%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW334+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 : n008.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 01:30:08 PM UTC 2026
% Result : Theorem 5.18s 2.04s
% Output : Refutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 29 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 7 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2,X3,X4] :
( c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0))
<=> c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Body__triple__valid__Suc) ).
fof(f707,axiom,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f5205,axiom,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5208,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f5209,conjecture,
c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f5210,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(negated_conjecture,[status(cth)],[f5209]) ).
fof(f5211,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(flattening,[],[f5210]) ).
fof(f5215,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(ennf_transformation,[],[f5208]) ).
fof(f5293,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0))
| ~ c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0)) )
& ( c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0))
| ~ c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f5343,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
inference(cnf_transformation,[],[f5205]) ).
fof(f5346,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(cnf_transformation,[],[f5215]) ).
fof(f5347,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(cnf_transformation,[],[f5211]) ).
fof(f5374,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X4,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X0))
| c_Hoare__Mirabelle_Otriple__valid(X4,hAPP(c_Nat_OSuc,X3),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X4),X2),hAPP(c_Com_Ocom_OBODY,X1)),X0)) ),
inference(cnf_transformation,[],[f5293]) ).
fof(f5418,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f707]) ).
fof(f5600,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(forward_demodulation,[],[f5347,f5418]) ).
fof(f5670,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs))
| c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0))) ),
inference(resolution,[],[f5346,f5374]) ).
fof(f5672,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(forward_demodulation,[],[f5670,f5418]) ).
fof(f5701,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
inference(resolution,[],[f5672,f5600]) ).
fof(f5708,plain,
$false,
inference(forward_subsumption_resolution,[],[f5701,f5343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW334+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 13:38:53 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 5.18/2.04 % (2254471)Detected formulas, will run a generic FOF schedule.
% 5.18/2.04 % (2254521)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3138420218:s2a=on:i=139:gtg=position_2994 on theBenchmark for (2994ds/139Mi)
% 5.18/2.04 % (2254519)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1905185447:i=109:sd=1:ins=1:gsp=on:ss=axioms_2994 on theBenchmark for (2994ds/109Mi)
% 5.18/2.04 % (2254519)First to succeed.
% 5.18/2.04 % (2254519)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2254471"
% 5.18/2.04 % (2254521)Instruction limit reached!
% 5.18/2.04 % (2254521)------------------------------
% 5.18/2.04 % (2254521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/2.04 % (2254521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/2.04 % (2254521)CaDiCaL version: 2.1.3
% 5.18/2.04 % (2254521)Termination reason: Instruction limit
% 5.18/2.04 % (2254521)Termination phase: SInE selection
% 5.18/2.04 % (2254521)Time elapsed: 0.060 s
% 5.18/2.04 % (2254521)Peak memory usage: 90 MB
% 5.18/2.04 % (2254521)Instructions burned: 139 (million)
% 5.18/2.04 % (2254516)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=892546539:i=141193_2994 on theBenchmark for (2994ds/141193Mi)
% 5.18/2.04 % (2254518)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=4135137577:i=141695:sd=1:nm=32:gsp=on:ss=included_2994 on theBenchmark for (2994ds/141695Mi)
% 5.18/2.04 % (2254517)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=4155384758:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2994 on theBenchmark for (2994ds/134677Mi)
% 5.18/2.04 % (2254520)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2312104695:i=119:av=off:ss=axioms_2994 on theBenchmark for (2994ds/119Mi)
% 5.18/2.04 % (2254522)dis-21_1_sil=8000:lcm=predicate:random_seed=2596094629: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)
% 5.18/2.04 % (2254520)Instruction limit reached!
% 5.18/2.04 % (2254520)------------------------------
% 5.18/2.04 % (2254520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/2.04 % (2254520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/2.04 % (2254520)CaDiCaL version: 2.1.3
% 5.18/2.04 % (2254520)Termination reason: Instruction limit
% 5.18/2.04 % (2254520)Termination phase: Property scanning
% 5.18/2.04 % (2254520)Time elapsed: 0.118 s
% 5.18/2.04 % (2254520)Peak memory usage: 93 MB
% 5.18/2.04 % (2254520)Instructions burned: 120 (million)
% 5.18/2.04 % (2254529)lrs+10_1_sil=8000:sp=occurrence:random_seed=3569211110:i=285:sd=3:ss=axioms:sgt=8_2992 on theBenchmark for (2992ds/285Mi)
% 5.18/2.04 % (2254522)Instruction limit reached!
% 5.18/2.04 % (2254522)------------------------------
% 5.18/2.04 % (2254522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/2.04 % (2254522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/2.04 % (2254522)CaDiCaL version: 2.1.3
% 5.18/2.04 % (2254522)Termination reason: Instruction limit
% 5.18/2.04 % (2254522)Termination phase: Preprocessing 3
% 5.18/2.04 % (2254522)Time elapsed: 0.132 s
% 5.18/2.04 % (2254522)Peak memory usage: 93 MB
% 5.18/2.04 % (2254522)Instructions burned: 130 (million)
% 5.18/2.04 % (2254533)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3417891055:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2991 on theBenchmark for (2991ds/157Mi)
% 5.18/2.04 % (2254529)Instruction limit reached!
% 5.18/2.04 % (2254529)------------------------------
% 5.18/2.04 % (2254529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/2.04 % (2254529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/2.04 % (2254529)CaDiCaL version: 2.1.3
% 5.18/2.04 % (2254529)Termination reason: Instruction limit
% 5.18/2.04 % (2254529)Termination phase: Saturation
% 5.18/2.04 % (2254529)Time elapsed: 0.146 s
% 5.18/2.04 % (2254529)Peak memory usage: 96 MB
% 5.18/2.04 % (2254529)Instructions burned: 285 (million)
% 5.18/2.04 % (2254519)Refutation found. Thanks to Tanya!
% 5.18/2.04 % SZS status Theorem for theBenchmark
% 5.18/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 5.18/2.04 % (2254519)------------------------------
% 5.18/2.04 % (2254519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/2.04 % (2254519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/2.04 % (2254519)CaDiCaL version: 2.1.3
% 5.18/2.04 % (2254519)Termination reason: Refutation
% 5.18/2.04 % (2254519)Time elapsed: 0.045 s
% 5.18/2.04 % (2254519)Peak memory usage: 95 MB
% 5.18/2.04 % (2254519)Instructions burned: 58 (million)
% 5.18/2.04 % (2254519)------------------------------
% 5.18/2.04 % (2254519)------------------------------
% 5.18/2.04 % (2254471)Success in time 1.117 s
% 5.18/2.04 % Vampire exiting
%------------------------------------------------------------------------------