%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO004^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 09:53:07 AM UTC 2026
% Result : Theorem 0.25s 1.33s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 77 ( 8 ~; 1 |; 4 &; 47 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 32 ( 15 ^; 13 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_14,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f39,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f12]) ).
thf(f12,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( leibeq @ sK1 @ sK0 )
= $true )
& ( sK1 != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( ( leibeq @ X1 @ X0 )
= $true )
& ( X0 != X1 ) )
=> ( ( ( leibeq @ sK1 @ sK0 )
= $true )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i,X1: $i] :
( ( ( leibeq @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i,X1: $i] :
( ( ( leibeq @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i] :
( ( leibeq @ X1 @ X0 )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( leibeq @ X0 @ X1 )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i] :
( ( leibeq @ X0 @ X1 )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.JgjAZjqgnv/DTF2THF_21091.p',conj) ).
thf(f21,plain,
sK1 = sK0,
inference(leibniz_equality_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i > $o] :
( $true
= ( ( X1 @ sK1 )
=> ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f13,f14]) ).
thf(f14,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/sandbox/tmp/tmp.JgjAZjqgnv/DTF2THF_21091.p',leibeq) ).
thf(f13,plain,
( ( leibeq @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO004^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n023.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 14:22:34 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SYO004^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.39 % Domain : Syntactic
% 0.18/0.39 % Problem : Relating Leibniz equality to primitive equality
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English :
% 0.18/0.39
% 0.18/0.39 % Refs : [And72] Andrews (1972), General Models and Extensionality
% 0.18/0.39 % : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.18/0.39 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Ben09]
% 0.18/0.39 % Names : Example 8 [BB05]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.18/0.39 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.18/0.39 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 2 ( 2 avg)
% 0.18/0.39 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.18/0.39 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 6 ( 4 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.39 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : Andrews property q is required
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(leibeq_decl,type,
% 0.18/0.39 leibeq: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(leibeq,definition,
% 0.18/0.39 ( leibeq
% 0.18/0.39 = ( ^ [X: $i,Y: $i] :
% 0.18/0.39 ! [P: $i > $o] :
% 0.18/0.39 ( ( P @ X )
% 0.18/0.39 => ( P @ Y ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(conj,conjecture,
% 0.18/0.39 ! [X: $i,Y: $i] :
% 0.18/0.39 ( ( leibeq @ X @ Y )
% 0.18/0.39 => ( X = Y ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 0.25/1.30 ---- Embedded in THF ---
% 0.25/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.25/1.30 %%% Generated on Tue Feb 24 14:22:35 EST 2026
% 0.25/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.25/1.30 %%% Logic specification used:
% 0.25/1.30 %%% thf(spec, logic, $$dhol).
% 0.25/1.30
% 0.25/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JgjAZjqgnv/DTF2DTF21091.p
% See solution above
% 0.25/1.30 ------------------------
% 0.25/1.31 ---- Cleaned THF ---
% 0.25/1.31 thf(leibeq_decl,type,
% 0.25/1.31 leibeq: $i > $i > $o ).
% 0.25/1.31
% 0.25/1.31 thf(leibeq,definition,
% 0.25/1.31 ( leibeq
% 0.25/1.31 = ( ^ [X: $i,Y: $i] :
% 0.25/1.31 ! [P: $i > $o] :
% 0.25/1.31 ( ( P @ X )
% 0.25/1.31 => ( P @ Y ) ) ) ) ).
% 0.25/1.31
% 0.25/1.31 thf(conj,conjecture,
% 0.25/1.31 ! [X: $i,Y: $i] :
% 0.25/1.31 ( ( leibeq @ X @ Y )
% 0.25/1.31 => ( X = Y ) ) ).
% 0.25/1.31 ------------------------
% 0.25/1.33 % (21190)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_21091 for (3000ds/27Mi)
% 0.25/1.33 % (21191)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21091 for (3000ds/2Mi)
% 0.25/1.33 % (21188)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21091 for (3000ds/183Mi)
% 0.25/1.33 % (21189)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_21091 for (3000ds/4Mi)
% 0.25/1.33 % (21193)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_21091 for (3000ds/275Mi)
% 0.25/1.33 % (21192)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_21091 for (3000ds/2Mi)
% 0.25/1.33 % (21194)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21091 for (3000ds/18Mi)
% 0.25/1.33 % (21191)Instruction limit reached!
% 0.25/1.33 % (21191)------------------------------
% 0.25/1.33 % (21191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (21193)Refutation not found, incomplete strategy
% 0.25/1.33 % (21193)------------------------------
% 0.25/1.33 % (21193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (21193)Termination reason: Refutation not found, incomplete strategy
% 0.25/1.33
% 0.25/1.33
% 0.25/1.33 % (21193)Memory used [KB]: 5500
% 0.25/1.33 % (21193)Time elapsed: 0.002 s
% 0.25/1.33 % (21193)Instructions burned: 1 (million)
% 0.25/1.33 % (21193)------------------------------
% 0.25/1.33 % (21193)------------------------------
% 0.25/1.33 % (21192)Instruction limit reached!
% 0.25/1.33 % (21192)------------------------------
% 0.25/1.33 % (21192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (21191)Termination reason: Unknown
% 0.25/1.33 % (21191)Termination phase: Saturation
% 0.25/1.33
% 0.25/1.33 % (21191)Memory used [KB]: 5500
% 0.25/1.33 % (21191)Time elapsed: 0.003 s
% 0.25/1.33 % (21191)Instructions burned: 2 (million)
% 0.25/1.33 % (21191)------------------------------
% 0.25/1.33 % (21191)------------------------------
% 0.25/1.33 % (21192)Termination reason: Unknown
% 0.25/1.33 % (21192)Termination phase: Saturation
% 0.25/1.33
% 0.25/1.33 % (21192)Memory used [KB]: 5500
% 0.25/1.33 % (21192)Time elapsed: 0.003 s
% 0.25/1.33 % (21192)Instructions burned: 2 (million)
% 0.25/1.33 % (21192)------------------------------
% 0.25/1.33 % (21192)------------------------------
% 0.25/1.33 % (21190)Refutation not found, incomplete strategy
% 0.25/1.33 % (21190)------------------------------
% 0.25/1.33 % (21190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (21190)Termination reason: Refutation not found, incomplete strategy
% 0.25/1.33
% 0.25/1.33
% 0.25/1.33 % (21190)Memory used [KB]: 5500
% 0.25/1.33 % (21190)Time elapsed: 0.003 s
% 0.25/1.33 % (21190)Instructions burned: 2 (million)
% 0.25/1.33 % (21190)------------------------------
% 0.25/1.33 % (21190)------------------------------
% 0.25/1.33 % (21188)First to succeed.
% 0.25/1.33 % (21194)Also succeeded, but the first one will report.
% 0.25/1.33 % (21189)Also succeeded, but the first one will report.
% 0.25/1.33 % (21188)Refutation found. Thanks to Tanya!
% 0.25/1.33 % SZS status Theorem for DTF2THF_21091
% 0.25/1.33 % SZS output start Proof for DTF2THF_21091
% 0.25/1.33 thf(func_def_0, type, leibeq: $i > $i > $o).
% 0.25/1.33 thf(func_def_14, type, ph3: !>[X0: $tType]:(X0)).
% 0.25/1.33 thf(f39,plain,(
% 0.25/1.33 $false),
% 0.25/1.33 inference(subsumption_resolution,[status(thm)],[f21,f12])).
% 0.25/1.33 thf(f12,plain,(
% 0.25/1.33 (sK1 != sK0)),
% 0.25/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 0.25/1.33 thf(f11,plain,(
% 0.25/1.33 ((leibeq @ sK1 @ sK0) = $true) & (sK1 != sK0)),
% 0.25/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 0.25/1.33 thf(f10,plain,(
% 0.25/1.33 ? [X0 : $i,X1 : $i] : (((leibeq @ X1 @ X0) = $true) & (X0 != X1)) => (((leibeq @ sK1 @ sK0) = $true) & (sK1 != sK0))),
% 0.25/1.33 introduced(definition,[],[choice_axiom])).
% 0.25/1.33 thf(f9,plain,(
% 0.25/1.33 ? [X0 : $i,X1 : $i] : (((leibeq @ X1 @ X0) = $true) & (X0 != X1))),
% 0.25/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 0.25/1.33 thf(f8,plain,(
% 0.25/1.33 ~! [X0 : $i,X1 : $i] : (((leibeq @ X1 @ X0) = $true) => (X0 = X1))),
% 0.25/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 0.25/1.33 thf(f7,plain,(
% 0.25/1.33 ~! [X0 : $i,X1 : $i] : ((leibeq @ X1 @ X0) => (X0 = X1))),
% 0.25/1.33 inference(rectify,[status(thm)],[f3])).
% 0.25/1.33 thf(f3,negated_conjecture,(
% 0.25/1.33 ~! [X1 : $i,X0 : $i] : ((leibeq @ X0 @ X1) => (X0 = X1))),
% 0.25/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 0.25/1.33 thf(f2,conjecture,(
% 0.25/1.33 ! [X1 : $i,X0 : $i] : ((leibeq @ X0 @ X1) => (X0 = X1))),
% 0.25/1.33 file('/export/starexec/sandbox/tmp/tmp.JgjAZjqgnv/DTF2THF_21091.p',conj)).
% 0.25/1.33 thf(f21,plain,(
% 0.25/1.33 (sK1 = sK0)),
% 0.25/1.33 inference(leibniz_equality_elimination,[status(thm)],[f19])).
% 0.25/1.33 thf(f19,plain,(
% 0.25/1.33 ( ! [X1 : $i > $o] : (($false = (X1 @ sK1)) | ((X1 @ sK0) = $true)) )),
% 0.25/1.33 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 0.25/1.33 thf(f18,plain,(
% 0.25/1.33 ( ! [X1 : $i > $o] : (($true = ((X1 @ sK1) => (X1 @ sK0)))) )),
% 0.25/1.33 inference(beta_eta_normalization,[status(thm)],[f17])).
% 0.25/1.33 thf(f17,plain,(
% 0.25/1.33 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((Y0 @ sK1) => (Y0 @ sK0))) @ X1))) )),
% 0.25/1.33 inference(pi_clausification,[status(thm)],[f16])).
% 0.25/1.33 thf(f16,plain,(
% 0.25/1.33 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK1) => (Y0 @ sK0)))))),
% 0.25/1.33 inference(beta_eta_normalization,[status(thm)],[f15])).
% 0.25/1.33 thf(f15,plain,(
% 0.25/1.33 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK1 @ sK0))),
% 0.25/1.33 inference(definition_unfolding,[status(thm)],[f13,f14])).
% 0.25/1.33 thf(f14,plain,(
% 0.25/1.33 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.25/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 0.25/1.33 thf(f6,plain,(
% 0.25/1.33 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.25/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 0.25/1.33 thf(f5,plain,(
% 0.25/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 0.25/1.33 inference(rectify,[status(thm)],[f1])).
% 0.25/1.33 thf(f1,axiom,(
% 0.25/1.33 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 0.25/1.33 file('/export/starexec/sandbox/tmp/tmp.JgjAZjqgnv/DTF2THF_21091.p',leibeq)).
% 0.25/1.33 thf(f13,plain,(
% 0.25/1.33 ((leibeq @ sK1 @ sK0) = $true)),
% 0.25/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 0.25/1.33 % SZS output end Proof for DTF2THF_21091
% 0.25/1.33 % (21188)------------------------------
% 0.25/1.33 % (21188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.33 % (21188)Termination reason: Refutation
% 0.25/1.33
% 0.25/1.33 % (21188)Memory used [KB]: 5500
% 0.25/1.33 % (21188)Time elapsed: 0.004 s
% 0.25/1.33 % (21188)Instructions burned: 2 (million)
% 0.25/1.33 % (21188)------------------------------
% 0.25/1.33 % (21188)------------------------------
% 0.25/1.33 % (21187)Success in time 0.017 s
%------------------------------------------------------------------------------