%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO356^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 107 ( 16 ~; 6 |; 6 &; 65 @)
% ( 0 <=>; 14 =>; 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 : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 12 ^; 16 !; 4 ?; 32 :)
% 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 ) > a ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_10,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f38,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f37,f10]) ).
thf(f10,plain,
( ( sK1 @ v )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ u @ v )
= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) )
& ( ( sK1 @ u )
= $true )
& ( ( sK1 @ v )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: a > a > $o] :
( ? [X1: a] :
( ( X0 @ X1 @ X1 )
!= $true )
=> ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X2: a > $o] :
( ( ( X2 @ u )
= $true )
& ( ( X2 @ v )
!= $true ) )
=> ( ( ( sK1 @ u )
= $true )
& ( ( sK1 @ v )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ u @ v )
= $true )
| ? [X1: a] :
( ( X0 @ X1 @ X1 )
!= $true ) )
& ? [X2: a > $o] :
( ( ( X2 @ u )
= $true )
& ( ( X2 @ v )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > a > $o] :
( ! [X1: a] :
( ( X0 @ X1 @ X1 )
= $true )
=> ( ( X0 @ u @ v )
= $true ) )
=> ! [X2: a > $o] :
( ( ( X2 @ u )
= $true )
=> ( ( X2 @ v )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > a > $o] :
( ! [X1: a] : ( X0 @ X1 @ X1 )
=> ( X0 @ u @ v ) )
=> ! [X2: a > $o] :
( ( X2 @ u )
=> ( X2 @ v ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > a > $o] :
( ! [X1: a] : ( X0 @ X1 @ X1 )
=> ( X0 @ u @ v ) )
=> ! [X2: a > $o] :
( ( X2 @ u )
=> ( X2 @ v ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > a > $o] :
( ! [X1: a] : ( X0 @ X1 @ X1 )
=> ( X0 @ u @ v ) )
=> ! [X2: a > $o] :
( ( X2 @ u )
=> ( X2 @ v ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0w9yqq50yJ/DTF2THF_32260.p',cE1LEIBEQ2_pme) ).
thf(f37,plain,
( ( sK1 @ v )
= $true ),
inference(superposition,[status(thm)],[f11,f23]) ).
thf(f23,plain,
u = v,
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( v = u ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true != $true )
| ( $true
= ( v = u ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ( sK0
@ ^ [Y0: a,Y1: a] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: a,Y1: a] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true
= ( v = u ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a,Y1: a] : ( Y1 = Y0 )
@ u
@ v )
= $true )
| ( $true
!= ( ^ [Y0: a,Y1: a] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: a,Y1: a] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: a,Y1: a] : ( Y1 = Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: a > a > $o] :
( ( $true
!= ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
| ( ( X0 @ u @ v )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( ( sK1 @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO356^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:28:29 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO356^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : TPS problem E1LEIBEQ2
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Example from [Ben9] about alternative defns of equality.
% 0.19/0.45
% 0.19/0.45 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0196 [Bro09]
% 0.19/0.45 % : E1LEIBEQ2 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.08 v9.1.0, 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v5.4.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.45 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 6 @)
% 0.19/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.19/0.45 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(v,type,
% 0.19/0.45 v: a ).
% 0.19/0.45
% 0.19/0.45 thf(u,type,
% 0.19/0.45 u: a ).
% 0.19/0.45
% 0.19/0.45 thf(cE1LEIBEQ2_pme,conjecture,
% 0.19/0.45 ( ! [Q: a > a > $o] :
% 0.19/0.45 ( ! [Z: a] : ( Q @ Z @ Z )
% 0.19/0.45 => ( Q @ u @ v ) )
% 0.19/0.45 => ! [Xq: a > $o] :
% 0.19/0.45 ( ( Xq @ u )
% 0.19/0.45 => ( Xq @ v ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 14:28:30 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.0w9yqq50yJ/DTF2DTF32260.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(a_type,type,
% 1.48/1.27 a: $tType ).
% 1.48/1.27
% 1.48/1.27 thf(v,type,
% 1.48/1.27 v: a ).
% 1.48/1.27
% 1.48/1.27 thf(u,type,
% 1.48/1.27 u: a ).
% 1.48/1.27
% 1.48/1.27 thf(cE1LEIBEQ2_pme,conjecture,
% 1.48/1.27 ( ! [Q: a > a > $o] :
% 1.48/1.27 ( ! [Z: a] : ( Q @ Z @ Z )
% 1.48/1.27 => ( Q @ u @ v ) )
% 1.48/1.27 => ! [Xq: a > $o] :
% 1.48/1.27 ( ( Xq @ u )
% 1.48/1.27 => ( Xq @ v ) ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.29 % (32421)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32260 for (2999ds/183Mi)
% 1.48/1.29 % (32424)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32260 for (2999ds/2Mi)
% 1.48/1.29 % (32424)Instruction limit reached!
% 1.48/1.29 % (32424)------------------------------
% 1.48/1.29 % (32424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (32424)Termination reason: Unknown
% 1.48/1.29 % (32424)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (32424)Memory used [KB]: 5500
% 1.48/1.29 % (32424)Time elapsed: 0.002 s
% 1.48/1.29 % (32424)Instructions burned: 3 (million)
% 1.48/1.29 % (32424)------------------------------
% 1.48/1.29 % (32424)------------------------------
% 1.48/1.29 % (32421)First to succeed.
% 1.48/1.29 % (32421)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_32260
% 1.48/1.29 % SZS output start Proof for DTF2THF_32260
% 1.48/1.29 thf(type_def_5, type, a: $tType).
% 1.48/1.29 thf(func_def_0, type, a: $tType).
% 1.48/1.29 thf(func_def_1, type, v: a).
% 1.48/1.29 thf(func_def_2, type, u: a).
% 1.48/1.29 thf(func_def_6, type, sK0: (a > a > $o) > a).
% 1.48/1.29 thf(func_def_7, type, sK1: a > $o).
% 1.48/1.29 thf(func_def_10, type, ph3: !>[X0: $tType]:(X0)).
% 1.48/1.29 thf(f38,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f37,f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ((sK1 @ v) != $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ! [X0 : a > a > $o] : (((X0 @ u @ v) = $true) | ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0)))) & (((sK1 @ u) = $true) & ((sK1 @ v) != $true))),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ! [X0 : a > a > $o] : (? [X1 : a] : ((X0 @ X1 @ X1) != $true) => ($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 ? [X2 : a > $o] : (((X2 @ u) = $true) & ((X2 @ v) != $true)) => (((sK1 @ u) = $true) & ((sK1 @ v) != $true))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ! [X0 : a > a > $o] : (((X0 @ u @ v) = $true) | ? [X1 : a] : ((X0 @ X1 @ X1) != $true)) & ? [X2 : a > $o] : (((X2 @ u) = $true) & ((X2 @ v) != $true))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ~(! [X0 : a > a > $o] : (! [X1 : a] : ((X0 @ X1 @ X1) = $true) => ((X0 @ u @ v) = $true)) => ! [X2 : a > $o] : (((X2 @ u) = $true) => ((X2 @ v) = $true)))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,plain,(
% 1.48/1.29 ~(! [X0 : a > a > $o] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : a > $o] : ((X2 @ u) => (X2 @ v)))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,negated_conjecture,(
% 1.48/1.29 ~(! [X0 : a > a > $o] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : a > $o] : ((X2 @ u) => (X2 @ v)))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.29 thf(f1,conjecture,(
% 1.48/1.29 ! [X0 : a > a > $o] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : a > $o] : ((X2 @ u) => (X2 @ v))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.0w9yqq50yJ/DTF2THF_32260.p',cE1LEIBEQ2_pme)).
% 1.48/1.29 thf(f37,plain,(
% 1.48/1.29 ((sK1 @ v) = $true)),
% 1.48/1.29 inference(superposition,[status(thm)],[f11,f23])).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 (u = v)),
% 1.48/1.29 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 ($true = (v = u))),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 ($true != $true) | ($true = (v = u))),
% 1.48/1.29 inference(boolean_simplification,[status(thm)],[f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 (((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1 = Y0)))))) != $true) | ($true = (v = u))),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 (((^[Y0 : a]: ((^[Y1 : a]: (Y1 = Y0)))) @ u @ v) = $true) | ($true != ((^[Y0 : a]: ((^[Y1 : a]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1 = Y0))))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1 = Y0)))))))),
% 1.48/1.29 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ( ! [X0 : a > a > $o] : (($true != (X0 @ (sK0 @ X0) @ (sK0 @ X0))) | ((X0 @ u @ v) = $true)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ((sK1 @ u) = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_32260
% 1.48/1.29 % (32421)------------------------------
% 1.48/1.29 % (32421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (32421)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (32421)Memory used [KB]: 5500
% 1.48/1.29 % (32421)Time elapsed: 0.004 s
% 1.48/1.29 % (32421)Instructions burned: 2 (million)
% 1.48/1.29 % (32421)------------------------------
% 1.48/1.29 % (32421)------------------------------
% 1.48/1.29 % (32418)Success in time 0.014 s
%------------------------------------------------------------------------------