%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN998^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:51:42 AM UTC 2026
% Result : Theorem 1.50s 1.26s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 66 ( 11 ~; 0 |; 0 &; 43 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 3 usr; 4 con; 0-2 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 24 ( 16 ^; 6 !; 2 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_12,type,
sK2: $i > $o ).
thf(f19,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: $i > $o] : $true
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : $true ) ),
inference(boolean_simplification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f12,f13]) ).
thf(f13,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox2/tmp/tmp.ePhUT1vSHi/DTF2THF_17811.p',leibeq) ).
thf(f12,plain,
( ( leibeq @ sK0 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( leibeq @ sK0 @ sK0 )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( leibeq @ X0 @ X0 )
!= $true )
=> ( ( leibeq @ sK0 @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i] :
( ( leibeq @ X0 @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i] :
( ( leibeq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i] : ( leibeq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] : ( leibeq @ X0 @ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i] : ( leibeq @ X0 @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.ePhUT1vSHi/DTF2THF_17811.p',conj) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN998^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n009.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:21:40 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SYN998^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.45 % Domain : Syntactic
% 0.31/0.45 % Problem : Leibniz equality is reflexive
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.31/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Ben09]
% 0.31/0.45 % Names : Example 6a [BB05]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.45 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.31/0.45 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.31/0.45 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.31/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 4 ( 3 avg)
% 0.31/0.45 % Number of types : 2 ( 0 usr)
% 0.31/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.31/0.45 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.31/0.45 % SPC : TH0_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments :
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(leibeq_decl,type,
% 0.31/0.45 leibeq: $i > $i > $o ).
% 0.31/0.45
% 0.31/0.45 thf(leibeq,definition,
% 0.31/0.45 ( leibeq
% 0.31/0.45 = ( ^ [X: $i,Y: $i] :
% 0.31/0.45 ! [P: $i > $o] :
% 0.31/0.45 ( ( P @ X )
% 0.31/0.45 => ( P @ Y ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(conj,conjecture,
% 0.31/0.45 ! [X: $i] : ( leibeq @ X @ X ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.50/1.22 ---- Embedded in THF ---
% 1.50/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.23 %%% Generated on Tue Feb 24 14:21:41 EST 2026
% 1.50/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.23 %%% Logic specification used:
% 1.50/1.23 %%% thf(spec, logic, $$dhol).
% 1.50/1.23
% 1.50/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ePhUT1vSHi/DTF2DTF17811.p
% See solution above
% 1.50/1.23 ------------------------
% 1.50/1.24 ---- Cleaned THF ---
% 1.50/1.24 thf(leibeq_decl,type,
% 1.50/1.24 leibeq: $i > $i > $o ).
% 1.50/1.24
% 1.50/1.24 thf(leibeq,definition,
% 1.50/1.24 ( leibeq
% 1.50/1.24 = ( ^ [X: $i,Y: $i] :
% 1.50/1.24 ! [P: $i > $o] :
% 1.50/1.24 ( ( P @ X )
% 1.50/1.24 => ( P @ Y ) ) ) ) ).
% 1.50/1.24
% 1.50/1.24 thf(conj,conjecture,
% 1.50/1.24 ! [X: $i] : ( leibeq @ X @ X ) ).
% 1.50/1.24 ------------------------
% 1.50/1.25 % (17932)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_17811 for (2999ds/275Mi)
% 1.50/1.25 % (17931)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_17811 for (2999ds/2Mi)
% 1.50/1.25 % (17932)Refutation not found, incomplete strategy
% 1.50/1.25 % (17932)------------------------------
% 1.50/1.25 % (17932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (17932)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.25
% 1.50/1.25
% 1.50/1.25 % (17932)Memory used [KB]: 5373
% 1.50/1.25 % (17932)Time elapsed: 0.002 s
% 1.50/1.25 % (17932)Instructions burned: 1 (million)
% 1.50/1.25 % (17932)------------------------------
% 1.50/1.25 % (17932)------------------------------
% 1.50/1.25 % (17931)Instruction limit reached!
% 1.50/1.25 % (17931)------------------------------
% 1.50/1.25 % (17931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (17931)Termination reason: Unknown
% 1.50/1.25 % (17931)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (17931)Memory used [KB]: 5500
% 1.50/1.25 % (17931)Time elapsed: 0.002 s
% 1.50/1.25 % (17931)Instructions burned: 2 (million)
% 1.50/1.25 % (17931)------------------------------
% 1.50/1.25 % (17931)------------------------------
% 1.50/1.26 % (17928)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_17811 for (2999ds/4Mi)
% 1.50/1.26 % (17927)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17811 for (2999ds/183Mi)
% 1.50/1.26 % (17929)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_17811 for (2999ds/27Mi)
% 1.50/1.26 % (17930)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17811 for (2999ds/2Mi)
% 1.50/1.26 % (17933)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17811 for (2999ds/18Mi)
% 1.50/1.26 % (17927)First to succeed.
% 1.50/1.26 % (17928)Also succeeded, but the first one will report.
% 1.50/1.26 % (17927)Refutation found. Thanks to Tanya!
% 1.50/1.26 % SZS status Theorem for DTF2THF_17811
% 1.50/1.26 % SZS output start Proof for DTF2THF_17811
% 1.50/1.26 thf(func_def_0, type, leibeq: $i > $i > $o).
% 1.50/1.26 thf(func_def_12, type, sK2: $i > $o).
% 1.50/1.26 thf(f19,plain,(
% 1.50/1.26 $false),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.50/1.26 thf(f18,plain,(
% 1.50/1.26 ($true = $false)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.50/1.26 thf(f17,plain,(
% 1.50/1.26 (((^[Y0 : $i > $o]: ($true)) @ sK2) = $false)),
% 1.50/1.26 inference(sigma_clausification,[status(thm)],[f16])).
% 1.50/1.26 thf(f16,plain,(
% 1.50/1.26 ($true != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))))),
% 1.50/1.26 inference(boolean_simplification,[status(thm)],[f15])).
% 1.50/1.26 thf(f15,plain,(
% 1.50/1.26 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK0)))) != $true)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.50/1.26 thf(f14,plain,(
% 1.50/1.26 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK0) != $true)),
% 1.50/1.26 inference(definition_unfolding,[status(thm)],[f12,f13])).
% 1.50/1.26 thf(f13,plain,(
% 1.50/1.26 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f6])).
% 1.50/1.26 thf(f6,plain,(
% 1.50/1.26 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.50/1.26 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.26 thf(f5,plain,(
% 1.50/1.26 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.50/1.26 inference(rectify,[status(thm)],[f1])).
% 1.50/1.26 thf(f1,axiom,(
% 1.50/1.26 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.50/1.26 file('/export/starexec/sandbox2/tmp/tmp.ePhUT1vSHi/DTF2THF_17811.p',leibeq)).
% 1.50/1.26 thf(f12,plain,(
% 1.50/1.26 ((leibeq @ sK0 @ sK0) != $true)),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.26 thf(f11,plain,(
% 1.50/1.26 ((leibeq @ sK0 @ sK0) != $true)),
% 1.50/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.50/1.26 thf(f10,plain,(
% 1.50/1.26 ? [X0 : $i] : ((leibeq @ X0 @ X0) != $true) => ((leibeq @ sK0 @ sK0) != $true)),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f9,plain,(
% 1.50/1.26 ? [X0 : $i] : ((leibeq @ X0 @ X0) != $true)),
% 1.50/1.26 inference(ennf_transformation,[status(thm)],[f8])).
% 1.50/1.26 thf(f8,plain,(
% 1.50/1.26 ~! [X0 : $i] : ((leibeq @ X0 @ X0) = $true)),
% 1.50/1.26 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.26 thf(f7,plain,(
% 1.50/1.26 ~! [X0 : $i] : (leibeq @ X0 @ X0)),
% 1.50/1.26 inference(rectify,[status(thm)],[f3])).
% 1.50/1.26 thf(f3,negated_conjecture,(
% 1.50/1.26 ~! [X0 : $i] : (leibeq @ X0 @ X0)),
% 1.50/1.26 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.26 thf(f2,conjecture,(
% 1.50/1.26 ! [X0 : $i] : (leibeq @ X0 @ X0)),
% 1.50/1.26 file('/export/starexec/sandbox2/tmp/tmp.ePhUT1vSHi/DTF2THF_17811.p',conj)).
% 1.50/1.26 % SZS output end Proof for DTF2THF_17811
% 1.50/1.26 % (17927)------------------------------
% 1.50/1.26 % (17927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (17927)Termination reason: Refutation
% 1.50/1.26
% 1.50/1.26 % (17927)Memory used [KB]: 5373
% 1.50/1.26 % (17927)Time elapsed: 0.003 s
% 1.50/1.26 % (17927)Instructions burned: 1 (million)
% 1.50/1.26 % (17927)------------------------------
% 1.50/1.26 % (17927)------------------------------
% 1.50/1.26 % (17926)Success in time 0.012 s
%------------------------------------------------------------------------------