%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYP117^1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 : Tue May 5 07:11:00 PM UTC 2026
% Result : Theorem 1.63s 1.31s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 8 ~; 0 |; 0 &; 18 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 4 ^; 7 !; 4 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
i:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_6,type,
sK1: sK0 ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
sK1 != sK1,
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( sK1
!= ( ^ [Y0: sK0] : Y0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f9,f10]) ).
thf(f10,plain,
! [X0: $tType] :
( i
@ ( X0
= ( ^ [Y0: X0] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $tType] :
( i
@ ( X0
= ( ^ [Y0: X0] : Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType] :
( ( ( ^ [X1: X0] : X1 )
= i )
@ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.a55WJJd25a/DTF2THF_23757.p','trivia/I_DEF_') ).
thf(f9,plain,
( sK1
!= ( i @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( sK1
!= ( i @ sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
!= X1 )
=> ( sK1
!= ( i @ sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
file('/export/starexec/sandbox2/tmp/tmp.a55WJJd25a/DTF2THF_23757.p','trivia/I_THM_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYP117^1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n026.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Mon May 4 17:51:53 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : SYP117^1 : TPTP v9.3.0. Released v9.3.0.
% 0.32/0.47 % Domain : Syntactic
% 0.32/0.47 % Problem : Polymorphic identity defining equation
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English :
% 0.32/0.47
% 0.32/0.47 % Refs :
% 0.32/0.47 % Source : [TPTP]
% 0.32/0.47 % Names : 001 [TPTP]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : ? v9.3.0
% 0.32/0.47 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.32/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.32/0.47 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 3 @)
% 0.32/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 3 ( 3 avg)
% 0.32/0.47 % Number of types : 0 ( 0 usr)
% 0.32/0.47 % Number of type decls : 1 ( 1 !>P; 0 !>D)
% 0.32/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.32/0.47 % Number of variables : 5 ( 1 ^; 3 !; 0 ?; 5 :)
% 0.32/0.47 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.47 % SPC : TH1_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : Originally from HOL Light
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf(i,type,
% 0.32/0.47 i:
% 0.32/0.47 !>[A: $tType] : ( A > A ) ).
% 0.32/0.47
% 0.32/0.47 thf('trivia/I_DEF_',definition,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( i @ A )
% 0.32/0.47 = ( ^ [X: A] : X ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('trivia/I_THM_',conjecture,
% 0.32/0.47 ! [A: $tType,X: A] :
% 0.32/0.47 ( ( i @ A @ X )
% 0.32/0.47 = X ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.45/1.28 ---- Embedded in THF ---
% 1.45/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.28 %%% Generated on Mon May 04 17:51:54 EDT 2026
% 1.45/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.28 %%% Logic specification used:
% 1.45/1.28 %%% thf(spec, logic, $$dhol).
% 1.45/1.28
% 1.45/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.a55WJJd25a/DTF2DTF23757.p
% See solution above
% 1.45/1.28 ------------------------
% 1.45/1.29 ---- Cleaned THF ---
% 1.45/1.29 thf(i,type,
% 1.45/1.29 i:
% 1.45/1.29 !>[A: $tType] : ( A > A ) ).
% 1.45/1.29
% 1.45/1.29 thf('trivia/I_DEF_',definition,
% 1.45/1.29 ! [A: $tType] :
% 1.45/1.29 ( ( i @ A )
% 1.45/1.29 = ( ^ [X: A] : X ) ) ).
% 1.45/1.29
% 1.45/1.29 thf('trivia/I_THM_',conjecture,
% 1.45/1.29 ! [A: $tType,X: A] :
% 1.45/1.29 ( ( i @ A @ X )
% 1.45/1.29 = X ) ).
% 1.45/1.29 ------------------------
% 1.63/1.31 % (24090)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23757 for (2999ds/18Mi)
% 1.63/1.31 % (24090)First to succeed.
% 1.63/1.31 % (24085)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23757 for (2999ds/4Mi)
% 1.63/1.31 % (24090)Refutation found. Thanks to Tanya!
% 1.63/1.31 % SZS status Theorem for DTF2THF_23757
% 1.63/1.31 % SZS output start Proof for DTF2THF_23757
% 1.63/1.31 thf(type_def_6, type, sK0: $tType).
% 1.63/1.31 thf(func_def_0, type, i: !>[X0: $tType]:(X0 > X0)).
% 1.63/1.31 thf(func_def_6, type, sK1: sK0).
% 1.63/1.31 thf(f13,plain,(
% 1.63/1.31 $false),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.63/1.31 thf(f12,plain,(
% 1.63/1.31 (sK1 != sK1)),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.63/1.31 thf(f11,plain,(
% 1.63/1.31 (sK1 != ((^[Y0 : sK0]: (Y0)) @ sK1))),
% 1.63/1.31 inference(definition_unfolding,[status(thm)],[f9,f10])).
% 1.63/1.31 thf(f10,plain,(
% 1.63/1.31 ( ! [X0 : $tType] : ((i @ X0 = (^[Y0 : X0]: (Y0)))) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f5])).
% 1.63/1.31 thf(f5,plain,(
% 1.63/1.31 ! [X0 : $tType] : (i @ X0 = (^[Y0 : X0]: (Y0)))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f1])).
% 1.63/1.31 thf(f1,axiom,(
% 1.63/1.31 ! [X0 : $tType] : ((^[X1 : X0] : (X1)) = i @ X0)),
% 1.63/1.31 file('/export/starexec/sandbox2/tmp/tmp.a55WJJd25a/DTF2THF_23757.p','trivia/I_DEF_')).
% 1.63/1.31 thf(f9,plain,(
% 1.63/1.31 (sK1 != (i @ sK0 @ sK1))),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.31 thf(f8,plain,(
% 1.63/1.31 (sK1 != (i @ sK0 @ sK1))),
% 1.63/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.63/1.31 thf(f7,plain,(
% 1.63/1.31 ? [X0 : $tType,X1 : X0] : ((i @ X0 @ X1) != X1) => (sK1 != (i @ sK0 @ sK1))),
% 1.63/1.31 introduced(definition,[],[choice_axiom])).
% 1.63/1.31 thf(f6,plain,(
% 1.63/1.31 ? [X0 : $tType,X1 : X0] : ((i @ X0 @ X1) != X1)),
% 1.63/1.31 inference(ennf_transformation,[status(thm)],[f3])).
% 1.63/1.31 thf(f3,negated_conjecture,(
% 1.63/1.31 ~! [X0 : $tType,X1 : X0] : ((i @ X0 @ X1) = X1)),
% 1.63/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.31 thf(f2,conjecture,(
% 1.63/1.31 ! [X0 : $tType,X1 : X0] : ((i @ X0 @ X1) = X1)),
% 1.63/1.31 file('/export/starexec/sandbox2/tmp/tmp.a55WJJd25a/DTF2THF_23757.p','trivia/I_THM_')).
% 1.63/1.31 % SZS output end Proof for DTF2THF_23757
% 1.63/1.31 % (24090)------------------------------
% 1.63/1.31 % (24090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (24090)Termination reason: Refutation
% 1.63/1.31
% 1.63/1.31 % (24090)Memory used [KB]: 5373
% 1.63/1.31 % (24090)Time elapsed: 0.002 s
% 1.63/1.31 % (24090)Instructions burned: 1 (million)
% 1.63/1.31 % (24090)------------------------------
% 1.63/1.31 % (24090)------------------------------
% 1.63/1.31 % (24083)Success in time 0.012 s
%------------------------------------------------------------------------------