%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO353^5 : 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 : n027.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 09:54:01 AM UTC 2026
% Result : Theorem 1.33s 1.14s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 28 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 111 ( 17 ~; 5 |; 8 &; 68 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 6 ^; 22 !; 3 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
v: a ).
thf(func_def_2,type,
u: a ).
thf(func_def_6,type,
sK0: a > a > $o ).
thf(func_def_9,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f26,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f12]) ).
thf(f12,plain,
! [X1: a] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: a] :
( $true
= ( sK0 @ X1 @ X1 ) )
& ( ( sK0 @ u @ v )
!= $true )
& ! [X2: a > $o] :
( ( ( X2 @ v )
= $true )
| ( ( X2 @ u )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: a > a > $o] :
( ! [X1: a] :
( ( X0 @ X1 @ X1 )
= $true )
& ( ( X0 @ u @ v )
!= $true ) )
=> ( ! [X1: a] :
( $true
= ( sK0 @ X1 @ X1 ) )
& ( ( sK0 @ u @ v )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ? [X0: a > a > $o] :
( ! [X1: a] :
( ( X0 @ X1 @ X1 )
= $true )
& ( ( X0 @ u @ v )
!= $true ) )
& ! [X2: a > $o] :
( ( ( X2 @ v )
= $true )
| ( ( X2 @ u )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X1: a > a > $o] :
( ! [X2: a] :
( ( X1 @ X2 @ X2 )
= $true )
& ( ( X1 @ u @ v )
!= $true ) )
& ! [X0: a > $o] :
( ( ( X0 @ v )
= $true )
| ( ( X0 @ u )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > $o] :
( ( ( X0 @ u )
= $true )
=> ( ( X0 @ v )
= $true ) )
=> ! [X1: a > a > $o] :
( ! [X2: a] :
( ( X1 @ X2 @ X2 )
= $true )
=> ( ( X1 @ u @ v )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o] :
( ( X0 @ u )
=> ( X0 @ v ) )
=> ! [X1: a > a > $o] :
( ! [X2: a] : ( X1 @ X2 @ X2 )
=> ( X1 @ u @ v ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o] :
( ( X0 @ u )
=> ( X0 @ v ) )
=> ! [X1: a > a > $o] :
( ! [X2: a] : ( X1 @ X2 @ X2 )
=> ( X1 @ u @ v ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > $o] :
( ( X0 @ u )
=> ( X0 @ v ) )
=> ! [X1: a > a > $o] :
( ! [X2: a] : ( X1 @ X2 @ X2 )
=> ( X1 @ u @ v ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8SGHkYfs0N/DTF2THF_1950.p',cE1LEIBEQ1_pme) ).
thf(f21,plain,
( ( sK0 @ u @ u )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: a] :
( sK0
@ ( ^ [Y1: a] : u
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ u ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
!= ( ^ [Y0: a] :
( sK0
@ ( ^ [Y1: a] : u
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ u ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X2: a > $o] :
( ( ( X2 @ v )
= $true )
| ( ( X2 @ u )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( ( sK0 @ u @ v )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO353^5 : TPTP v9.2.1. Released v4.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 14:28:52 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 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 : SYO353^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Syntactic
% 0.16/0.42 % Problem : TPS problem E1LEIBEQ1
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English : Example about alternative defns of equality.
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0101 [Bro09]
% 0.16/0.42 % : E1LEIBEQ1 [TPS]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.42 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.42 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 6 @)
% 0.16/0.42 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 7 ( 7 avg)
% 0.16/0.42 % Number of types : 2 ( 1 usr)
% 0.16/0.42 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.16/0.42 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.16/0.42 % SPC : TH0_THM_NEQ_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(v,type,
% 0.16/0.42 v: a ).
% 0.16/0.42
% 0.16/0.42 thf(u,type,
% 0.16/0.42 u: a ).
% 0.16/0.42
% 0.16/0.42 thf(cE1LEIBEQ1_pme,conjecture,
% 0.16/0.42 ( ! [Xq: a > $o] :
% 0.16/0.42 ( ( Xq @ u )
% 0.16/0.42 => ( Xq @ v ) )
% 0.16/0.42 => ! [Q: a > a > $o] :
% 0.16/0.42 ( ! [Z: a] : ( Q @ Z @ Z )
% 0.16/0.42 => ( Q @ u @ v ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.12/1.12 ---- Embedded in THF ---
% 1.12/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.12 %%% Generated on Tue Feb 24 14:28:52 EST 2026
% 1.12/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.12 %%% Logic specification used:
% 1.12/1.12 %%% thf(spec, logic, $$dhol).
% 1.12/1.12
% 1.12/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8SGHkYfs0N/DTF2DTF1950.p
% See solution above
% 1.12/1.12 ------------------------
% 1.33/1.13 ---- Cleaned THF ---
% 1.33/1.13 thf(a_type,type,
% 1.33/1.13 a: $tType ).
% 1.33/1.13
% 1.33/1.13 thf(v,type,
% 1.33/1.13 v: a ).
% 1.33/1.13
% 1.33/1.13 thf(u,type,
% 1.33/1.13 u: a ).
% 1.33/1.13
% 1.33/1.13 thf(cE1LEIBEQ1_pme,conjecture,
% 1.33/1.13 ( ! [Xq: a > $o] :
% 1.33/1.13 ( ( Xq @ u )
% 1.33/1.13 => ( Xq @ v ) )
% 1.33/1.13 => ! [Q: a > a > $o] :
% 1.33/1.13 ( ! [Z: a] : ( Q @ Z @ Z )
% 1.33/1.13 => ( Q @ u @ v ) ) ) ).
% 1.33/1.13 ------------------------
% 1.33/1.14 % (2048)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1950 for (3000ds/183Mi)
% 1.33/1.14 % (2048)First to succeed.
% 1.33/1.14 % (2048)Refutation found. Thanks to Tanya!
% 1.33/1.14 % SZS status Theorem for DTF2THF_1950
% 1.33/1.14 % SZS output start Proof for DTF2THF_1950
% 1.33/1.14 thf(type_def_5, type, a: $tType).
% 1.33/1.14 thf(func_def_0, type, a: $tType).
% 1.33/1.14 thf(func_def_1, type, v: a).
% 1.33/1.14 thf(func_def_2, type, u: a).
% 1.33/1.14 thf(func_def_6, type, sK0: a > a > $o).
% 1.33/1.14 thf(func_def_9, type, ph2: !>[X0: $tType]:(X0)).
% 1.33/1.14 thf(f26,plain,(
% 1.33/1.14 $false),
% 1.33/1.14 inference(subsumption_resolution,[status(thm)],[f21,f12])).
% 1.33/1.14 thf(f12,plain,(
% 1.33/1.14 ( ! [X1 : a] : (($true = (sK0 @ X1 @ X1))) )),
% 1.33/1.14 inference(cnf_transformation,[status(thm)],[f9])).
% 1.33/1.14 thf(f9,plain,(
% 1.33/1.14 (! [X1 : a] : ($true = (sK0 @ X1 @ X1)) & ((sK0 @ u @ v) != $true)) & ! [X2 : a > $o] : (((X2 @ v) = $true) | ((X2 @ u) != $true))),
% 1.33/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.33/1.14 thf(f8,plain,(
% 1.33/1.14 ? [X0 : a > a > $o] : (! [X1 : a] : ((X0 @ X1 @ X1) = $true) & ((X0 @ u @ v) != $true)) => (! [X1 : a] : ($true = (sK0 @ X1 @ X1)) & ((sK0 @ u @ v) != $true))),
% 1.33/1.14 introduced(definition,[],[choice_axiom])).
% 1.33/1.14 thf(f7,plain,(
% 1.33/1.14 ? [X0 : a > a > $o] : (! [X1 : a] : ((X0 @ X1 @ X1) = $true) & ((X0 @ u @ v) != $true)) & ! [X2 : a > $o] : (((X2 @ v) = $true) | ((X2 @ u) != $true))),
% 1.33/1.14 inference(rectify,[status(thm)],[f6])).
% 1.33/1.14 thf(f6,plain,(
% 1.33/1.14 ? [X1 : a > a > $o] : (! [X2 : a] : ((X1 @ X2 @ X2) = $true) & ((X1 @ u @ v) != $true)) & ! [X0 : a > $o] : (((X0 @ v) = $true) | ((X0 @ u) != $true))),
% 1.33/1.14 inference(ennf_transformation,[status(thm)],[f5])).
% 1.33/1.14 thf(f5,plain,(
% 1.33/1.14 ~(! [X0 : a > $o] : (((X0 @ u) = $true) => ((X0 @ v) = $true)) => ! [X1 : a > a > $o] : (! [X2 : a] : ((X1 @ X2 @ X2) = $true) => ((X1 @ u @ v) = $true)))),
% 1.33/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 1.33/1.14 thf(f4,plain,(
% 1.33/1.14 ~(! [X0 : a > $o] : ((X0 @ u) => (X0 @ v)) => ! [X1 : a > a > $o] : (! [X2 : a] : (X1 @ X2 @ X2) => (X1 @ u @ v)))),
% 1.33/1.14 inference(rectify,[status(thm)],[f2])).
% 1.33/1.14 thf(f2,negated_conjecture,(
% 1.33/1.14 ~(! [X0 : a > $o] : ((X0 @ u) => (X0 @ v)) => ! [X1 : a > a > $o] : (! [X2 : a] : (X1 @ X2 @ X2) => (X1 @ u @ v)))),
% 1.33/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.33/1.14 thf(f1,conjecture,(
% 1.33/1.14 ! [X0 : a > $o] : ((X0 @ u) => (X0 @ v)) => ! [X1 : a > a > $o] : (! [X2 : a] : (X1 @ X2 @ X2) => (X1 @ u @ v))),
% 1.33/1.14 file('/export/starexec/sandbox/tmp/tmp.8SGHkYfs0N/DTF2THF_1950.p',cE1LEIBEQ1_pme)).
% 1.33/1.14 thf(f21,plain,(
% 1.33/1.14 ((sK0 @ u @ u) != $true)),
% 1.33/1.14 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.33/1.14 thf(f20,plain,(
% 1.33/1.14 ($true != ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (u)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0))) @ u))),
% 1.33/1.14 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.33/1.14 thf(f18,plain,(
% 1.33/1.14 ($true != ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (u)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0))) @ u)) | ($true != $true)),
% 1.33/1.14 inference(superposition,[status(thm)],[f11,f10])).
% 1.33/1.14 thf(f10,plain,(
% 1.33/1.14 ( ! [X2 : a > $o] : (((X2 @ v) = $true) | ((X2 @ u) != $true)) )),
% 1.33/1.14 inference(cnf_transformation,[status(thm)],[f9])).
% 1.33/1.14 thf(f11,plain,(
% 1.33/1.14 ((sK0 @ u @ v) != $true)),
% 1.33/1.14 inference(cnf_transformation,[status(thm)],[f9])).
% 1.33/1.14 % SZS output end Proof for DTF2THF_1950
% 1.33/1.14 % (2048)------------------------------
% 1.33/1.14 % (2048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.14 % (2048)Termination reason: Refutation
% 1.33/1.14
% 1.33/1.14 % (2048)Memory used [KB]: 5500
% 1.33/1.14 % (2048)Time elapsed: 0.003 s
% 1.33/1.14 % (2048)Instructions burned: 1 (million)
% 1.33/1.14 % (2048)------------------------------
% 1.33/1.14 % (2048)------------------------------
% 1.33/1.14 % (2047)Success in time 0.012 s
%------------------------------------------------------------------------------