%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO538^1 : 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 : n007.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 09:54:29 AM UTC 2026
% Result : Theorem 1.53s 1.23s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 345 ( 147 equ; 12 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 322 ( 69 ~; 73 |; 37 &; 137 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 72 ( 41 ^; 24 !; 7 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
if: $o > $i > $i > $i ).
thf(func_def_17,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK4: $i > $i ).
thf(f68,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f65,f67]) ).
thf(f67,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f38,f40]) ).
thf(f40,plain,
! [X0: $i] :
( ( eps @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2THF_11231.p',choiceax) ).
thf(f38,plain,
( ( sK0
!= ( eps @ ( (=) @ sK0 ) ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl2_2
<=> ( sK0
= ( eps @ ( (=) @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f65,plain,
spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( sK1 != sK1 )
| spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( sK1 != sK1 )
| ( sK1 != sK1 )
| ( sK1 != sK1 )
| spl2_1 ),
inference(superposition,[status(thm)],[f57,f61]) ).
thf(f61,plain,
( ( ( sK4 @ sK1 )
= sK1 )
| spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( sK4 @ sK1 )
= sK1 )
| ( ( sK4 @ sK1 )
= sK1 )
| spl2_1 ),
inference(equality_resolution,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( ( sK4 @ X0 )
= X0 )
| ( sK1
= ( sK4 @ X0 ) ) )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X0: $i] :
( ( sK1
= ( sK4 @ X0 ) )
| ( sK1 != X0 )
| ( ( X0
= ( sK4 @ X0 ) )
= $true ) )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X0: $i] :
( ( ( sK1
= ( sK4 @ X0 ) )
= $true )
| ( ( X0
= ( sK4 @ X0 ) )
= $true )
| ( sK1 != X0 ) )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ! [X0: $i] :
( ( ( sK1
= ( sK4 @ X0 ) )
!= ( X0
= ( sK4 @ X0 ) ) )
| ( sK1 != X0 ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X0: $i] :
( ( ( (=) @ sK1 )
!= ( (=) @ X0 ) )
| ( sK1 != X0 ) )
| spl2_1 ),
inference(constrained_superposition,[status(thm)],[f34,f40]) ).
thf(f34,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl2_1
<=> ( sK1
= ( eps @ ( (=) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f57,plain,
( ! [X0: $i] :
( ( sK1
!= ( sK4 @ X0 ) )
| ( sK1 != X0 )
| ( ( sK4 @ X0 )
!= X0 ) )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ! [X0: $i] :
( ( ( sK1
= ( sK4 @ X0 ) )
= $false )
| ( sK1 != X0 )
| ( ( sK4 @ X0 )
!= X0 ) )
| spl2_1 ),
inference(equality_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X0: $i] :
( ( ( X0
= ( sK4 @ X0 ) )
= $false )
| ( sK1 != X0 )
| ( ( sK1
= ( sK4 @ X0 ) )
= $false ) )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f39,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f36,f32]) ).
thf(f30,plain,
( ( sK0
!= ( eps @ ( (=) @ sK0 ) ) )
| ( sK1
!= ( eps @ ( (=) @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( eps
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
!= sK0 )
| ( sK1
!= ( eps @ ( (=) @ sK1 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( eps
@ ^ [Y0: $i] :
( $false
| ( sK0 = Y0 ) ) )
!= sK0 )
| ( sK1
!= ( eps @ ( (=) @ sK1 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( sK0 = Y0 ) ) ) )
| ( sK1
!= ( eps @ ( (=) @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( sK0 = Y0 ) ) ) )
| ( ( eps
@ ^ [Y0: $i] : ( sK1 = Y0 ) )
!= sK1 ) ),
inference(boolean_simplification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( $true
& ( sK1 = Y0 ) ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( sK0 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK1 = Y0 ) )
| $false ) )
!= sK1 )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( sK0 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& $false ) ) )
!= sK1 )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( sK0 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& $true ) ) ) )
| ( ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& $false ) ) )
!= sK1 ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& ~ $false ) ) ) )
| ( ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& $false ) ) )
!= sK1 ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& ~ $true ) ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK1 = Y0 ) )
| ( ( sK0 = Y0 )
& ~ $false ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( sK0
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) )
@ $false
@ sK1
@ sK0 ) )
| ( sK1
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) )
@ $true
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f17,f17]) ).
thf(f17,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [X0: $o,X1: $i,X2: $i] :
( eps
@ ^ [X3: $i] :
( ( ~ X0
& ( X2 = X3 ) )
| ( ( X1 = X3 )
& X0 ) ) ) )
= if ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: $o,X1: $i,X3: $i] :
( eps
@ ^ [X4: $i] :
( ( ~ X2
& ( X3 = X4 ) )
| ( ( X1 = X4 )
& X2 ) ) ) )
= if ),
file('/export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2THF_11231.p',ifd) ).
thf(f18,plain,
( ( sK0
!= ( if @ $false @ sK1 @ sK0 ) )
| ( sK1
!= ( if @ $true @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK0
!= ( if @ $false @ sK1 @ sK0 ) )
| ( sK1
!= ( if @ $true @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ( ( if @ $false @ X1 @ X0 )
!= X0 )
| ( ( if @ $true @ X1 @ X0 )
!= X1 ) )
=> ( ( sK0
!= ( if @ $false @ sK1 @ sK0 ) )
| ( sK1
!= ( if @ $true @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $i,X1: $i] :
( ( ( if @ $false @ X1 @ X0 )
!= X0 )
| ( ( if @ $true @ X1 @ X0 )
!= X1 ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $i,X1: $i] :
( ( ( if @ $false @ X1 @ X0 )
= X0 )
& ( ( if @ $true @ X1 @ X0 )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i,X1: $i] :
( ( ( if @ $true @ X1 @ X0 )
= X1 )
& ( X0
= ( if @ $false @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X3: $i,X1: $i] :
( ( ( if @ $true @ X1 @ X3 )
= X1 )
& ( X3
= ( if @ $false @ X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X3: $i,X1: $i] :
( ( ( if @ $true @ X1 @ X3 )
= X1 )
& ( X3
= ( if @ $false @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2THF_11231.p',conj) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO538^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:32:38 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SYO538^1 : TPTP v9.2.1. Released v5.2.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : If-then-else on $i defined from choice on $i
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English : A choice operator on $i is used to define an if-then-else operator
% 0.30/0.45 % at $i. Check that it works.
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro11]
% 0.30/0.45 % Names : CHOICE15 [Bro11]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % 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
% 0.30/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 2 typ; 1 def)
% 0.30/0.45 % Number of atoms : 7 ( 5 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.45 % Number of connectives : 16 ( 1 ~; 1 |; 3 &; 10 @)
% 0.30/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 5 ( 3 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 5 ( 2 usr; 2 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 8 ( 4 ^; 3 !; 1 ?; 8 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments :
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(eps,type,
% 0.30/0.45 eps: ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(choiceax,axiom,
% 0.30/0.45 ! [P: $i > $o] :
% 0.30/0.45 ( ? [X: $i] : ( P @ X )
% 0.30/0.45 => ( P @ ( eps @ P ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(if,type,
% 0.30/0.45 if: $o > $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(ifd,definition,
% 0.30/0.45 ( if
% 0.30/0.45 = ( ^ [B: $o,X: $i,Y: $i] :
% 0.30/0.45 ( eps
% 0.30/0.45 @ ^ [Z: $i] :
% 0.30/0.45 ( ( B
% 0.30/0.45 & ( Z = X ) )
% 0.30/0.45 | ( ~ B
% 0.30/0.45 & ( Z = Y ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(conj,conjecture,
% 0.30/0.45 ! [X: $i,Y: $i] :
% 0.30/0.45 ( ( ( if @ $true @ X @ Y )
% 0.30/0.45 = X )
% 0.30/0.45 & ( ( if @ $false @ X @ Y )
% 0.30/0.45 = Y ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.37/1.20 ---- Embedded in THF ---
% 1.53/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.20 %%% Generated on Tue Feb 24 14:32:39 EST 2026
% 1.53/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.20 %%% Logic specification used:
% 1.53/1.20 %%% thf(spec, logic, $$dhol).
% 1.53/1.20
% 1.53/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2DTF11231.p
% See solution above
% 1.53/1.20 ------------------------
% 1.53/1.21 ---- Cleaned THF ---
% 1.53/1.21 thf(eps,type,
% 1.53/1.21 eps: ( $i > $o ) > $i ).
% 1.53/1.21
% 1.53/1.21 thf(choiceax,axiom,
% 1.53/1.21 ! [P: $i > $o] :
% 1.53/1.21 ( ? [X: $i] : ( P @ X )
% 1.53/1.21 => ( P @ ( eps @ P ) ) ) ).
% 1.53/1.21
% 1.53/1.21 thf(if,type,
% 1.53/1.21 if: $o > $i > $i > $i ).
% 1.53/1.21
% 1.53/1.21 thf(ifd,definition,
% 1.53/1.21 ( if
% 1.53/1.21 = ( ^ [B: $o,X: $i,Y: $i] :
% 1.53/1.21 ( eps
% 1.53/1.21 @ ^ [Z: $i] :
% 1.53/1.21 ( ( B
% 1.53/1.21 & ( Z = X ) )
% 1.53/1.21 | ( ~ B
% 1.53/1.21 & ( Z = Y ) ) ) ) ) ) ).
% 1.53/1.21
% 1.53/1.21 thf(conj,conjecture,
% 1.53/1.21 ! [X: $i,Y: $i] :
% 1.53/1.21 ( ( ( if @ $true @ X @ Y )
% 1.53/1.21 = X )
% 1.53/1.21 & ( ( if @ $false @ X @ Y )
% 1.53/1.21 = Y ) ) ).
% 1.53/1.21 ------------------------
% 1.53/1.23 % (11349)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_11231 for (2999ds/2Mi)
% 1.53/1.23 % (11349)Instruction limit reached!
% 1.53/1.23 % (11349)------------------------------
% 1.53/1.23 % (11349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.23 % (11349)Termination reason: Unknown
% 1.53/1.23 % (11349)Termination phase: Saturation
% 1.53/1.23
% 1.53/1.23 % (11349)Memory used [KB]: 895
% 1.53/1.23 % (11349)Time elapsed: 0.002 s
% 1.53/1.23 % (11349)Instructions burned: 2 (million)
% 1.53/1.23 % (11349)------------------------------
% 1.53/1.23 % (11349)------------------------------
% 1.53/1.23 % (11351)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11231 for (2999ds/18Mi)
% 1.53/1.23 % (11351)First to succeed.
% 1.53/1.23 % (11351)Refutation found. Thanks to Tanya!
% 1.53/1.23 % SZS status Theorem for DTF2THF_11231
% 1.53/1.23 % SZS output start Proof for DTF2THF_11231
% 1.53/1.23 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.53/1.23 thf(func_def_2, type, if: $o > $i > $i > $i).
% 1.53/1.23 thf(func_def_17, type, ph3: !>[X0: $tType]:(X0)).
% 1.53/1.23 thf(func_def_18, type, sK4: $i > $i).
% 1.53/1.23 thf(f68,plain,(
% 1.53/1.23 $false),
% 1.53/1.23 inference(avatar_sat_refutation,[status(thm)],[f39,f65,f67])).
% 1.53/1.23 thf(f67,plain,(
% 1.53/1.23 spl2_2),
% 1.53/1.23 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 1.53/1.23 thf(f66,plain,(
% 1.53/1.23 $false | spl2_2),
% 1.53/1.23 inference(subsumption_resolution,[status(thm)],[f38,f40])).
% 1.53/1.23 thf(f40,plain,(
% 1.53/1.23 ( ! [X0 : $i] : (((eps @ (= @ X0)) = X0)) )),
% 1.53/1.23 inference(leibniz_equality_elimination,[status(thm)],[f16])).
% 1.53/1.23 thf(f16,plain,(
% 1.53/1.23 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true)) )),
% 1.53/1.23 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.23 thf(f12,plain,(
% 1.53/1.23 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true))),
% 1.53/1.23 inference(ennf_transformation,[status(thm)],[f9])).
% 1.53/1.23 thf(f9,plain,(
% 1.53/1.23 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps @ X0)) = $true))),
% 1.53/1.23 inference(fool_elimination,[status(thm)],[f8])).
% 1.53/1.23 thf(f8,plain,(
% 1.53/1.23 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.53/1.23 inference(rectify,[status(thm)],[f1])).
% 1.53/1.23 thf(f1,axiom,(
% 1.53/1.23 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.53/1.23 file('/export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2THF_11231.p',choiceax)).
% 1.53/1.23 thf(f38,plain,(
% 1.53/1.23 (sK0 != (eps @ (= @ sK0))) | spl2_2),
% 1.53/1.23 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.53/1.23 thf(f36,definition,(
% 1.53/1.23 spl2_2 <=> (sK0 = (eps @ (= @ sK0)))),
% 1.53/1.23 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.53/1.23 thf(f65,plain,(
% 1.53/1.23 spl2_1),
% 1.53/1.23 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.53/1.23 thf(f64,plain,(
% 1.53/1.23 $false | spl2_1),
% 1.53/1.23 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.53/1.23 thf(f63,plain,(
% 1.53/1.23 (sK1 != sK1) | spl2_1),
% 1.53/1.23 inference(duplicate_literal_removal,[status(thm)],[f62])).
% 1.53/1.23 thf(f62,plain,(
% 1.53/1.23 (sK1 != sK1) | (sK1 != sK1) | (sK1 != sK1) | spl2_1),
% 1.53/1.23 inference(superposition,[status(thm)],[f57,f61])).
% 1.53/1.23 thf(f61,plain,(
% 1.53/1.23 ((sK4 @ sK1) = sK1) | spl2_1),
% 1.53/1.23 inference(duplicate_literal_removal,[status(thm)],[f60])).
% 1.53/1.23 thf(f60,plain,(
% 1.53/1.23 ((sK4 @ sK1) = sK1) | ((sK4 @ sK1) = sK1) | spl2_1),
% 1.53/1.23 inference(equality_resolution,[status(thm)],[f59])).
% 1.53/1.23 thf(f59,plain,(
% 1.53/1.23 ( ! [X0 : $i] : ((sK1 != X0) | ((sK4 @ X0) = X0) | (sK1 = (sK4 @ X0))) ) | spl2_1),
% 1.53/1.23 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.53/1.23 thf(f58,plain,(
% 1.53/1.23 ( ! [X0 : $i] : ((sK1 = (sK4 @ X0)) | (sK1 != X0) | ((X0 = (sK4 @ X0)) = $true)) ) | spl2_1),
% 1.53/1.23 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.53/1.23 thf(f54,plain,(
% 1.53/1.23 ( ! [X0 : $i] : (((sK1 = (sK4 @ X0)) = $true) | ((X0 = (sK4 @ X0)) = $true) | (sK1 != X0)) ) | spl2_1),
% 1.53/1.23 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.53/1.23 thf(f53,plain,(
% 1.53/1.23 ( ! [X0 : $i] : (((sK1 = (sK4 @ X0)) != (X0 = (sK4 @ X0))) | (sK1 != X0)) ) | spl2_1),
% 1.53/1.23 inference(negative_extensionality,[status(thm)],[f52])).
% 1.53/1.23 thf(f52,plain,(
% 1.53/1.23 ( ! [X0 : $i] : (((= @ sK1) != (= @ X0)) | (sK1 != X0)) ) | spl2_1),
% 1.53/1.23 inference(constrained_superposition,[status(thm)],[f34,f40])).
% 1.53/1.23 thf(f34,plain,(
% 1.53/1.23 (sK1 != (eps @ (= @ sK1))) | spl2_1),
% 1.53/1.23 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.53/1.23 thf(f32,definition,(
% 1.53/1.23 spl2_1 <=> (sK1 = (eps @ (= @ sK1)))),
% 1.53/1.23 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.53/1.23 thf(f57,plain,(
% 1.53/1.23 ( ! [X0 : $i] : ((sK1 != (sK4 @ X0)) | (sK1 != X0) | ((sK4 @ X0) != X0)) ) | spl2_1),
% 1.53/1.23 inference(equality_proxy_clausification,[status(thm)],[f56])).
% 1.53/1.23 thf(f56,plain,(
% 1.53/1.23 ( ! [X0 : $i] : (((sK1 = (sK4 @ X0)) = $false) | (sK1 != X0) | ((sK4 @ X0) != X0)) ) | spl2_1),
% 1.53/1.23 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 1.53/1.23 thf(f55,plain,(
% 1.53/1.23 ( ! [X0 : $i] : (((X0 = (sK4 @ X0)) = $false) | (sK1 != X0) | ((sK1 = (sK4 @ X0)) = $false)) ) | spl2_1),
% 1.53/1.23 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.53/1.23 thf(f39,plain,(
% 1.53/1.23 ~spl2_1 | ~spl2_2),
% 1.53/1.23 inference(avatar_split_clause,[status(thm)],[f30,f36,f32])).
% 1.53/1.23 thf(f30,plain,(
% 1.53/1.23 (sK0 != (eps @ (= @ sK0))) | (sK1 != (eps @ (= @ sK1)))),
% 1.53/1.23 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.53/1.23 thf(f29,plain,(
% 1.53/1.23 ((eps @ (^[Y0 : $i]: (sK0 = Y0))) != sK0) | (sK1 != (eps @ (= @ sK1)))),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f28])).
% 1.53/1.23 thf(f28,plain,(
% 1.53/1.23 ((eps @ (^[Y0 : $i]: ($false | (sK0 = Y0)))) != sK0) | (sK1 != (eps @ (= @ sK1)))),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f27])).
% 1.53/1.23 thf(f27,plain,(
% 1.53/1.23 (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | (sK0 = Y0))))) | (sK1 != (eps @ (= @ sK1)))),
% 1.53/1.23 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.53/1.23 thf(f26,plain,(
% 1.53/1.23 (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | (sK0 = Y0))))) | ((eps @ (^[Y0 : $i]: (sK1 = Y0))) != sK1)),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f25])).
% 1.53/1.23 thf(f25,plain,(
% 1.53/1.23 (sK1 != (eps @ (^[Y0 : $i]: ($true & (sK1 = Y0))))) | (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | (sK0 = Y0)))))),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f24])).
% 1.53/1.23 thf(f24,plain,(
% 1.53/1.23 ((eps @ (^[Y0 : $i]: (($true & (sK1 = Y0)) | $false))) != sK1) | (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | (sK0 = Y0)))))),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f23])).
% 1.53/1.23 thf(f23,plain,(
% 1.53/1.23 ((eps @ (^[Y0 : $i]: (($true & (sK1 = Y0)) | ((sK0 = Y0) & $false)))) != sK1) | (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | (sK0 = Y0)))))),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f22])).
% 1.53/1.23 thf(f22,plain,(
% 1.53/1.23 (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | ((sK0 = Y0) & $true))))) | ((eps @ (^[Y0 : $i]: (($true & (sK1 = Y0)) | ((sK0 = Y0) & $false)))) != sK1)),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f21])).
% 1.53/1.23 thf(f21,plain,(
% 1.53/1.23 (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | ((sK0 = Y0) & (~ $false)))))) | ((eps @ (^[Y0 : $i]: (($true & (sK1 = Y0)) | ((sK0 = Y0) & $false)))) != sK1)),
% 1.53/1.23 inference(boolean_simplification,[status(thm)],[f20])).
% 1.53/1.23 thf(f20,plain,(
% 1.53/1.23 (sK1 != (eps @ (^[Y0 : $i]: (($true & (sK1 = Y0)) | ((sK0 = Y0) & (~ $true)))))) | (sK0 != (eps @ (^[Y0 : $i]: (($false & (sK1 = Y0)) | ((sK0 = Y0) & (~ $false))))))),
% 1.53/1.23 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.53/1.23 thf(f19,plain,(
% 1.53/1.23 (sK0 != ((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))) @ $false @ sK1 @ sK0)) | (sK1 != ((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))) @ $true @ sK1 @ sK0))),
% 1.53/1.23 inference(definition_unfolding,[status(thm)],[f18,f17,f17])).
% 1.53/1.23 thf(f17,plain,(
% 1.53/1.23 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 1.53/1.23 inference(cnf_transformation,[status(thm)],[f7])).
% 1.53/1.23 thf(f7,plain,(
% 1.53/1.23 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 1.53/1.23 inference(fool_elimination,[status(thm)],[f6])).
% 1.53/1.23 thf(f6,plain,(
% 1.53/1.23 ((^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : ((~X0 & (X2 = X3)) | ((X1 = X3) & X0))))) = if)),
% 1.53/1.23 inference(rectify,[status(thm)],[f2])).
% 1.53/1.23 thf(f2,axiom,(
% 1.53/1.23 ((^[X2 : $o, X1 : $i, X3 : $i] : (eps @ (^[X4 : $i] : ((~X2 & (X3 = X4)) | ((X1 = X4) & X2))))) = if)),
% 1.53/1.23 file('/export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2THF_11231.p',ifd)).
% 1.53/1.23 thf(f18,plain,(
% 1.53/1.23 (sK0 != (if @ $false @ sK1 @ sK0)) | (sK1 != (if @ $true @ sK1 @ sK0))),
% 1.53/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.53/1.23 thf(f15,plain,(
% 1.53/1.23 (sK0 != (if @ $false @ sK1 @ sK0)) | (sK1 != (if @ $true @ sK1 @ sK0))),
% 1.53/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.53/1.23 thf(f14,plain,(
% 1.53/1.23 ? [X0 : $i,X1 : $i] : (((if @ $false @ X1 @ X0) != X0) | ((if @ $true @ X1 @ X0) != X1)) => ((sK0 != (if @ $false @ sK1 @ sK0)) | (sK1 != (if @ $true @ sK1 @ sK0)))),
% 1.53/1.23 introduced(definition,[],[choice_axiom])).
% 1.53/1.23 thf(f13,plain,(
% 1.53/1.23 ? [X0 : $i,X1 : $i] : (((if @ $false @ X1 @ X0) != X0) | ((if @ $true @ X1 @ X0) != X1))),
% 1.53/1.23 inference(ennf_transformation,[status(thm)],[f11])).
% 1.53/1.23 thf(f11,plain,(
% 1.53/1.23 ~! [X0 : $i,X1 : $i] : (((if @ $false @ X1 @ X0) = X0) & ((if @ $true @ X1 @ X0) = X1))),
% 1.53/1.23 inference(fool_elimination,[status(thm)],[f10])).
% 1.53/1.23 thf(f10,plain,(
% 1.53/1.23 ~! [X0 : $i,X1 : $i] : (((if @ $true @ X1 @ X0) = X1) & (X0 = (if @ $false @ X1 @ X0)))),
% 1.53/1.23 inference(rectify,[status(thm)],[f4])).
% 1.53/1.23 thf(f4,negated_conjecture,(
% 1.53/1.23 ~! [X3 : $i,X1 : $i] : (((if @ $true @ X1 @ X3) = X1) & (X3 = (if @ $false @ X1 @ X3)))),
% 1.53/1.23 inference(negated_conjecture,[status(cth)],[f3])).
% 1.53/1.23 thf(f3,conjecture,(
% 1.53/1.23 ! [X3 : $i,X1 : $i] : (((if @ $true @ X1 @ X3) = X1) & (X3 = (if @ $false @ X1 @ X3)))),
% 1.53/1.23 file('/export/starexec/sandbox/tmp/tmp.Tf3JYJb2V1/DTF2THF_11231.p',conj)).
% 1.53/1.23 % SZS output end Proof for DTF2THF_11231
% 1.53/1.23 % (11351)------------------------------
% 1.53/1.23 % (11351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.23 % (11351)Termination reason: Refutation
% 1.53/1.23
% 1.53/1.23 % (11351)Memory used [KB]: 5500
% 1.53/1.23 % (11351)Time elapsed: 0.005 s
% 1.53/1.23 % (11351)Instructions burned: 5 (million)
% 1.53/1.23 % (11351)------------------------------
% 1.53/1.23 % (11351)------------------------------
% 1.53/1.23 % (11344)Success in time 0.007 s
%------------------------------------------------------------------------------