
% 1.79/1.52 inference(cnf_transformation,[status(thm)],[f10])).
% 1.79/1.52 thf(f23,plain,(
% 1.79/1.52 ($true != (y @ sK1)) | ~spl2_2),
% 1.79/1.52 inference(equality_resolution,[status(thm)],[f21])).
% 1.79/1.52 thf(f21,plain,(
% 1.79/1.52 ( ! [X2 : b] : (((f @ X2) != (f @ sK1)) | ($true != (y @ X2))) ) | ~spl2_2),
% 1.79/1.52 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.79/1.52 thf(f20,definition,(
% 1.79/1.52 spl2_2 <=> ! [X2 : b] : (($true != (y @ X2)) | ((f @ X2) != (f @ sK1)))),
% 1.79/1.52 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.79/1.52 thf(f22,plain,(
% 1.79/1.52 spl2_1 | spl2_2),
% 1.79/1.52 inference(avatar_split_clause,[status(thm)],[f15,f20,f17])).
% 1.79/1.52 thf(f15,plain,(
% 1.79/1.52 ( ! [X2 : b,X1 : b] : (((x @ X1) != $true) | ((f @ X1) != (f @ sK1)) | ($true != (y @ X2)) | ((f @ X2) != (f @ sK1))) )),
% 1.79/1.52 inference(definition_unfolding,[status(thm)],[f14,f13,f13])).
% 1.79/1.52 thf(f13,plain,(
% 1.79/1.52 (sK0 = (f @ sK1))),
% 1.79/1.52 inference(cnf_transformation,[status(thm)],[f10])).
% 1.79/1.52 thf(f14,plain,(
% 1.79/1.52 ( ! [X2 : b,X1 : b] : (((f @ X1) != sK0) | ((x @ X1) != $true) | ((f @ X2) != sK0) | ($true != (y @ X2))) )),
% 1.79/1.52 inference(cnf_transformation,[status(thm)],[f10])).
% 1.79/1.52 % SZS output end Proof for DTF2THF_2761
% 1.79/1.52 % (2863)------------------------------
% 1.79/1.52 % (2863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.79/1.52 % (2863)Termination reason: Refutation
% 1.79/1.52
% 1.79/1.52 % (2863)Memory used [KB]: 5500
% 1.79/1.52 % (2863)Time elapsed: 0.004 s
% 1.79/1.52 % (2863)Instructions burned: 1 (million)
% 1.79/1.52 % (2863)------------------------------
% 1.79/1.52 % (2863)------------------------------
% 1.79/1.52 % (2857)Success in time 0.02 s
%------------------------------------------------------------------------------