%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO541^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 09:54:30 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 170 ( 107 equ; 11 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 265 ( 59 ~; 41 |; 34 &; 125 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 67 ( 42 ^; 18 !; 7 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_2,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_14,type,
sK0: $i > $i ).
thf(func_def_15,type,
sK1: $i > $i ).
thf(func_def_17,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f59,f61]) ).
thf(f61,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f38,f40]) ).
thf(f40,plain,
! [X0: $i > $i] :
( ( epsii @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: ( $i > $i ) > $o,X1: $i > $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $i ) > $o] :
( ! [X1: $i > $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] : ( X0 @ X1 )
=> ( X0 @ ( epsii @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] : ( X0 @ X1 )
=> ( X0 @ ( epsii @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2THF_22324.p',choiceaxii) ).
thf(f38,plain,
( ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl2_2
<=> ( sK0
= ( epsii @ ( (=) @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f59,plain,
spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f53,f51]) ).
thf(f51,plain,
! [X0: $i > $i,X1: $i] :
( ( epsii @ ( (=) @ X0 ) @ X1 )
= ( X0 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f40]) ).
thf(f53,plain,
( ( ( sK1 @ sK4 )
!= ( epsii @ ( (=) @ sK1 ) @ sK4 ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f34]) ).
thf(f34,plain,
( ( sK1
!= ( epsii @ ( (=) @ sK1 ) ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl2_1
<=> ( sK1
= ( epsii @ ( (=) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f39,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f36,f32]) ).
thf(f30,plain,
( ( sK1
!= ( epsii @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( sK1
!= ( epsii @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( epsii
@ ^ [Y0: $i > $i] : ( sK0 = Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( sK1
!= ( epsii @ ( (=) @ sK1 ) ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0 = Y0 )
& $true ) )
!= sK0 ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0 = Y0 )
& $true ) )
!= sK0 )
| ( ( epsii
@ ^ [Y0: $i > $i] : ( sK1 = Y0 ) )
!= sK1 ) ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( $false
| ( sK1 = Y0 ) ) ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0 = Y0 )
& $true ) )
!= sK0 ) ),
inference(boolean_simplification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& $false )
| ( sK1 = Y0 ) ) )
!= sK1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0 = Y0 )
& $true ) )
!= sK0 ) ),
inference(boolean_simplification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $true )
| ( sK1 = Y0 ) ) )
!= sK1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0 = Y0 )
& $true ) )
!= sK0 ) ),
inference(boolean_simplification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( sK0 = Y0 )
& ~ $false ) )
!= sK0 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $true )
| ( sK1 = Y0 ) ) )
!= sK1 ) ),
inference(boolean_simplification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( sK0
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $false )
| $false ) ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $true )
| ( sK1 = Y0 ) ) )
!= sK1 ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $true )
| ( ( sK1 = Y0 )
& $true ) ) )
!= sK1 )
| ( sK0
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $false )
| $false ) ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $false )
| ( ( sK1 = Y0 )
& $false ) ) )
!= sK0 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ( sK0 = Y0 )
& ~ $true )
| ( ( sK1 = Y0 )
& $true ) ) )
!= sK1 ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ $true
@ sK1
@ sK0 )
!= sK1 )
| ( ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ $false
@ sK1
@ sK0 )
!= sK0 ) ),
inference(definition_unfolding,[status(thm)],[f16,f17,f17]) ).
thf(f17,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( X0
& ( X1 = X3 ) )
| ( ~ X0
& ( X2 = X3 ) ) ) ) )
= if ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: $o,X1: $i > $i,X3: $i > $i] :
( epsii
@ ^ [X4: $i > $i] :
( ( X2
& ( X1 = X4 ) )
| ( ~ X2
& ( X3 = X4 ) ) ) ) )
= if ),
file('/export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2THF_22324.p',ifd) ).
thf(f16,plain,
( ( sK0
!= ( if @ $false @ sK1 @ sK0 ) )
| ( ( if @ $true @ sK1 @ sK0 )
!= sK1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK0
!= ( if @ $false @ sK1 @ sK0 ) )
| ( ( if @ $true @ sK1 @ sK0 )
!= sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i > $i,X1: $i > $i] :
( ( ( if @ $false @ X1 @ X0 )
!= X0 )
| ( ( if @ $true @ X1 @ X0 )
!= X1 ) )
=> ( ( sK0
!= ( if @ $false @ sK1 @ sK0 ) )
| ( ( if @ $true @ sK1 @ sK0 )
!= sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $i > $i,X1: $i > $i] :
( ( ( if @ $false @ X1 @ X0 )
!= X0 )
| ( ( if @ $true @ X1 @ X0 )
!= X1 ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( ( if @ $true @ X1 @ X0 )
= X1 )
& ( ( if @ $false @ X1 @ X0 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( X1
= ( if @ $true @ X1 @ X0 ) )
& ( X0
= ( if @ $false @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X3: $i > $i,X1: $i > $i] :
( ( X1
= ( if @ $true @ X1 @ X3 ) )
& ( X3
= ( if @ $false @ X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X3: $i > $i,X1: $i > $i] :
( ( X1
= ( if @ $true @ X1 @ X3 ) )
& ( X3
= ( if @ $false @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2THF_22324.p',conj) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO541^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:33:46 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
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO541^1 : TPTP v9.2.1. Released v5.2.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : If-then-else on $i>$i defined from choice on $i>$i
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : A choice operator on ($i>$i) is used to define an if-then-else
% 0.19/0.46 % operator at ($i>$i). Check that it works.
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro11]
% 0.19/0.46 % Names : CHOICE16 [Bro11]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% 0.19/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 2 typ; 1 def)
% 0.19/0.46 % Number of atoms : 7 ( 5 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.46 % Number of connectives : 16 ( 1 ~; 1 |; 3 &; 10 @)
% 0.19/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 5 ( 2 usr; 2 con; 0-4 aty)
% 0.19/0.46 % Number of variables : 8 ( 4 ^; 3 !; 1 ?; 8 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(epsii,type,
% 0.19/0.46 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(choiceaxii,axiom,
% 0.19/0.46 ! [P: ( $i > $i ) > $o] :
% 0.19/0.46 ( ? [X: $i > $i] : ( P @ X )
% 0.19/0.46 => ( P @ ( epsii @ P ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(if,type,
% 0.19/0.46 if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(ifd,definition,
% 0.19/0.46 ( if
% 0.19/0.46 = ( ^ [B: $o,X: $i > $i,Y: $i > $i] :
% 0.19/0.46 ( epsii
% 0.19/0.46 @ ^ [Z: $i > $i] :
% 0.19/0.46 ( ( B
% 0.19/0.46 & ( Z = X ) )
% 0.19/0.46 | ( ~ B
% 0.19/0.46 & ( Z = Y ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(conj,conjecture,
% 0.19/0.46 ! [X: $i > $i,Y: $i > $i] :
% 0.19/0.46 ( ( ( if @ $true @ X @ Y )
% 0.19/0.46 = X )
% 0.19/0.46 & ( ( if @ $false @ X @ Y )
% 0.19/0.46 = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 14:33:47 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2DTF22324.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.29 thf(epsii,type,
% 1.46/1.29 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 1.46/1.29
% 1.46/1.29 thf(choiceaxii,axiom,
% 1.46/1.29 ! [P: ( $i > $i ) > $o] :
% 1.46/1.29 ( ? [X: $i > $i] : ( P @ X )
% 1.46/1.29 => ( P @ ( epsii @ P ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(if,type,
% 1.46/1.29 if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 1.46/1.29
% 1.46/1.29 thf(ifd,definition,
% 1.46/1.29 ( if
% 1.46/1.29 = ( ^ [B: $o,X: $i > $i,Y: $i > $i] :
% 1.46/1.29 ( epsii
% 1.46/1.29 @ ^ [Z: $i > $i] :
% 1.46/1.29 ( ( B
% 1.46/1.29 & ( Z = X ) )
% 1.46/1.29 | ( ~ B
% 1.46/1.29 & ( Z = Y ) ) ) ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(conj,conjecture,
% 1.46/1.29 ! [X: $i > $i,Y: $i > $i] :
% 1.46/1.29 ( ( ( if @ $true @ X @ Y )
% 1.46/1.29 = X )
% 1.46/1.29 & ( ( if @ $false @ X @ Y )
% 1.46/1.29 = Y ) ) ).
% 1.46/1.29 ------------------------
% 1.64/1.30 % (22514)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_22324 for (3000ds/4Mi)
% 1.64/1.30 % (22514)Instruction limit reached!
% 1.64/1.30 % (22514)------------------------------
% 1.64/1.30 % (22514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (22514)Termination reason: Unknown
% 1.64/1.30 % (22514)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (22514)Memory used [KB]: 5500
% 1.64/1.30 % (22514)Time elapsed: 0.003 s
% 1.64/1.30 % (22514)Instructions burned: 4 (million)
% 1.64/1.30 % (22514)------------------------------
% 1.64/1.30 % (22514)------------------------------
% 1.64/1.30 % (22518)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_22324 for (3000ds/275Mi)
% 1.64/1.31 % (22519)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22324 for (3000ds/18Mi)
% 1.64/1.31 % (22518)Refutation not found, incomplete strategy
% 1.64/1.31 % (22518)------------------------------
% 1.64/1.31 % (22518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (22518)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (22518)Memory used [KB]: 5500
% 1.64/1.31 % (22518)Time elapsed: 0.001 s
% 1.64/1.31 % (22518)Instructions burned: 1 (million)
% 1.64/1.31 % (22518)------------------------------
% 1.64/1.31 % (22518)------------------------------
% 1.64/1.31 % (22513)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22324 for (3000ds/183Mi)
% 1.64/1.31 % (22515)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_22324 for (3000ds/27Mi)
% 1.64/1.31 % (22517)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_22324 for (3000ds/2Mi)
% 1.64/1.31 % (22519)First to succeed.
% 1.64/1.31 % (22517)Instruction limit reached!
% 1.64/1.31 % (22517)------------------------------
% 1.64/1.31 % (22517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (22517)Termination reason: Unknown
% 1.64/1.31 % (22517)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (22517)Memory used [KB]: 5500
% 1.64/1.31 % (22517)Time elapsed: 0.004 s
% 1.64/1.31 % (22517)Instructions burned: 3 (million)
% 1.64/1.31 % (22517)------------------------------
% 1.64/1.31 % (22517)------------------------------
% 1.64/1.31 % (22515)Also succeeded, but the first one will report.
% 1.64/1.31 % (22519)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_22324
% 1.64/1.31 % SZS output start Proof for DTF2THF_22324
% 1.64/1.31 thf(func_def_0, type, epsii: (($i > $i) > $o) > $i > $i).
% 1.64/1.31 thf(func_def_2, type, if: $o > ($i > $i) > ($i > $i) > $i > $i).
% 1.64/1.31 thf(func_def_14, type, sK0: $i > $i).
% 1.64/1.31 thf(func_def_15, type, sK1: $i > $i).
% 1.64/1.31 thf(func_def_17, type, ph3: !>[X0: $tType]:(X0)).
% 1.64/1.31 thf(f62,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(avatar_sat_refutation,[status(thm)],[f39,f59,f61])).
% 1.64/1.31 thf(f61,plain,(
% 1.64/1.31 spl2_2),
% 1.64/1.31 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.64/1.31 thf(f60,plain,(
% 1.64/1.31 $false | spl2_2),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f38,f40])).
% 1.64/1.31 thf(f40,plain,(
% 1.64/1.31 ( ! [X0 : $i > $i] : (((epsii @ (= @ X0)) = X0)) )),
% 1.64/1.31 inference(leibniz_equality_elimination,[status(thm)],[f18])).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 ( ! [X0 : ($i > $i) > $o,X1 : $i > $i] : (((X0 @ X1) != $true) | ((X0 @ (epsii @ X0)) = $true)) )),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.31 thf(f12,plain,(
% 1.64/1.31 ! [X0 : ($i > $i) > $o] : (! [X1 : $i > $i] : ((X0 @ X1) != $true) | ((X0 @ (epsii @ X0)) = $true))),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,plain,(
% 1.64/1.31 ! [X0 : ($i > $i) > $o] : (? [X1 : $i > $i] : ((X0 @ X1) = $true) => ((X0 @ (epsii @ X0)) = $true))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.31 thf(f6,plain,(
% 1.64/1.31 ! [X0 : ($i > $i) > $o] : (? [X1 : $i > $i] : (X0 @ X1) => (X0 @ (epsii @ X0)))),
% 1.64/1.31 inference(rectify,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 ! [X0 : ($i > $i) > $o] : (? [X1 : $i > $i] : (X0 @ X1) => (X0 @ (epsii @ X0)))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2THF_22324.p',choiceaxii)).
% 1.64/1.31 thf(f38,plain,(
% 1.64/1.31 (sK0 != (epsii @ (= @ sK0))) | spl2_2),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.64/1.31 thf(f36,definition,(
% 1.64/1.31 spl2_2 <=> (sK0 = (epsii @ (= @ sK0)))),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.64/1.31 thf(f59,plain,(
% 1.64/1.31 spl2_1),
% 1.64/1.31 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.64/1.31 thf(f58,plain,(
% 1.64/1.31 $false | spl2_1),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f53,f51])).
% 1.64/1.31 thf(f51,plain,(
% 1.64/1.31 ( ! [X0 : $i > $i,X1 : $i] : (((epsii @ (= @ X0) @ X1) = (X0 @ X1))) )),
% 1.64/1.31 inference(argument_congruence,[status(thm)],[f40])).
% 1.64/1.31 thf(f53,plain,(
% 1.64/1.31 ((sK1 @ sK4) != (epsii @ (= @ sK1) @ sK4)) | spl2_1),
% 1.64/1.31 inference(negative_extensionality,[status(thm)],[f34])).
% 1.64/1.31 thf(f34,plain,(
% 1.64/1.31 (sK1 != (epsii @ (= @ sK1))) | spl2_1),
% 1.64/1.31 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.64/1.31 thf(f32,definition,(
% 1.64/1.31 spl2_1 <=> (sK1 = (epsii @ (= @ sK1)))),
% 1.64/1.31 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.64/1.31 thf(f39,plain,(
% 1.64/1.31 ~spl2_1 | ~spl2_2),
% 1.64/1.31 inference(avatar_split_clause,[status(thm)],[f30,f36,f32])).
% 1.64/1.31 thf(f30,plain,(
% 1.64/1.31 (sK1 != (epsii @ (= @ sK1))) | (sK0 != (epsii @ (= @ sK0)))),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.64/1.31 thf(f29,plain,(
% 1.64/1.31 (sK1 != (epsii @ (= @ sK1))) | (sK0 != (epsii @ (^[Y0 : $i > $i]: (sK0 = Y0))))),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f28])).
% 1.64/1.31 thf(f28,plain,(
% 1.64/1.31 (sK1 != (epsii @ (= @ sK1))) | ((epsii @ (^[Y0 : $i > $i]: ((sK0 = Y0) & $true))) != sK0)),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.64/1.31 thf(f27,plain,(
% 1.64/1.31 ((epsii @ (^[Y0 : $i > $i]: ((sK0 = Y0) & $true))) != sK0) | ((epsii @ (^[Y0 : $i > $i]: (sK1 = Y0))) != sK1)),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f26])).
% 1.64/1.31 thf(f26,plain,(
% 1.64/1.31 (sK1 != (epsii @ (^[Y0 : $i > $i]: ($false | (sK1 = Y0))))) | ((epsii @ (^[Y0 : $i > $i]: ((sK0 = Y0) & $true))) != sK0)),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f25])).
% 1.64/1.31 thf(f25,plain,(
% 1.64/1.31 ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & $false) | (sK1 = Y0)))) != sK1) | ((epsii @ (^[Y0 : $i > $i]: ((sK0 = Y0) & $true))) != sK0)),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f24])).
% 1.64/1.31 thf(f24,plain,(
% 1.64/1.31 ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $true)) | (sK1 = Y0)))) != sK1) | ((epsii @ (^[Y0 : $i > $i]: ((sK0 = Y0) & $true))) != sK0)),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f23])).
% 1.64/1.31 thf(f23,plain,(
% 1.64/1.31 ((epsii @ (^[Y0 : $i > $i]: ((sK0 = Y0) & (~ $false)))) != sK0) | ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $true)) | (sK1 = Y0)))) != sK1)),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f22])).
% 1.64/1.31 thf(f22,plain,(
% 1.64/1.31 (sK0 != (epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $false)) | $false)))) | ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $true)) | (sK1 = Y0)))) != sK1)),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f21])).
% 1.64/1.31 thf(f21,plain,(
% 1.64/1.31 ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $true)) | ((sK1 = Y0) & $true)))) != sK1) | (sK0 != (epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $false)) | $false))))),
% 1.64/1.31 inference(boolean_simplification,[status(thm)],[f20])).
% 1.64/1.31 thf(f20,plain,(
% 1.64/1.31 ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $false)) | ((sK1 = Y0) & $false)))) != sK0) | ((epsii @ (^[Y0 : $i > $i]: (((sK0 = Y0) & (~ $true)) | ((sK1 = Y0) & $true)))) != sK1)),
% 1.64/1.31 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 (((^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))) @ $true @ sK1 @ sK0) != sK1) | (((^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))) @ $false @ sK1 @ sK0) != sK0)),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f16,f17,f17])).
% 1.64/1.31 thf(f17,plain,(
% 1.64/1.31 (if = (^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))))),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.31 thf(f11,plain,(
% 1.64/1.31 (if = (^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.31 thf(f10,plain,(
% 1.64/1.31 ((^[X0 : $o, X1 : $i > $i, X2 : $i > $i] : (epsii @ (^[X3 : $i > $i] : ((X0 & (X1 = X3)) | (~X0 & (X2 = X3)))))) = if)),
% 1.64/1.31 inference(rectify,[status(thm)],[f2])).
% 1.64/1.31 thf(f2,axiom,(
% 1.64/1.31 ((^[X2 : $o, X1 : $i > $i, X3 : $i > $i] : (epsii @ (^[X4 : $i > $i] : ((X2 & (X1 = X4)) | (~X2 & (X3 = X4)))))) = if)),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2THF_22324.p',ifd)).
% 1.64/1.31 thf(f16,plain,(
% 1.64/1.31 (sK0 != (if @ $false @ sK1 @ sK0)) | ((if @ $true @ sK1 @ sK0) != sK1)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.31 thf(f15,plain,(
% 1.64/1.31 (sK0 != (if @ $false @ sK1 @ sK0)) | ((if @ $true @ sK1 @ sK0) != sK1)),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.64/1.31 thf(f14,plain,(
% 1.64/1.31 ? [X0 : $i > $i,X1 : $i > $i] : (((if @ $false @ X1 @ X0) != X0) | ((if @ $true @ X1 @ X0) != X1)) => ((sK0 != (if @ $false @ sK1 @ sK0)) | ((if @ $true @ sK1 @ sK0) != sK1))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 ? [X0 : $i > $i,X1 : $i > $i] : (((if @ $false @ X1 @ X0) != X0) | ((if @ $true @ X1 @ X0) != X1))),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.64/1.31 thf(f9,plain,(
% 1.64/1.31 ~! [X0 : $i > $i,X1 : $i > $i] : (((if @ $true @ X1 @ X0) = X1) & ((if @ $false @ X1 @ X0) = X0))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.31 thf(f8,plain,(
% 1.64/1.31 ~! [X0 : $i > $i,X1 : $i > $i] : ((X1 = (if @ $true @ X1 @ X0)) & (X0 = (if @ $false @ X1 @ X0)))),
% 1.64/1.31 inference(rectify,[status(thm)],[f4])).
% 1.64/1.31 thf(f4,negated_conjecture,(
% 1.64/1.31 ~! [X3 : $i > $i,X1 : $i > $i] : ((X1 = (if @ $true @ X1 @ X3)) & (X3 = (if @ $false @ X1 @ X3)))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.31 thf(f3,conjecture,(
% 1.64/1.31 ! [X3 : $i > $i,X1 : $i > $i] : ((X1 = (if @ $true @ X1 @ X3)) & (X3 = (if @ $false @ X1 @ X3)))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.marZ0zI7Lp/DTF2THF_22324.p',conj)).
% 1.64/1.31 % SZS output end Proof for DTF2THF_22324
% 1.64/1.31 % (22519)------------------------------
% 1.64/1.31 % (22519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (22519)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (22519)Memory used [KB]: 5500
% 1.64/1.31 % (22519)Time elapsed: 0.005 s
% 1.64/1.31 % (22519)Instructions burned: 5 (million)
% 1.64/1.31 % (22519)------------------------------
% 1.64/1.31 % (22519)------------------------------
% 1.64/1.31 % (22512)Success in time 0.018 s
%------------------------------------------------------------------------------