%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO363^5 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:02 AM UTC 2026
% Result : Theorem 1.32s 1.12s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 157 ( 17 ~; 1 |; 18 &; 112 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 31 !; 4 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
j: a > a ).
thf(func_def_2,type,
g: ( a > a ) > a > a ).
thf(func_def_3,type,
h: a > a ).
thf(func_def_4,type,
f: ( a > a ) > a > a ).
thf(func_def_8,type,
sK0: ( a > a ) > $o ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_12,type,
sK4: a ).
thf(f21,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f20,f12]) ).
thf(f12,plain,
! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( sK0 @ ( f @ h ) ) )
& ( ( sK0 @ ( g @ j ) )
!= $true )
& ! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) )
& ! [X2: a,X3: a > a] :
( ( g @ X3 @ X2 )
= ( f @ X3 @ X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: ( a > a ) > $o] :
( ( $true
= ( X0 @ ( f @ h ) ) )
& ( $true
!= ( X0 @ ( g @ j ) ) ) )
=> ( ( $true
= ( sK0 @ ( f @ h ) ) )
& ( ( sK0 @ ( g @ j ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: ( a > a ) > $o] :
( ( $true
= ( X0 @ ( f @ h ) ) )
& ( $true
!= ( X0 @ ( g @ j ) ) ) )
& ! [X1: a] :
( ( h @ X1 )
= ( j @ X1 ) )
& ! [X2: a,X3: a > a] :
( ( g @ X3 @ X2 )
= ( f @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X3: ( a > a ) > $o] :
( ( ( X3 @ ( f @ h ) )
= $true )
& ( ( X3 @ ( g @ j ) )
!= $true ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) )
& ! [X1: a,X0: a > a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X3: ( a > a ) > $o] :
( ( ( X3 @ ( f @ h ) )
= $true )
& ( ( X3 @ ( g @ j ) )
!= $true ) )
& ! [X1: a,X0: a > a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X1: a,X0: a > a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ) )
=> ! [X3: ( a > a ) > $o] :
( ( ( X3 @ ( f @ h ) )
= $true )
=> ( ( X3 @ ( g @ j ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a > a,X1: a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ) )
=> ! [X3: ( a > a ) > $o] :
( ( X3 @ ( f @ h ) )
=> ( X3 @ ( g @ j ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a > a,X1: a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ) )
=> ! [X3: ( a > a ) > $o] :
( ( X3 @ ( f @ h ) )
=> ( X3 @ ( g @ j ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a > a,X1: a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ) )
=> ! [X3: ( a > a ) > $o] :
( ( X3 @ ( f @ h ) )
=> ( X3 @ ( g @ j ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.amHjJrLz40/DTF2THF_10166.p',cEDEC2_pme) ).
thf(f20,plain,
( ( h @ sK4 )
!= ( j @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f19]) ).
thf(f19,plain,
h != j,
inference(equality_resolution,[status(thm)],[f18]) ).
thf(f18,plain,
( ( g @ h @ sK3 )
!= ( g @ j @ sK3 ) ),
inference(superposition,[status(thm)],[f17,f11]) ).
thf(f11,plain,
! [X2: a,X3: a > a] :
( ( g @ X3 @ X2 )
= ( f @ X3 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f17,plain,
( ( f @ h @ sK3 )
!= ( g @ j @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( f @ h )
!= ( g @ j ) )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f13,f14]) ).
thf(f14,plain,
( $true
= ( sK0 @ ( f @ h ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
( ( sK0 @ ( g @ j ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO363^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n020.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 14:28:57 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SYO363^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Syntactic
% 0.16/0.42 % Problem : TPS problem EDEC2
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English : EDEC from [Ben99], using Primeq in the antecedent instead of
% 0.16/0.42 % Leibeq.
% 0.16/0.42
% 0.16/0.42 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.16/0.42 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0469 [Bro09]
% 0.16/0.42 % : EDEC2 [TPS]
% 0.16/0.42 % : EDEC [Ben99]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.3.0, 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, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.16/0.42 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.42 % Number of connectives : 13 ( 0 ~; 0 |; 1 &; 10 @)
% 0.16/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 6 ( 6 avg)
% 0.16/0.42 % Number of types : 2 ( 1 usr)
% 0.16/0.42 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.16/0.42 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % : Polymorphic definitions expanded.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(a_type,type,
% 0.16/0.42 a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(j,type,
% 0.16/0.42 j: a > a ).
% 0.16/0.42
% 0.16/0.42 thf(g,type,
% 0.16/0.42 g: ( a > a ) > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(h,type,
% 0.16/0.42 h: a > a ).
% 0.16/0.42
% 0.16/0.42 thf(f,type,
% 0.16/0.42 f: ( a > a ) > a > a ).
% 0.16/0.42
% 0.16/0.42 thf(cEDEC2_pme,conjecture,
% 0.16/0.42 ( ( ! [X: a > a,Y: a] :
% 0.16/0.42 ( ( f @ X @ Y )
% 0.16/0.42 = ( g @ X @ Y ) )
% 0.16/0.42 & ! [Z: a] :
% 0.16/0.42 ( ( h @ Z )
% 0.16/0.42 = ( j @ Z ) ) )
% 0.16/0.42 => ! [Xq: ( a > a ) > $o] :
% 0.16/0.42 ( ( Xq @ ( f @ h ) )
% 0.16/0.42 => ( Xq @ ( g @ j ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.11/1.10 ---- Embedded in THF ---
% 1.11/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.11/1.10 %%% Generated on Tue Feb 24 14:28:57 EST 2026
% 1.11/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.11/1.10 %%% Logic specification used:
% 1.11/1.10 %%% thf(spec, logic, $$dhol).
% 1.11/1.10
% 1.11/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.amHjJrLz40/DTF2DTF10166.p
% See solution above
% 1.11/1.10 ------------------------
% 1.11/1.10 ---- Cleaned THF ---
% 1.11/1.10 thf(a_type,type,
% 1.11/1.10 a: $tType ).
% 1.11/1.10
% 1.11/1.10 thf(j,type,
% 1.11/1.10 j: a > a ).
% 1.11/1.10
% 1.11/1.10 thf(g,type,
% 1.11/1.10 g: ( a > a ) > a > a ).
% 1.11/1.10
% 1.11/1.10 thf(h,type,
% 1.11/1.10 h: a > a ).
% 1.11/1.10
% 1.11/1.10 thf(f,type,
% 1.11/1.10 f: ( a > a ) > a > a ).
% 1.11/1.10
% 1.11/1.10 thf(cEDEC2_pme,conjecture,
% 1.11/1.10 ( ( ! [X: a > a,Y: a] :
% 1.11/1.10 ( ( f @ X @ Y )
% 1.11/1.10 = ( g @ X @ Y ) )
% 1.11/1.10 & ! [Z: a] :
% 1.11/1.10 ( ( h @ Z )
% 1.11/1.10 = ( j @ Z ) ) )
% 1.11/1.10 => ! [Xq: ( a > a ) > $o] :
% 1.11/1.10 ( ( Xq @ ( f @ h ) )
% 1.11/1.10 => ( Xq @ ( g @ j ) ) ) ) ).
% 1.11/1.10 ------------------------
% 1.32/1.12 % (10266)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10166 for (3000ds/183Mi)
% 1.32/1.12 % (10266)First to succeed.
% 1.32/1.12 % (10266)Refutation found. Thanks to Tanya!
% 1.32/1.12 % SZS status Theorem for DTF2THF_10166
% 1.32/1.12 % SZS output start Proof for DTF2THF_10166
% 1.32/1.12 thf(type_def_5, type, a: $tType).
% 1.32/1.12 thf(func_def_0, type, a: $tType).
% 1.32/1.12 thf(func_def_1, type, j: a > a).
% 1.32/1.12 thf(func_def_2, type, g: (a > a) > a > a).
% 1.32/1.12 thf(func_def_3, type, h: a > a).
% 1.32/1.12 thf(func_def_4, type, f: (a > a) > a > a).
% 1.32/1.12 thf(func_def_8, type, sK0: (a > a) > $o).
% 1.32/1.12 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.32/1.12 thf(func_def_11, type, sK3: a).
% 1.32/1.12 thf(func_def_12, type, sK4: a).
% 1.32/1.12 thf(f21,plain,(
% 1.32/1.12 $false),
% 1.32/1.12 inference(subsumption_resolution,[status(thm)],[f20,f12])).
% 1.32/1.12 thf(f12,plain,(
% 1.32/1.12 ( ! [X1 : a] : (((h @ X1) = (j @ X1))) )),
% 1.32/1.12 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.12 thf(f10,plain,(
% 1.32/1.12 (($true = (sK0 @ (f @ h))) & ((sK0 @ (g @ j)) != $true)) & ! [X1 : a] : ((h @ X1) = (j @ X1)) & ! [X2 : a,X3 : a > a] : ((g @ X3 @ X2) = (f @ X3 @ X2))),
% 1.32/1.12 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.32/1.12 thf(f9,plain,(
% 1.32/1.12 ? [X0 : (a > a) > $o] : (($true = (X0 @ (f @ h))) & ($true != (X0 @ (g @ j)))) => (($true = (sK0 @ (f @ h))) & ((sK0 @ (g @ j)) != $true))),
% 1.32/1.12 introduced(definition,[],[choice_axiom])).
% 1.32/1.12 thf(f8,plain,(
% 1.32/1.12 ? [X0 : (a > a) > $o] : (($true = (X0 @ (f @ h))) & ($true != (X0 @ (g @ j)))) & ! [X1 : a] : ((h @ X1) = (j @ X1)) & ! [X2 : a,X3 : a > a] : ((g @ X3 @ X2) = (f @ X3 @ X2))),
% 1.32/1.12 inference(rectify,[status(thm)],[f7])).
% 1.32/1.12 thf(f7,plain,(
% 1.32/1.12 ? [X3 : (a > a) > $o] : (((X3 @ (f @ h)) = $true) & ((X3 @ (g @ j)) != $true)) & ! [X2 : a] : ((h @ X2) = (j @ X2)) & ! [X1 : a,X0 : a > a] : ((f @ X0 @ X1) = (g @ X0 @ X1))),
% 1.32/1.12 inference(flattening,[status(thm)],[f6])).
% 1.32/1.12 thf(f6,plain,(
% 1.32/1.12 ? [X3 : (a > a) > $o] : (((X3 @ (f @ h)) = $true) & ((X3 @ (g @ j)) != $true)) & (! [X1 : a,X0 : a > a] : ((f @ X0 @ X1) = (g @ X0 @ X1)) & ! [X2 : a] : ((h @ X2) = (j @ X2)))),
% 1.32/1.12 inference(ennf_transformation,[status(thm)],[f5])).
% 1.32/1.12 thf(f5,plain,(
% 1.32/1.12 ~((! [X1 : a,X0 : a > a] : ((f @ X0 @ X1) = (g @ X0 @ X1)) & ! [X2 : a] : ((h @ X2) = (j @ X2))) => ! [X3 : (a > a) > $o] : (((X3 @ (f @ h)) = $true) => ((X3 @ (g @ j)) = $true)))),
% 1.32/1.12 inference(fool_elimination,[status(thm)],[f4])).
% 1.32/1.12 thf(f4,plain,(
% 1.32/1.12 ~((! [X0 : a > a,X1 : a] : ((f @ X0 @ X1) = (g @ X0 @ X1)) & ! [X2 : a] : ((h @ X2) = (j @ X2))) => ! [X3 : (a > a) > $o] : ((X3 @ (f @ h)) => (X3 @ (g @ j))))),
% 1.32/1.12 inference(rectify,[status(thm)],[f2])).
% 1.32/1.12 thf(f2,negated_conjecture,(
% 1.32/1.12 ~((! [X0 : a > a,X1 : a] : ((f @ X0 @ X1) = (g @ X0 @ X1)) & ! [X2 : a] : ((h @ X2) = (j @ X2))) => ! [X3 : (a > a) > $o] : ((X3 @ (f @ h)) => (X3 @ (g @ j))))),
% 1.32/1.12 inference(negated_conjecture,[status(cth)],[f1])).
% 1.32/1.12 thf(f1,conjecture,(
% 1.32/1.12 (! [X0 : a > a,X1 : a] : ((f @ X0 @ X1) = (g @ X0 @ X1)) & ! [X2 : a] : ((h @ X2) = (j @ X2))) => ! [X3 : (a > a) > $o] : ((X3 @ (f @ h)) => (X3 @ (g @ j)))),
% 1.32/1.12 file('/export/starexec/sandbox/tmp/tmp.amHjJrLz40/DTF2THF_10166.p',cEDEC2_pme)).
% 1.32/1.12 thf(f20,plain,(
% 1.32/1.12 ((h @ sK4) != (j @ sK4))),
% 1.32/1.12 inference(negative_extensionality,[status(thm)],[f19])).
% 1.32/1.12 thf(f19,plain,(
% 1.32/1.12 (h != j)),
% 1.32/1.12 inference(equality_resolution,[status(thm)],[f18])).
% 1.32/1.12 thf(f18,plain,(
% 1.32/1.12 ((g @ h @ sK3) != (g @ j @ sK3))),
% 1.32/1.12 inference(superposition,[status(thm)],[f17,f11])).
% 1.32/1.12 thf(f11,plain,(
% 1.32/1.12 ( ! [X2 : a,X3 : a > a] : (((g @ X3 @ X2) = (f @ X3 @ X2))) )),
% 1.32/1.12 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.12 thf(f17,plain,(
% 1.32/1.12 ((f @ h @ sK3) != (g @ j @ sK3))),
% 1.32/1.12 inference(negative_extensionality,[status(thm)],[f16])).
% 1.32/1.12 thf(f16,plain,(
% 1.32/1.12 ((f @ h) != (g @ j))),
% 1.32/1.12 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.32/1.12 thf(f15,plain,(
% 1.32/1.12 ((f @ h) != (g @ j)) | ($true != $true)),
% 1.32/1.12 inference(constrained_superposition,[status(thm)],[f13,f14])).
% 1.32/1.12 thf(f14,plain,(
% 1.32/1.12 ($true = (sK0 @ (f @ h)))),
% 1.32/1.12 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.12 thf(f13,plain,(
% 1.32/1.12 ((sK0 @ (g @ j)) != $true)),
% 1.32/1.12 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.12 % SZS output end Proof for DTF2THF_10166
% 1.32/1.12 % (10266)------------------------------
% 1.32/1.12 % (10266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.12 % (10266)Termination reason: Refutation
% 1.32/1.12
% 1.32/1.12 % (10266)Memory used [KB]: 5500
% 1.32/1.12 % (10266)Time elapsed: 0.003 s
% 1.32/1.12 % (10266)Instructions burned: 3 (million)
% 1.32/1.12 % (10266)------------------------------
% 1.32/1.12 % (10266)------------------------------
% 1.32/1.12 % (10265)Success in time 0.012 s
%------------------------------------------------------------------------------