%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW323+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 : n015.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 01:30:06 PM UTC 2026
% Result : Theorem 0.16s 1.71s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 2 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-3 aty)
% Number of variables : 3 ( 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5228,axiom,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5232,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
& c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f5233,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(f5234,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5233]) ).
fof(f5235,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(flattening,[],[f5234]) ).
fof(f5238,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
inference(ennf_transformation,[],[f5228]) ).
fof(f5374,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X0)),hAPP(v_c0,X0)),hAPP(v_Q_H,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X0)),hAPP(v_c0,X0)),hAPP(v_Q,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
inference(cnf_transformation,[],[f5238]) ).
fof(f5379,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5232]) ).
fof(f5380,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5235]) ).
fof(f5626,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(resolution,[],[f5374,f5379]) ).
fof(f5633,plain,
$false,
inference(forward_subsumption_resolution,[],[f5626,f5380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW323+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n015.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 13:39:02 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 0.16/1.71 % (2631163)Detected formulas, will run a generic FOF schedule.
% 0.16/1.71 % (2631172)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1530609207:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 0.16/1.71 % (2631172)Instruction limit reached!
% 0.16/1.71 % (2631172)------------------------------
% 0.16/1.71 % (2631172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.71 % (2631172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.71 % (2631172)CaDiCaL version: 2.1.3
% 0.16/1.71 % (2631172)Termination reason: Instruction limit
% 0.16/1.71 % (2631172)Termination phase: Equality resolution with deletion
% 0.16/1.71 % (2631172)Time elapsed: 0.042 s
% 0.16/1.71 % (2631172)Peak memory usage: 93 MB
% 0.16/1.71 % (2631172)Instructions burned: 121 (million)
% 0.16/1.71 % (2631170)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=807826972:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 0.16/1.71 % (2631169)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=4266935423:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 0.16/1.71 % (2631168)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=1860389196:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 0.16/1.71 % (2631173)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3557484687:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 0.16/1.71 % (2631171)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=96087943:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 0.16/1.71 % (2631174)dis-21_1_sil=8000:lcm=predicate:random_seed=455196658:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 0.16/1.71 % (2631171)First to succeed.
% 0.16/1.71 % (2631171)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2631163"
% 0.16/1.71 % (2631173)Instruction limit reached!
% 0.16/1.71 % (2631173)------------------------------
% 0.16/1.71 % (2631173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.71 % (2631173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.71 % (2631173)CaDiCaL version: 2.1.3
% 0.16/1.71 % (2631173)Termination reason: Instruction limit
% 0.16/1.71 % (2631173)Termination phase: SInE selection
% 0.16/1.71 % (2631173)Time elapsed: 0.059 s
% 0.16/1.71 % (2631173)Peak memory usage: 90 MB
% 0.16/1.71 % (2631173)Instructions burned: 140 (million)
% 0.16/1.71 % (2631174)Instruction limit reached!
% 0.16/1.71 % (2631174)------------------------------
% 0.16/1.71 % (2631174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.71 % (2631174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.71 % (2631174)CaDiCaL version: 2.1.3
% 0.16/1.71 % (2631174)Termination reason: Instruction limit
% 0.16/1.71 % (2631174)Termination phase: Preprocessing 3
% 0.16/1.71 % (2631174)Time elapsed: 0.086 s
% 0.16/1.71 % (2631174)Peak memory usage: 93 MB
% 0.16/1.71 % (2631174)Instructions burned: 130 (million)
% 0.16/1.71 % (2631180)lrs+10_1_sil=8000:sp=occurrence:random_seed=161028600:i=285:sd=3:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/285Mi)
% 0.16/1.71 % (2631180)Instruction limit reached!
% 0.16/1.71 % (2631180)------------------------------
% 0.16/1.71 % (2631180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.71 % (2631180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.71 % (2631180)CaDiCaL version: 2.1.3
% 0.16/1.71 % (2631180)Termination reason: Instruction limit
% 0.16/1.71 % (2631180)Termination phase: Saturation
% 0.16/1.71 % (2631180)Time elapsed: 0.091 s
% 0.16/1.71 % (2631180)Peak memory usage: 97 MB
% 0.16/1.71 % (2631180)Instructions burned: 285 (million)
% 0.16/1.71 % (2631184)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4281345549:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 0.16/1.71 % (2631185)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2994310647:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 0.16/1.71 % (2631171)Refutation found. Thanks to Tanya!
% 0.16/1.71 % SZS status Theorem for theBenchmark
% 0.16/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.71 % (2631171)------------------------------
% 0.16/1.71 % (2631171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.71 % (2631171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.71 % (2631171)CaDiCaL version: 2.1.3
% 0.16/1.71 % (2631171)Termination reason: Refutation
% 0.16/1.71 % (2631171)Time elapsed: 0.042 s
% 0.16/1.71 % (2631171)Peak memory usage: 95 MB
% 0.16/1.71 % (2631171)Instructions burned: 65 (million)
% 0.16/1.71 % (2631171)------------------------------
% 0.16/1.71 % (2631171)------------------------------
% 0.16/1.71 % (2631163)Success in time 0.866 s
% 0.16/1.71 % Vampire exiting
%------------------------------------------------------------------------------