%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO226^5 : 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 : n021.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 09:53:42 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 44 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 102 ( 20 ~; 9 |; 5 &; 58 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 12 ^; 23 !; 11 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
sK2: ( $i > $i > $o ) > $i ).
thf(func_def_8,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f34,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f23,f11]) ).
thf(f11,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X2: $i > $i > $o] :
( ( $true
= ( X2 @ sK0 @ sK1 ) )
| ( $true
!= ( X2 @ ( sK2 @ X2 ) @ ( sK2 @ X2 ) ) ) )
& ( sK0 != sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true ) )
& ( X0 != X1 ) )
=> ( ! [X2: $i > $i > $o] :
( ( $true
= ( X2 @ sK0 @ sK1 ) )
| ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true ) )
& ( sK0 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X2: $i > $i > $o] :
( ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true )
=> ( $true
!= ( X2 @ ( sK2 @ X2 ) @ ( sK2 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ X0 @ X1 )
= $true )
| ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true ) )
& ( X0 != X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: $i,X0: $i] :
( ! [X2: $i > $i > $o] :
( ( ( X2 @ X1 @ X0 )
= $true )
| ? [X3: $i] :
( ( X2 @ X3 @ X3 )
!= $true ) )
& ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: $i,X0: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
=> ( ( X2 @ X1 @ X0 )
= $true ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X1 @ X0 ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1r3A0IJkZD/DTF2THF_3622.p',cTHM47B) ).
thf(f23,plain,
sK0 = sK1,
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( sK1 = sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true != $true )
| ( ( sK1 = sK0 )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( sK1 = sK0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ sK0
@ sK1 )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: $i > $i > $o] :
( ( $true
!= ( X2 @ ( sK2 @ X2 ) @ ( sK2 @ X2 ) ) )
| ( $true
= ( X2 @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO226^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:26:24 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SYO226^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.46 % Domain : Syntactic
% 0.26/0.46 % Problem : TPS problem THM47B
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Bro09]
% 0.26/0.46 % Names : tps_0507 [Bro09]
% 0.26/0.46 % : THM47B [TPS]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0
% 0.26/0.46 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.26/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.26/0.46 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.26/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.26/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(cTHM47B,conjecture,
% 0.26/0.46 ! [X: $i,Y: $i] :
% 0.26/0.46 ( ! [R: $i > $i > $o] :
% 0.26/0.46 ( ! [Z: $i] : ( R @ Z @ Z )
% 0.26/0.46 => ( R @ X @ Y ) )
% 0.26/0.46 => ( X = Y ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 14:26:25 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.1r3A0IJkZD/DTF2DTF3622.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(cTHM47B,conjecture,
% 1.46/1.26 ! [X: $i,Y: $i] :
% 1.46/1.26 ( ! [R: $i > $i > $o] :
% 1.46/1.26 ( ! [Z: $i] : ( R @ Z @ Z )
% 1.46/1.26 => ( R @ X @ Y ) )
% 1.46/1.26 => ( X = Y ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.28 % (3792)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3622 for (3000ds/18Mi)
% 1.46/1.28 % (3787)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3622 for (3000ds/4Mi)
% 1.46/1.28 % (3792)First to succeed.
% 1.46/1.28 % (3788)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3622 for (3000ds/27Mi)
% 1.46/1.28 % (3788)Refutation not found, incomplete strategy
% 1.46/1.28 % (3788)------------------------------
% 1.46/1.28 % (3788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (3788)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.28
% 1.46/1.28
% 1.46/1.28 % (3788)Memory used [KB]: 5500
% 1.46/1.28 % (3788)Time elapsed: 0.001 s
% 1.46/1.28 % (3788)------------------------------
% 1.46/1.28 % (3788)------------------------------
% 1.46/1.28 % (3787)Also succeeded, but the first one will report.
% 1.46/1.28 % (3792)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_3622
% 1.46/1.28 % SZS output start Proof for DTF2THF_3622
% 1.46/1.28 thf(func_def_5, type, sK2: ($i > $i > $o) > $i).
% 1.46/1.28 thf(func_def_8, type, ph4: !>[X0: $tType]:(X0)).
% 1.46/1.28 thf(f34,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(subsumption_resolution,[status(thm)],[f23,f11])).
% 1.46/1.28 thf(f11,plain,(
% 1.46/1.28 (sK0 != sK1)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ! [X2 : $i > $i > $o] : (($true = (X2 @ sK0 @ sK1)) | ($true != (X2 @ (sK2 @ X2) @ (sK2 @ X2)))) & (sK0 != sK1)),
% 1.46/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8])).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 ? [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | ? [X3 : $i] : ((X2 @ X3 @ X3) != $true)) & (X0 != X1)) => (! [X2 : $i > $i > $o] : (($true = (X2 @ sK0 @ sK1)) | ? [X3 : $i] : ((X2 @ X3 @ X3) != $true)) & (sK0 != sK1))),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 ! [X2 : $i > $i > $o] : (? [X3 : $i] : ((X2 @ X3 @ X3) != $true) => ($true != (X2 @ (sK2 @ X2) @ (sK2 @ X2))))),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 ? [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ X0 @ X1) = $true) | ? [X3 : $i] : ((X2 @ X3 @ X3) != $true)) & (X0 != X1))),
% 1.46/1.28 inference(rectify,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 ? [X1 : $i,X0 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ X1 @ X0) = $true) | ? [X3 : $i] : ((X2 @ X3 @ X3) != $true)) & (X0 != X1))),
% 1.46/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.28 thf(f5,plain,(
% 1.46/1.28 ~! [X1 : $i,X0 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : ((X2 @ X3 @ X3) = $true) => ((X2 @ X1 @ X0) = $true)) => (X0 = X1))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,plain,(
% 1.46/1.28 ~! [X0 : $i,X1 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X1 @ X0)) => (X0 = X1))),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,negated_conjecture,(
% 1.46/1.28 ~! [X1 : $i,X0 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) => (X0 = X1))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.28 thf(f1,conjecture,(
% 1.46/1.28 ! [X1 : $i,X0 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) => (X0 = X1))),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.1r3A0IJkZD/DTF2THF_3622.p',cTHM47B)).
% 1.46/1.28 thf(f23,plain,(
% 1.46/1.28 (sK0 = sK1)),
% 1.46/1.28 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.46/1.28 thf(f22,plain,(
% 1.46/1.28 ((sK1 = sK0) = $true)),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.46/1.28 thf(f21,plain,(
% 1.46/1.28 ($true != $true) | ((sK1 = sK0) = $true)),
% 1.46/1.28 inference(boolean_simplification,[status(thm)],[f20])).
% 1.46/1.28 thf(f20,plain,(
% 1.46/1.28 (((sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) != $true) | ((sK1 = sK0) = $true)),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.46/1.28 thf(f13,plain,(
% 1.46/1.28 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ sK0 @ sK1) = $true)),
% 1.46/1.28 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.46/1.28 thf(f12,plain,(
% 1.46/1.28 ( ! [X2 : $i > $i > $o] : (($true != (X2 @ (sK2 @ X2) @ (sK2 @ X2))) | ($true = (X2 @ sK0 @ sK1))) )),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.28 % SZS output end Proof for DTF2THF_3622
% 1.46/1.28 % (3792)------------------------------
% 1.46/1.28 % (3792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (3792)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (3792)Memory used [KB]: 5500
% 1.46/1.28 % (3792)Time elapsed: 0.004 s
% 1.46/1.28 % (3792)Instructions burned: 1 (million)
% 1.46/1.28 % (3792)------------------------------
% 1.46/1.28 % (3792)------------------------------
% 1.46/1.28 % (3785)Success in time 0.004 s
%------------------------------------------------------------------------------