%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWW469^1 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 09:48:04 AM UTC 2026
% Result : Theorem 1.65s 1.48s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 22 ~; 8 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 17 !; 14 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
state: $tType ).
tff(func_def_0,type,
state: $tType ).
tff(func_def_6,type,
sK0: state ).
tff(func_def_7,type,
sK1: state ).
tff(func_def_8,type,
sK2: state ).
tff(f41,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f40,f29]) ).
tff(f29,plain,
! [X1: state] : ( sK0 = X1 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
tff(f24,plain,
! [X1: state] : ( sK0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
tff(f23,plain,
( ? [X0: state] :
! [X1: state] : ( X0 = X1 )
=> ! [X1: state] : ( sK0 = X1 ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f22,plain,
? [X0: state] :
! [X1: state] : ( X0 = X1 ),
inference(ennf_transformation,[status(thm)],[f21]) ).
tff(f21,plain,
~ ! [X0: state] :
~ ! [X1: state] : ( X0 = X1 ),
inference(rectify,[status(thm)],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X1: state] :
~ ! [X0: state] : ( X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f6,conjecture,
! [X1: state] :
~ ! [X0: state] : ( X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2THF_15196.p',conj_1) ).
tff(f40,plain,
sK1 != sK0,
inference(backward_demodulation,[status(thm)],[f39,f29]) ).
tff(f39,plain,
sK1 != sK2,
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
tff(f37,plain,
( ( sK1 != sK2 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f32]) ).
tff(f32,plain,
hoare_1821564147gleton = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
tff(f15,plain,
hoare_1821564147gleton = $true,
inference(fool_elimination,[status(thm)],[f14]) ).
tff(f14,plain,
hoare_1821564147gleton,
inference(rectify,[status(thm)],[f5]) ).
tff(f5,axiom,
hoare_1821564147gleton,
file('/export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2THF_15196.p',conj_0) ).
tff(f33,plain,
( ( sK1 != sK2 )
| ( hoare_1821564147gleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
tff(f28,plain,
( ( ( hoare_1821564147gleton = $true )
| ! [X0: state,X1: state] : ( X0 = X1 ) )
& ( ( sK1 != sK2 )
| ( hoare_1821564147gleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f26,f27]) ).
tff(f27,plain,
( ? [X2: state,X3: state] : ( X2 != X3 )
=> ( sK1 != sK2 ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f26,plain,
( ( ( hoare_1821564147gleton = $true )
| ! [X0: state,X1: state] : ( X0 = X1 ) )
& ( ? [X2: state,X3: state] : ( X2 != X3 )
| ( hoare_1821564147gleton != $true ) ) ),
inference(rectify,[status(thm)],[f25]) ).
tff(f25,plain,
( ( ( hoare_1821564147gleton = $true )
| ! [X0: state,X1: state] : ( X0 = X1 ) )
& ( ? [X0: state,X1: state] : ( X0 != X1 )
| ( hoare_1821564147gleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
tff(f19,plain,
( ( hoare_1821564147gleton = $true )
<=> ? [X0: state,X1: state] : ( X0 != X1 ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
tff(f18,plain,
( ? [X0: state,X1: state] : ( X0 != X1 )
<=> hoare_1821564147gleton ),
inference(rectify,[status(thm)],[f1]) ).
tff(f1,axiom,
( ? [X0: state,X1: state] : ( X0 != X1 )
<=> hoare_1821564147gleton ),
file('/export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2THF_15196.p',fact_0_state__not__singleton__def) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW469^1 : TPTP v9.2.1. Released v5.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 13:40:20 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.50 ---- Original DTF file ---
% 0.30/0.50 thf(spec,logic,$$dhol).
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 % File : SWW469^1 : TPTP v9.2.1. Released v5.3.0.
% 0.30/0.50 % Domain : Software Verification
% 0.30/0.50 % Problem : Hoare's Logic with Procedures line 112, 100 axioms selected
% 0.30/0.50 % Version : Especial.
% 0.30/0.50 % English :
% 0.30/0.50
% 0.30/0.50 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.30/0.50 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.30/0.50 % Source : [Bla11]
% 0.30/0.50 % Names : hoare_100_thf_l112 [Bla11]
% 0.30/0.50
% 0.30/0.50 % Status : Theorem
% 0.30/0.50 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0
% 0.30/0.50 % Syntax : Number of formulae : 10 ( 5 unt; 4 typ; 0 def)
% 0.30/0.50 % Number of atoms : 7 ( 2 equ; 0 cnn)
% 0.30/0.50 % Maximal formula atoms : 2 ( 1 avg)
% 0.30/0.50 % Number of connectives : 4 ( 3 ~; 0 |; 0 &; 0 @)
% 0.30/0.50 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.50 % Maximal formula depth : 5 ( 2 avg)
% 0.30/0.50 % Number of types : 2 ( 1 usr)
% 0.30/0.50 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.30/0.50 % Number of symbols : 4 ( 3 usr; 3 con; 0-2 aty)
% 0.30/0.50 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.30/0.50 % SPC : TH0_THM_EQU_NAR
% 0.30/0.50
% 0.30/0.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.50 % 2011-08-09 18:59:06
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 %----Should-be-implicit typings (1)
% 0.30/0.50 thf(ty_ty_tc__Com__Ostate,type,
% 0.30/0.50 state: $tType ).
% 0.30/0.50
% 0.30/0.50 %----Explicit typings (3)
% 0.30/0.50 thf(sy_c_HOL_Oinduct__false,type,
% 0.30/0.50 induct_false: $o ).
% 0.30/0.50
% 0.30/0.50 thf(sy_c_HOL_Oinduct__true,type,
% 0.30/0.50 induct_true: $o ).
% 0.30/0.50
% 0.30/0.50 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton,type,
% 0.30/0.50 hoare_1821564147gleton: $o ).
% 0.30/0.50
% 0.30/0.50 %----Relevant facts (4)
% 0.30/0.50 thf(fact_0_state__not__singleton__def,axiom,
% 0.30/0.50 ( hoare_1821564147gleton
% 0.30/0.50 <=> ? [S: state,T: state] : ( S != T ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(fact_1_induct__false__def,axiom,
% 0.30/0.50 ~ induct_false ).
% 0.30/0.50
% 0.30/0.50 thf(fact_2_induct__trueI,axiom,
% 0.30/0.50 induct_true ).
% 0.30/0.50
% 0.30/0.50 thf(fact_3_induct__true__def,axiom,
% 0.30/0.50 induct_true ).
% 0.30/0.50
% 0.30/0.50 %----Conjectures (2)
% 0.30/0.50 thf(conj_0,hypothesis,
% 0.30/0.50 hoare_1821564147gleton ).
% 0.30/0.50
% 0.30/0.50 thf(conj_1,conjecture,
% 0.30/0.50 ! [T: state] :
% 0.30/0.50 ~ ! [S: state] : ( S = T ) ).
% 0.30/0.50
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 ------------------------
% 1.65/1.45 ---- Embedded in THF ---
% 1.65/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.45 %%% Generated on Tue Feb 24 13:40:21 EST 2026
% 1.65/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.45 %%% Logic specification used:
% 1.65/1.45 %%% thf(spec, logic, $$dhol).
% 1.65/1.45
% 1.65/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2DTF15196.p
% See solution above
% 1.65/1.45 ------------------------
% 1.65/1.46 ---- Cleaned THF ---
% 1.65/1.46 thf(ty_ty_tc__Com__Ostate,type,
% 1.65/1.46 state: $tType ).
% 1.65/1.46
% 1.65/1.46 thf(sy_c_HOL_Oinduct__false,type,
% 1.65/1.46 induct_false: $o ).
% 1.65/1.46
% 1.65/1.46 thf(sy_c_HOL_Oinduct__true,type,
% 1.65/1.46 induct_true: $o ).
% 1.65/1.46
% 1.65/1.46 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton,type,
% 1.65/1.46 hoare_1821564147gleton: $o ).
% 1.65/1.46
% 1.65/1.46 thf(fact_0_state__not__singleton__def,axiom,
% 1.65/1.46 ( hoare_1821564147gleton
% 1.65/1.46 <=> ? [S: state,T: state] : ( S != T ) ) ).
% 1.65/1.46
% 1.65/1.46 thf(fact_1_induct__false__def,axiom,
% 1.65/1.46 ~ induct_false ).
% 1.65/1.46
% 1.65/1.46 thf(fact_2_induct__trueI,axiom,
% 1.65/1.46 induct_true ).
% 1.65/1.46
% 1.65/1.46 thf(fact_3_induct__true__def,axiom,
% 1.65/1.46 induct_true ).
% 1.65/1.46
% 1.65/1.46 thf(conj_0,hypothesis,
% 1.65/1.46 hoare_1821564147gleton ).
% 1.65/1.46
% 1.65/1.46 thf(conj_1,conjecture,
% 1.65/1.46 ! [T: state] :
% 1.65/1.46 ~ ! [S: state] : ( S = T ) ).
% 1.65/1.46 ------------------------
% 1.65/1.48 % (15298)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_15196 for (3000ds/2Mi)
% 1.65/1.48 % (15296)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_15196 for (3000ds/27Mi)
% 1.65/1.48 % (15297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15196 for (3000ds/2Mi)
% 1.65/1.48 % (15295)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_15196 for (3000ds/4Mi)
% 1.65/1.48 % (15294)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15196 for (3000ds/183Mi)
% 1.65/1.48 % (15299)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_15196 for (3000ds/275Mi)
% 1.65/1.48 % (15300)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15196 for (3000ds/18Mi)
% 1.65/1.48 % (15298)First to succeed.
% 1.65/1.48 % (15294)Also succeeded, but the first one will report.
% 1.65/1.48 % (15299)Also succeeded, but the first one will report.
% 1.65/1.48 % (15298)Refutation found. Thanks to Tanya!
% 1.65/1.48 % SZS status Theorem for DTF2THF_15196
% 1.65/1.48 % SZS output start Proof for DTF2THF_15196
% 1.65/1.48 tff(type_def_5, type, state: $tType).
% 1.65/1.48 tff(func_def_0, type, state: $tType).
% 1.65/1.48 tff(func_def_6, type, sK0: state).
% 1.65/1.48 tff(func_def_7, type, sK1: state).
% 1.65/1.48 tff(func_def_8, type, sK2: state).
% 1.65/1.48 tff(f41,plain,(
% 1.65/1.48 $false),
% 1.65/1.48 inference(subsumption_resolution,[status(thm)],[f40,f29])).
% 1.65/1.48 tff(f29,plain,(
% 1.65/1.48 ( ! [X1 : state] : (sK0 = X1) )),
% 1.65/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.65/1.48 tff(f24,plain,(
% 1.65/1.48 ! [X1 : state] : sK0 = X1),
% 1.65/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23])).
% 1.65/1.48 tff(f23,plain,(
% 1.65/1.48 ? [X0 : state] : ! [X1 : state] : X0 = X1 => ! [X1 : state] : sK0 = X1),
% 1.65/1.48 introduced(definition,[],[choice_axiom])).
% 1.65/1.48 tff(f22,plain,(
% 1.65/1.48 ? [X0 : state] : ! [X1 : state] : X0 = X1),
% 1.65/1.48 inference(ennf_transformation,[status(thm)],[f21])).
% 1.65/1.48 tff(f21,plain,(
% 1.65/1.48 ~! [X0 : state] : ~! [X1 : state] : X0 = X1),
% 1.65/1.48 inference(rectify,[status(thm)],[f7])).
% 1.65/1.48 tff(f7,negated_conjecture,(
% 1.65/1.48 ~! [X1 : state] : ~! [X0 : state] : X0 = X1),
% 1.65/1.48 inference(negated_conjecture,[status(cth)],[f6])).
% 1.65/1.48 tff(f6,conjecture,(
% 1.65/1.48 ! [X1 : state] : ~! [X0 : state] : X0 = X1),
% 1.65/1.48 file('/export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2THF_15196.p',conj_1)).
% 1.65/1.48 tff(f40,plain,(
% 1.65/1.48 sK1 != sK0),
% 1.65/1.48 inference(backward_demodulation,[status(thm)],[f39,f29])).
% 1.65/1.48 tff(f39,plain,(
% 1.65/1.48 sK1 != sK2),
% 1.65/1.48 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.65/1.48 tff(f37,plain,(
% 1.65/1.48 sK1 != sK2 | ($true != $true)),
% 1.65/1.48 inference(definition_unfolding,[status(thm)],[f33,f32])).
% 1.65/1.48 tff(f32,plain,(
% 1.65/1.48 (hoare_1821564147gleton = $true)),
% 1.65/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.48 tff(f15,plain,(
% 1.65/1.48 (hoare_1821564147gleton = $true)),
% 1.65/1.48 inference(fool_elimination,[status(thm)],[f14])).
% 1.65/1.48 tff(f14,plain,(
% 1.65/1.48 hoare_1821564147gleton),
% 1.65/1.48 inference(rectify,[status(thm)],[f5])).
% 1.65/1.48 tff(f5,axiom,(
% 1.65/1.48 hoare_1821564147gleton),
% 1.65/1.48 file('/export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2THF_15196.p',conj_0)).
% 1.65/1.48 tff(f33,plain,(
% 1.65/1.48 sK1 != sK2 | (hoare_1821564147gleton != $true)),
% 1.65/1.48 inference(cnf_transformation,[status(thm)],[f28])).
% 1.65/1.48 tff(f28,plain,(
% 1.65/1.48 ((hoare_1821564147gleton = $true) | ! [X0 : state,X1 : state] : X0 = X1) & (sK1 != sK2 | (hoare_1821564147gleton != $true))),
% 1.65/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f26,f27])).
% 1.65/1.48 tff(f27,plain,(
% 1.65/1.48 ? [X2 : state,X3 : state] : X2 != X3 => sK1 != sK2),
% 1.65/1.48 introduced(definition,[],[choice_axiom])).
% 1.65/1.48 tff(f26,plain,(
% 1.65/1.48 ((hoare_1821564147gleton = $true) | ! [X0 : state,X1 : state] : X0 = X1) & (? [X2 : state,X3 : state] : X2 != X3 | (hoare_1821564147gleton != $true))),
% 1.65/1.48 inference(rectify,[status(thm)],[f25])).
% 1.65/1.48 tff(f25,plain,(
% 1.65/1.48 ((hoare_1821564147gleton = $true) | ! [X0 : state,X1 : state] : X0 = X1) & (? [X0 : state,X1 : state] : X0 != X1 | (hoare_1821564147gleton != $true))),
% 1.65/1.48 inference(nnf_transformation,[status(thm)],[f19])).
% 1.65/1.48 tff(f19,plain,(
% 1.65/1.48 (hoare_1821564147gleton = $true) <=> ? [X0 : state,X1 : state] : X0 != X1),
% 1.65/1.48 inference(fool_elimination,[status(thm)],[f18])).
% 1.65/1.48 tff(f18,plain,(
% 1.65/1.48 ? [X0 : state,X1 : state] : X0 != X1 <=> hoare_1821564147gleton),
% 1.65/1.48 inference(rectify,[status(thm)],[f1])).
% 1.65/1.48 tff(f1,axiom,(
% 1.65/1.48 ? [X0 : state,X1 : state] : X0 != X1 <=> hoare_1821564147gleton),
% 1.65/1.48 file('/export/starexec/sandbox/tmp/tmp.VFhtm9l1Tk/DTF2THF_15196.p',fact_0_state__not__singleton__def)).
% 1.65/1.48 % SZS output end Proof for DTF2THF_15196
% 1.65/1.48 % (15298)------------------------------
% 1.65/1.48 % (15298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (15298)Termination reason: Refutation
% 1.65/1.48
% 1.65/1.48 % (15298)Memory used [KB]: 5500
% 1.65/1.48 % (15298)Time elapsed: 0.003 s
% 1.65/1.48 % (15298)Instructions burned: 1 (million)
% 1.65/1.48 % (15298)------------------------------
% 1.65/1.48 % (15298)------------------------------
% 1.65/1.48 % (15293)Success in time 0.018 s
%------------------------------------------------------------------------------