%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU945^5 : 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 : 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 09:37:49 AM UTC 2026
% Result : Theorem 1.27s 1.09s
% Output : Refutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 81 ( 12 ~; 6 |; 4 &; 55 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 26 ^; 21 !; 7 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $i > $i > $o ) > $i ).
thf(func_def_4,type,
sK1: ( $i > $i > $o ) > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f73,plain,
$false,
inference(equality_resolution,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $i] :
( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
!= X0 ),
inference(duplicate_literal_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: $i] :
( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
!= X0 )
| ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
!= X0 ) ),
inference(superposition,[status(thm)],[f9,f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= X1 )
| ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
!= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
!= X1 )
| ( $true
= ( X1
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( ( X1
= ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= $false )
| ( $true
= ( X1
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ X1 ) ) ),
inference(primitive_instantiation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK0 @ X0 ) @ X1 ) )
| ( ( X0 @ ( sK1 @ X0 ) @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( X0 @ ( sK1 @ X0 ) @ X1 )
= ( X0 @ ( sK0 @ X0 ) @ X1 ) ),
inference(argument_congruence,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $i > $o] :
( ( X0 @ ( sK1 @ X0 ) )
= ( X0 @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $i > $o] :
( ( ( sK0 @ X0 )
!= ( sK1 @ X0 ) )
& ( ( X0 @ ( sK1 @ X0 ) )
= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6]) ).
thf(f6,plain,
! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= ( X0 @ X2 ) ) )
=> ( ( ( sK0 @ X0 )
!= ( sK1 @ X0 ) )
& ( ( X0 @ ( sK1 @ X0 ) )
= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f5,plain,
! [X0: $i > $i > $o] :
? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= ( X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.P0sGKe4LAu/DTF2THF_28233.p',cTHM3_pme) ).
thf(f9,plain,
! [X0: $i > $i > $o] :
( ( sK0 @ X0 )
!= ( sK1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU945^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.26 % Computer : n020.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue Feb 24 12:36:57 EST 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.26 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 ---- Original DTF file ---
% 0.08/0.34 thf(spec,logic,$$dhol).
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 % File : SEU945^5 : TPTP v9.2.1. Released v4.0.0.
% 0.08/0.34 % Domain : Set Theory (Functions)
% 0.08/0.34 % Problem : TPS problem THM3
% 0.08/0.34 % Version : Especial.
% 0.08/0.34 % English :
% 0.08/0.34
% 0.08/0.34 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.08/0.34 % Source : [Bro09]
% 0.08/0.34 % Names : tps_0515 [Bro09]
% 0.08/0.34 % : THM3 [TPS]
% 0.08/0.34 % : THM3-TPS2 [TPS]
% 0.08/0.34
% 0.08/0.34 % Status : Theorem
% 0.08/0.34 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.43 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, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.08/0.34 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.08/0.34 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.08/0.34 % Maximal formula atoms : 2 ( 2 avg)
% 0.08/0.34 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 2 @)
% 0.08/0.34 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.08/0.34 % Maximal formula depth : 5 ( 5 avg)
% 0.08/0.34 % Number of types : 2 ( 0 usr)
% 0.08/0.34 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.08/0.34 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.08/0.34 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.08/0.34 % SPC : TH0_THM_EQU_NAR
% 0.08/0.34
% 0.08/0.34 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.08/0.34 % project in the Department of Mathematical Sciences at Carnegie
% 0.08/0.34 % Mellon University. Distributed under the Creative Commons copyleft
% 0.08/0.34 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.08/0.34 % : Polymorphic definitions expanded.
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 thf(cTHM3_pme,conjecture,
% 0.08/0.34 ? [Xf: $i > $i > $o] :
% 0.08/0.34 ! [Xx: $i,Xy: $i] :
% 0.08/0.34 ( ( ( Xf @ Xx )
% 0.08/0.34 = ( Xf @ Xy ) )
% 0.08/0.34 => ( Xx = Xy ) ) ).
% 0.08/0.34
% 0.08/0.34 %------------------------------------------------------------------------------
% 0.08/0.34 ------------------------
% 1.27/1.06 ---- Embedded in THF ---
% 1.27/1.06 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.27/1.06 %%% Generated on Tue Feb 24 12:36:57 EST 2026
% 1.27/1.06 %%% using '$$dhol' embedding, version 1.3.0.
% 1.27/1.06 %%% Logic specification used:
% 1.27/1.06 %%% thf(spec, logic, $$dhol).
% 1.27/1.06
% 1.27/1.06 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.P0sGKe4LAu/DTF2DTF28233.p
% See solution above
% 1.27/1.06 ------------------------
% 1.27/1.07 ---- Cleaned THF ---
% 1.27/1.08 thf(cTHM3_pme,conjecture,
% 1.27/1.08 ? [Xf: $i > $i > $o] :
% 1.27/1.08 ! [Xx: $i,Xy: $i] :
% 1.27/1.08 ( ( ( Xf @ Xx )
% 1.27/1.08 = ( Xf @ Xy ) )
% 1.27/1.08 => ( Xx = Xy ) ) ).
% 1.27/1.08 ------------------------
% 1.27/1.09 % (28471)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_28233 for (2999ds/275Mi)
% 1.27/1.09 % (28469)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28233 for (2999ds/2Mi)
% 1.27/1.09 % (28469)Instruction limit reached!
% 1.27/1.09 % (28469)------------------------------
% 1.27/1.09 % (28469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.09 % (28469)Termination reason: Unknown
% 1.27/1.09 % (28469)Termination phase: Saturation
% 1.27/1.09
% 1.27/1.09 % (28469)Memory used [KB]: 5500
% 1.27/1.09 % (28469)Time elapsed: 0.002 s
% 1.27/1.09 % (28469)Instructions burned: 2 (million)
% 1.27/1.09 % (28469)------------------------------
% 1.27/1.09 % (28469)------------------------------
% 1.27/1.09 % (28471)First to succeed.
% 1.27/1.09 % (28471)Refutation found. Thanks to Tanya!
% 1.27/1.09 % SZS status Theorem for DTF2THF_28233
% 1.27/1.09 % SZS output start Proof for DTF2THF_28233
% 1.27/1.09 thf(func_def_3, type, sK0: ($i > $i > $o) > $i).
% 1.27/1.09 thf(func_def_4, type, sK1: ($i > $i > $o) > $i).
% 1.27/1.09 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.27/1.09 thf(f73,plain,(
% 1.27/1.09 $false),
% 1.27/1.09 inference(equality_resolution,[status(thm)],[f57])).
% 1.27/1.09 thf(f57,plain,(
% 1.27/1.09 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) != X0)) )),
% 1.27/1.09 inference(duplicate_literal_removal,[status(thm)],[f52])).
% 1.27/1.09 thf(f52,plain,(
% 1.27/1.09 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) != X0) | ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) != X0)) )),
% 1.27/1.09 inference(superposition,[status(thm)],[f9,f21])).
% 1.27/1.09 thf(f21,plain,(
% 1.27/1.09 ( ! [X1 : $i] : (((sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = X1) | ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) != X1)) )),
% 1.27/1.09 inference(equality_proxy_clausification,[status(thm)],[f20])).
% 1.27/1.09 thf(f20,plain,(
% 1.27/1.09 ( ! [X1 : $i] : (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) != X1) | ($true = (X1 = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))))) )),
% 1.27/1.09 inference(equality_proxy_clausification,[status(thm)],[f19])).
% 1.27/1.09 thf(f19,plain,(
% 1.27/1.09 ( ! [X1 : $i] : (((X1 = (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = $false) | ($true = (X1 = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))))) )),
% 1.27/1.09 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.27/1.09 thf(f13,plain,(
% 1.27/1.09 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ X1)) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ X1))) )),
% 1.27/1.09 inference(primitive_instantiation,[status(thm)],[f11])).
% 1.27/1.09 thf(f11,plain,(
% 1.27/1.09 ( ! [X0 : $i > $i > $o,X1 : $i] : (($false = (X0 @ (sK0 @ X0) @ X1)) | ((X0 @ (sK1 @ X0) @ X1) = $true)) )),
% 1.27/1.09 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.27/1.09 thf(f10,plain,(
% 1.27/1.09 ( ! [X0 : $i > $i > $o,X1 : $i] : (((X0 @ (sK1 @ X0) @ X1) = (X0 @ (sK0 @ X0) @ X1))) )),
% 1.27/1.09 inference(argument_congruence,[status(thm)],[f8])).
% 1.27/1.09 thf(f8,plain,(
% 1.27/1.09 ( ! [X0 : $i > $i > $o] : (((X0 @ (sK1 @ X0)) = (X0 @ (sK0 @ X0)))) )),
% 1.27/1.09 inference(cnf_transformation,[status(thm)],[f7])).
% 1.27/1.09 thf(f7,plain,(
% 1.27/1.09 ! [X0 : $i > $i > $o] : (((sK0 @ X0) != (sK1 @ X0)) & ((X0 @ (sK1 @ X0)) = (X0 @ (sK0 @ X0))))),
% 1.27/1.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6])).
% 1.27/1.09 thf(f6,plain,(
% 1.27/1.09 ! [X0 : $i > $i > $o] : (? [X1 : $i,X2 : $i] : ((X1 != X2) & ((X0 @ X1) = (X0 @ X2))) => (((sK0 @ X0) != (sK1 @ X0)) & ((X0 @ (sK1 @ X0)) = (X0 @ (sK0 @ X0)))))),
% 1.27/1.09 introduced(definition,[],[choice_axiom])).
% 1.27/1.09 thf(f5,plain,(
% 1.27/1.09 ! [X0 : $i > $i > $o] : ? [X1 : $i,X2 : $i] : ((X1 != X2) & ((X0 @ X1) = (X0 @ X2)))),
% 1.27/1.09 inference(ennf_transformation,[status(thm)],[f4])).
% 1.27/1.09 thf(f4,plain,(
% 1.27/1.09 ~? [X0 : $i > $i > $o] : ! [X1 : $i,X2 : $i] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.27/1.09 inference(rectify,[status(thm)],[f2])).
% 1.27/1.09 thf(f2,negated_conjecture,(
% 1.27/1.09 ~? [X0 : $i > $i > $o] : ! [X2 : $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.27/1.09 inference(negated_conjecture,[status(cth)],[f1])).
% 1.27/1.09 thf(f1,conjecture,(
% 1.27/1.09 ? [X0 : $i > $i > $o] : ! [X2 : $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2))),
% 1.27/1.09 file('/export/starexec/sandbox2/tmp/tmp.P0sGKe4LAu/DTF2THF_28233.p',cTHM3_pme)).
% 1.27/1.09 thf(f9,plain,(
% 1.27/1.09 ( ! [X0 : $i > $i > $o] : (((sK0 @ X0) != (sK1 @ X0))) )),
% 1.27/1.09 inference(cnf_transformation,[status(thm)],[f7])).
% 1.27/1.09 % SZS output end Proof for DTF2THF_28233
% 1.27/1.09 % (28471)------------------------------
% 1.27/1.09 % (28471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.09 % (28471)Termination reason: Refutation
% 1.27/1.09
% 1.27/1.09 % (28471)Memory used [KB]: 5500
% 1.27/1.09 % (28471)Time elapsed: 0.005 s
% 1.27/1.09 % (28471)Instructions burned: 10 (million)
% 1.27/1.09 % (28471)------------------------------
% 1.27/1.09 % (28471)------------------------------
% 1.27/1.09 % (28465)Success in time 0.015 s
%------------------------------------------------------------------------------