%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW386+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:14 PM UTC 2026
% Result : Theorem 5.03s 2.20s
% Output : Refutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 17 unt; 1 def)
% Number of atoms : 64 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 23 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,X0))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_MGF) ).
fof(f9,axiom,
! [X0] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0)))
<=> ? [X1] : hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
fof(f5244,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f5245,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f5247,axiom,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(f5248,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(f5249,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5248]) ).
fof(f5250,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(flattening,[],[f5249]) ).
fof(f5259,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X0))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(ennf_transformation,[],[f4]) ).
fof(f5260,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X0))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(flattening,[],[f5259]) ).
fof(f5335,plain,
! [X0] :
( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0)))
| ! [X1] : hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) )
& ( ? [X1] : hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0))) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f5336,plain,
! [X0] :
( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0)))
| ! [X1] : hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) )
& ( ? [X2] : hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2)
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0))) ) ),
inference(rectify,[],[f5335]) ).
fof(f5337,plain,
! [X0] :
( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0)))
| ! [X1] : hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) )
& ( hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK5(X0))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0))],[f5336]) ).
fof(f5377,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[],[f5244]) ).
fof(f5378,plain,
c_Com_OWT__bodies,
inference(cnf_transformation,[],[f5245]) ).
fof(f5380,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(cnf_transformation,[],[f5247]) ).
fof(f5381,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5250]) ).
fof(f5386,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X0))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(cnf_transformation,[],[f5260]) ).
fof(f5413,plain,
! [X0,X1] :
( hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0))) ),
inference(cnf_transformation,[],[f5337]) ).
fof(f5559,plain,
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(resolution,[],[f5381,f5386]) ).
fof(f5564,plain,
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(forward_subsumption_resolution,[],[f5559,f5378]) ).
fof(f5570,definition,
( spl20_2
<=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f5572,plain,
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| spl20_2 ),
inference(avatar_component_clause,[],[f5570]) ).
fof(f5574,plain,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))),
inference(forward_subsumption_resolution,[],[f5564,f5377]) ).
fof(f5575,plain,
~ spl20_2,
inference(avatar_split_clause,[],[f5574,f5570]) ).
fof(f5589,plain,
! [X0] :
( hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y)
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))) ),
inference(superposition,[],[f5413,f5380]) ).
fof(f5602,plain,
( ! [X0] : hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y)
| spl20_2 ),
inference(forward_subsumption_resolution,[],[f5589,f5572]) ).
fof(f5606,plain,
( $false
| spl20_2 ),
inference(equality_resolution,[],[f5602]) ).
fof(f5607,plain,
spl20_2,
inference(avatar_contradiction_clause,[],[f5606]) ).
cnf(s2,plain,
~ spl20_2,
inference(sat_conversion,[],[f5575]) ).
cnf(s4,plain,
spl20_2,
inference(sat_conversion,[],[f5607]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
fof(f5610,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW386+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 % Computer : n010.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 13:46:02 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running first-order theorem proving
% 0.25/0.31 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.94/2.20 % (1931122)Detected formulas, will run a generic FOF schedule.
% 4.94/2.20 % (1931132)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3793155442:i=109:sd=1:ins=1:gsp=on:ss=axioms_2994 on theBenchmark for (2994ds/109Mi)
% 4.94/2.20 % (1931132)First to succeed.
% 4.94/2.20 % (1931132)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1931122"
% 4.94/2.20 % (1931129)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1141580363:i=141193_2994 on theBenchmark for (2994ds/141193Mi)
% 4.94/2.20 % (1931131)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3314336021:i=141695:sd=1:nm=32:gsp=on:ss=included_2994 on theBenchmark for (2994ds/141695Mi)
% 4.94/2.20 % (1931130)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1249115063:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2994 on theBenchmark for (2994ds/134677Mi)
% 4.94/2.20 % (1931135)dis-21_1_sil=8000:lcm=predicate:random_seed=358658367:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2994 on theBenchmark for (2994ds/129Mi)
% 4.94/2.20 % (1931134)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=146375615:s2a=on:i=139:gtg=position_2994 on theBenchmark for (2994ds/139Mi)
% 4.94/2.20 % (1931133)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2126753576:i=119:av=off:ss=axioms_2994 on theBenchmark for (2994ds/119Mi)
% 4.94/2.20 % (1931134)Instruction limit reached!
% 4.94/2.20 % (1931134)------------------------------
% 4.94/2.20 % (1931134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.20 % (1931134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.20 % (1931134)CaDiCaL version: 2.1.3
% 4.94/2.20 % (1931134)Termination reason: Instruction limit
% 4.94/2.20 % (1931134)Termination phase: SInE selection
% 4.94/2.20 % (1931134)Time elapsed: 0.113 s
% 4.94/2.20 % (1931134)Peak memory usage: 90 MB
% 4.94/2.20 % (1931134)Instructions burned: 139 (million)
% 4.94/2.20 % (1931133)Instruction limit reached!
% 5.03/2.20 % (1931133)------------------------------
% 5.03/2.20 % (1931133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/2.20 % (1931133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/2.20 % (1931133)CaDiCaL version: 2.1.3
% 5.03/2.20 % (1931133)Termination reason: Instruction limit
% 5.03/2.20 % (1931133)Termination phase: Property scanning
% 5.03/2.20 % (1931133)Time elapsed: 0.119 s
% 5.03/2.20 % (1931133)Peak memory usage: 93 MB
% 5.03/2.20 % (1931133)Instructions burned: 120 (million)
% 5.03/2.20 % (1931135)Instruction limit reached!
% 5.03/2.20 % (1931135)------------------------------
% 5.03/2.20 % (1931135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/2.20 % (1931135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/2.20 % (1931135)CaDiCaL version: 2.1.3
% 5.03/2.20 % (1931135)Termination reason: Instruction limit
% 5.03/2.20 % (1931135)Termination phase: Preprocessing 3
% 5.03/2.20 % (1931135)Time elapsed: 0.131 s
% 5.03/2.20 % (1931135)Peak memory usage: 93 MB
% 5.03/2.20 % (1931135)Instructions burned: 129 (million)
% 5.03/2.20 % (1931132)Refutation found. Thanks to Tanya!
% 5.03/2.20 % SZS status Theorem for theBenchmark
% 5.03/2.20 % SZS output start Proof for theBenchmark
% See solution above
% 5.03/2.20 % (1931132)------------------------------
% 5.03/2.20 % (1931132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/2.20 % (1931132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/2.20 % (1931132)CaDiCaL version: 2.1.3
% 5.03/2.20 % (1931132)Termination reason: Refutation
% 5.03/2.20 % (1931132)Time elapsed: 0.040 s
% 5.03/2.20 % (1931132)Peak memory usage: 96 MB
% 5.03/2.20 % (1931132)Instructions burned: 62 (million)
% 5.03/2.20 % (1931132)------------------------------
% 5.03/2.20 % (1931132)------------------------------
% 5.03/2.20 % (1931122)Success in time 1.007 s
% 5.03/2.20 % Vampire exiting
%------------------------------------------------------------------------------