%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW387+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 3.84s 1.25s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 52 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 27 ~; 20 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 18 ( 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
fof(f5244,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5245,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f5249,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/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(f5250,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)],[f5249]) ).
fof(f5251,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,[],[f5250]) ).
fof(f5258,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(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(flattening,[],[f5258]) ).
fof(f5341,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(f5342,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,[],[f5341]) ).
fof(f5343,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),sK4(X0))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f5342]) ).
fof(f5393,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[],[f5244]) ).
fof(f5394,plain,
c_Com_OWT__bodies,
inference(cnf_transformation,[],[f5245]) ).
fof(f5396,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(cnf_transformation,[],[f5247]) ).
fof(f5398,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,[],[f5251]) ).
fof(f5402,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,[],[f5259]) ).
fof(f5410,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,[],[f5343]) ).
fof(f5631,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,[],[f5398,f5402]) ).
fof(f5639,plain,
( ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(forward_subsumption_resolution,[],[f5631,f5394]) ).
fof(f5640,plain,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))),
inference(forward_subsumption_resolution,[],[f5639,f5393]) ).
fof(f5644,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,[],[f5410,f5396]) ).
fof(f5669,plain,
! [X0] : hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(forward_subsumption_resolution,[],[f5644,f5640]) ).
fof(f5704,plain,
$false,
inference(equality_resolution,[],[f5669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW387+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 13:45:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.25 % (789311)Detected formulas, will run a generic FOF schedule.
% 3.84/1.25 % (789316)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=1587147807:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.84/1.25 % (789321)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=909571749:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.84/1.25 % (789320)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1533051130:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.84/1.25 % (789319)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1218007716:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.84/1.25 % (789318)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=1936463123:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.84/1.25 % (789317)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=3362850444:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.84/1.25 % (789322)dis-21_1_sil=8000:lcm=predicate:random_seed=1836646857:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.84/1.25 % (789319)First to succeed.
% 3.84/1.25 % (789319)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-789311"
% 3.84/1.25 % (789321)Instruction limit reached!
% 3.84/1.25 % (789321)------------------------------
% 3.84/1.25 % (789321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.25 % (789321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.25 % (789321)CaDiCaL version: 2.1.3
% 3.84/1.25 % (789321)Termination reason: Instruction limit
% 3.84/1.25 % (789321)Termination phase: SInE selection
% 3.84/1.25 % (789321)Time elapsed: 0.056 s
% 3.84/1.25 % (789321)Peak memory usage: 90 MB
% 3.84/1.25 % (789321)Instructions burned: 140 (million)
% 3.84/1.25 % (789320)Instruction limit reached!
% 3.84/1.25 % (789320)------------------------------
% 3.84/1.25 % (789320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.25 % (789320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.25 % (789320)CaDiCaL version: 2.1.3
% 3.84/1.25 % (789320)Termination reason: Instruction limit
% 3.84/1.25 % (789320)Termination phase: Property scanning
% 3.84/1.25 % (789320)Time elapsed: 0.069 s
% 3.84/1.25 % (789320)Peak memory usage: 93 MB
% 3.84/1.25 % (789320)Instructions burned: 121 (million)
% 3.84/1.25 % (789322)Instruction limit reached!
% 3.84/1.25 % (789322)------------------------------
% 3.84/1.25 % (789322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.25 % (789322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.25 % (789322)CaDiCaL version: 2.1.3
% 3.84/1.25 % (789322)Termination reason: Instruction limit
% 3.84/1.25 % (789322)Termination phase: Preprocessing 3
% 3.84/1.25 % (789322)Time elapsed: 0.082 s
% 3.84/1.25 % (789322)Peak memory usage: 93 MB
% 3.84/1.25 % (789322)Instructions burned: 129 (million)
% 3.84/1.25 % (789330)lrs+10_1_sil=8000:sp=occurrence:random_seed=2072679569:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.84/1.25 % (789331)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1361766073:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.84/1.25 % (789332)lrs+1011_1_sil=32000:sp=occurrence:random_seed=48146115:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 3.84/1.25 % (789331)Instruction limit reached!
% 3.84/1.25 % (789331)------------------------------
% 3.84/1.25 % (789331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.25 % (789331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.25 % (789331)CaDiCaL version: 2.1.3
% 3.84/1.25 % (789331)Termination reason: Instruction limit
% 3.84/1.25 % (789331)Termination phase: Equality resolution with deletion
% 3.84/1.25 % (789331)Time elapsed: 0.070 s
% 3.84/1.25 % (789331)Peak memory usage: 92 MB
% 3.84/1.25 % (789331)Instructions burned: 159 (million)
% 3.84/1.25 % (789319)Refutation found. Thanks to Tanya!
% 3.84/1.25 % SZS status Theorem for theBenchmark
% 3.84/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.25 % (789319)------------------------------
% 3.84/1.25 % (789319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.25 % (789319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.25 % (789319)CaDiCaL version: 2.1.3
% 3.84/1.25 % (789319)Termination reason: Refutation
% 3.84/1.25 % (789319)Time elapsed: 0.048 s
% 3.84/1.25 % (789319)Peak memory usage: 95 MB
% 3.84/1.25 % (789319)Instructions burned: 77 (million)
% 3.84/1.25 % (789319)------------------------------
% 3.84/1.25 % (789319)------------------------------
% 3.84/1.25 % (789311)Success in time 0.63 s
% 3.84/1.25 % Vampire exiting
%------------------------------------------------------------------------------