%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW298+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 : n016.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 01:30:03 PM UTC 2026
% Result : Theorem 3.14s 1.60s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 4 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0)
=> c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
fof(f5224,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f5225,conjecture,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f5226,negated_conjecture,
~ ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0) ),
inference(negated_conjecture,[status(cth)],[f5225]) ).
fof(f5228,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(ennf_transformation,[],[f5224]) ).
fof(f5229,plain,
? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(ennf_transformation,[],[f5226]) ).
fof(f5230,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f5283,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0),v_ts)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5229]) ).
fof(f5324,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0) ),
inference(cnf_transformation,[],[f5228]) ).
fof(f5325,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0),v_ts)),
inference(cnf_transformation,[],[f5283]) ).
fof(f5326,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK0),
inference(cnf_transformation,[],[f5283]) ).
fof(f5327,plain,
! [X2,X0,X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0)
| c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0) ),
inference(cnf_transformation,[],[f5230]) ).
fof(f5532,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),sK0),
inference(resolution,[],[f5324,f5325]) ).
fof(f5533,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK0),
inference(resolution,[],[f5532,f5327]) ).
fof(f5534,plain,
$false,
inference(forward_subsumption_resolution,[],[f5533,f5326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n016.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Mon Sep 28 13:36:03 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running first-order theorem proving
% 0.08/0.25 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
% 3.14/1.60 % (3626333)Detected formulas, will run a generic FOF schedule.
% 3.14/1.60 % (3626341)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2887558966:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 3.14/1.60 % (3626341)First to succeed.
% 3.14/1.60 % (3626341)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3626333"
% 3.14/1.60 % (3626338)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=491734232:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 3.14/1.60 % (3626340)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=3279240376:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 3.14/1.60 % (3626343)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1411016792:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 3.14/1.60 % (3626339)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=1157421936:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 3.14/1.60 % (3626344)dis-21_1_sil=8000:lcm=predicate:random_seed=722137253: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)
% 3.14/1.60 % (3626342)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=381058433:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 3.14/1.60 % (3626343)Instruction limit reached!
% 3.14/1.60 % (3626343)------------------------------
% 3.14/1.60 % (3626343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.60 % (3626343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.60 % (3626343)CaDiCaL version: 2.1.3
% 3.14/1.60 % (3626343)Termination reason: Instruction limit
% 3.14/1.60 % (3626343)Termination phase: SInE selection
% 3.14/1.60 % (3626343)Time elapsed: 0.056 s
% 3.14/1.60 % (3626343)Peak memory usage: 90 MB
% 3.14/1.60 % (3626343)Instructions burned: 139 (million)
% 3.14/1.60 % (3626342)Instruction limit reached!
% 3.14/1.60 % (3626342)------------------------------
% 3.14/1.60 % (3626342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.60 % (3626342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.60 % (3626342)CaDiCaL version: 2.1.3
% 3.14/1.60 % (3626342)Termination reason: Instruction limit
% 3.14/1.60 % (3626342)Termination phase: Saturation
% 3.14/1.60 % (3626342)Time elapsed: 0.068 s
% 3.14/1.60 % (3626342)Peak memory usage: 94 MB
% 3.14/1.60 % (3626342)Instructions burned: 120 (million)
% 3.14/1.60 % (3626344)Instruction limit reached!
% 3.14/1.60 % (3626344)------------------------------
% 3.14/1.60 % (3626344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.60 % (3626344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.60 % (3626344)CaDiCaL version: 2.1.3
% 3.14/1.60 % (3626344)Termination reason: Instruction limit
% 3.14/1.60 % (3626344)Termination phase: Preprocessing 3
% 3.14/1.60 % (3626344)Time elapsed: 0.084 s
% 3.14/1.60 % (3626344)Peak memory usage: 93 MB
% 3.14/1.60 % (3626344)Instructions burned: 130 (million)
% 3.14/1.60 % (3626341)Refutation found. Thanks to Tanya!
% 3.14/1.60 % SZS status Theorem for theBenchmark
% 3.14/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 3.14/1.60 % (3626341)------------------------------
% 3.14/1.60 % (3626341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.60 % (3626341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.60 % (3626341)CaDiCaL version: 2.1.3
% 3.14/1.60 % (3626341)Termination reason: Refutation
% 3.14/1.60 % (3626341)Time elapsed: 0.019 s
% 3.14/1.60 % (3626341)Peak memory usage: 94 MB
% 3.14/1.60 % (3626341)Instructions burned: 45 (million)
% 3.14/1.60 % (3626341)------------------------------
% 3.14/1.60 % (3626341)------------------------------
% 3.14/1.60 % (3626333)Success in time 0.706 s
% 3.14/1.60 % Vampire exiting
%------------------------------------------------------------------------------