%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO278+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:52:19 AM UTC 2026
% Result : Theorem 3.94s 1.55s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 13 unt; 1 def)
% Number of atoms : 133 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 183 ( 85 ~; 71 |; 23 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ron(vd1096,X0)
& rcenter(vd1089,X0)
& rcircle(X0) )
=> X0 = vd1102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(theu(the(231), 1), imp(the(231)))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ron(vd1096,X0)
& rcenter(vd1089,X0)
& rcircle(X0) )
=> X0 = vd1102 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( ron(vd1096,vd1102)
& rcenter(vd1089,vd1102)
& rcircle(vd1102) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(comma_conjunct2(the(231)), 0), and(pred(comma_conjunct1(the(231)), 0), pred(the(231), 0)))') ).
fof(f8,axiom,
rpoint(vd1096),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(229, 0)') ).
fof(f41,axiom,
! [X0,X1,X2,X3,X4] :
( ( vf(X2,X0) = vf(X2,X1)
& ron(X1,X4)
& ron(X0,X3)
& rcenter(X2,X4)
& rcenter(X2,X3)
& ? [X5] :
( X1 = X5
& rpoint(X5) )
& ? [X6] :
( X0 = X6
& rpoint(X6) ) )
=> X3 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))') ).
fof(f136,plain,
? [X0] :
( vd1102 != X0
& ron(vd1096,X0)
& rcenter(vd1089,X0)
& rcircle(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f137,plain,
? [X0] :
( vd1102 != X0
& ron(vd1096,X0)
& rcenter(vd1089,X0)
& rcircle(X0) ),
inference(flattening,[],[f136]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4] :
( X3 = X4
| vf(X2,X0) != vf(X2,X1)
| ~ ron(X1,X4)
| ~ ron(X0,X3)
| ~ rcenter(X2,X4)
| ~ rcenter(X2,X3)
| ! [X5] :
( X1 != X5
| ~ rpoint(X5) )
| ! [X6] :
( X0 != X6
| ~ rpoint(X6) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4] :
( X3 = X4
| vf(X2,X0) != vf(X2,X1)
| ~ ron(X1,X4)
| ~ ron(X0,X3)
| ~ rcenter(X2,X4)
| ~ rcenter(X2,X3)
| ! [X5] :
( X1 != X5
| ~ rpoint(X5) )
| ! [X6] :
( X0 != X6
| ~ rpoint(X6) ) ),
inference(flattening,[],[f172]) ).
fof(f340,plain,
( vd1102 != sK1
& ron(vd1096,sK1)
& rcenter(vd1089,sK1)
& rcircle(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f137]) ).
fof(f414,plain,
rcenter(vd1089,sK1),
inference(cnf_transformation,[],[f340]) ).
fof(f415,plain,
ron(vd1096,sK1),
inference(cnf_transformation,[],[f340]) ).
fof(f416,plain,
vd1102 != sK1,
inference(cnf_transformation,[],[f340]) ).
fof(f418,plain,
rcenter(vd1089,vd1102),
inference(cnf_transformation,[],[f3]) ).
fof(f419,plain,
ron(vd1096,vd1102),
inference(cnf_transformation,[],[f3]) ).
fof(f426,plain,
rpoint(vd1096),
inference(cnf_transformation,[],[f8]) ).
fof(f494,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( X3 = X4
| vf(X2,X0) != vf(X2,X1)
| ~ ron(X1,X4)
| ~ ron(X0,X3)
| ~ rcenter(X2,X4)
| ~ rcenter(X2,X3)
| X1 != X5
| ~ rpoint(X5)
| X0 != X6
| ~ rpoint(X6) ),
inference(cnf_transformation,[],[f173]) ).
fof(f793,plain,
! [X2,X3,X0,X6,X4,X5] :
( X3 = X4
| vf(X2,X0) != vf(X2,X5)
| ~ ron(X5,X4)
| ~ ron(X0,X3)
| ~ rcenter(X2,X4)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X0 != X6
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f494]) ).
fof(f794,plain,
! [X2,X3,X6,X4,X5] :
( ~ rcenter(X2,X4)
| vf(X2,X5) != vf(X2,X6)
| ~ ron(X5,X4)
| ~ ron(X6,X3)
| X3 = X4
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f793]) ).
fof(f1679,plain,
! [X2,X0,X1] :
( ~ rcenter(vd1089,X2)
| ~ ron(X0,sK1)
| ~ ron(X1,X2)
| sK1 = X2
| vf(vd1089,X0) != vf(vd1089,X1)
| ~ rpoint(X0)
| ~ rpoint(X1) ),
inference(resolution,[],[f794,f414]) ).
fof(f2040,plain,
! [X0,X1] :
( ~ ron(X0,sK1)
| ~ ron(X1,vd1102)
| vd1102 = sK1
| vf(vd1089,X0) != vf(vd1089,X1)
| ~ rpoint(X0)
| ~ rpoint(X1) ),
inference(resolution,[],[f1679,f418]) ).
fof(f2043,plain,
! [X0,X1] :
( vf(vd1089,X0) != vf(vd1089,X1)
| ~ ron(X1,vd1102)
| ~ ron(X0,sK1)
| ~ rpoint(X0)
| ~ rpoint(X1) ),
inference(forward_subsumption_resolution,[],[f2040,f416]) ).
fof(f2066,plain,
! [X0] :
( ~ ron(X0,vd1102)
| ~ ron(X0,sK1)
| ~ rpoint(X0)
| ~ rpoint(X0) ),
inference(equality_resolution,[],[f2043]) ).
fof(f2067,plain,
! [X0] :
( ~ ron(X0,vd1102)
| ~ ron(X0,sK1)
| ~ rpoint(X0) ),
inference(duplicate_literal_removal,[],[f2066]) ).
fof(f2088,definition,
( spl49_36
<=> ! [X2] :
( ~ ron(X2,vd1102)
| ~ ron(X2,sK1)
| ~ rpoint(X2) ) ),
introduced(definition,[new_symbols(definition,[spl49_36])],[avatar_definition]) ).
fof(f2089,plain,
( ! [X2] :
( ~ ron(X2,vd1102)
| ~ ron(X2,sK1)
| ~ rpoint(X2) )
| ~ spl49_36 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f2110,plain,
spl49_36,
inference(avatar_split_clause,[],[f2067,f2088]) ).
fof(f2117,plain,
( ~ ron(vd1096,sK1)
| ~ rpoint(vd1096)
| ~ spl49_36 ),
inference(resolution,[],[f2089,f419]) ).
fof(f2160,plain,
( ~ rpoint(vd1096)
| ~ spl49_36 ),
inference(forward_subsumption_resolution,[],[f2117,f415]) ).
fof(f2193,plain,
( $false
| ~ spl49_36 ),
inference(forward_subsumption_resolution,[],[f2160,f426]) ).
fof(f2194,plain,
~ spl49_36,
inference(avatar_contradiction_clause,[],[f2193]) ).
cnf(s49,plain,
spl49_36,
inference(sat_conversion,[],[f2110]) ).
cnf(s56,plain,
~ spl49_36,
inference(sat_conversion,[],[f2194]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s49,s56]) ).
fof(f2195,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO278+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 07:58:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.94/1.55 % (3662649)Detected formulas, will run a generic FOF schedule.
% 3.94/1.55 % (3662654)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=1195660683:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.94/1.55 % (3662656)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=4242323317:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.94/1.55 % (3662655)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=2463276601:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.94/1.55 % (3662659)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1203830337:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.94/1.55 % (3662657)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3978548801:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.94/1.55 % (3662658)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3385876458:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.94/1.55 % (3662660)dis-21_1_sil=8000:lcm=predicate:random_seed=2330311328:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.94/1.55 % (3662657)Refutation not found, incomplete strategy
% 3.94/1.55 % (3662657)------------------------------
% 3.94/1.55 % (3662657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.55 % (3662657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.55 % (3662657)CaDiCaL version: 2.1.3
% 3.94/1.55 % (3662657)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.55 % (3662657)Time elapsed: 0.003 s
% 3.94/1.55 % (3662657)Peak memory usage: 88 MB
% 3.94/1.55 % (3662657)Instructions burned: 3 (million)
% 3.94/1.55 % (3662659)First to succeed.
% 3.94/1.55 % (3662659)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3662649"
% 3.94/1.55 % (3662658)Instruction limit reached!
% 3.94/1.55 % (3662658)------------------------------
% 3.94/1.55 % (3662658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.55 % (3662658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.55 % (3662658)CaDiCaL version: 2.1.3
% 3.94/1.55 % (3662658)Termination reason: Instruction limit
% 3.94/1.55 % (3662658)Termination phase: Saturation
% 3.94/1.55 % (3662658)Time elapsed: 0.066 s
% 3.94/1.55 % (3662658)Peak memory usage: 89 MB
% 3.94/1.55 % (3662658)Instructions burned: 121 (million)
% 3.94/1.55 % (3662660)Instruction limit reached!
% 3.94/1.55 % (3662660)------------------------------
% 3.94/1.55 % (3662660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.55 % (3662660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.55 % (3662660)CaDiCaL version: 2.1.3
% 3.94/1.55 % (3662660)Termination reason: Instruction limit
% 3.94/1.55 % (3662660)Termination phase: Saturation
% 3.94/1.55 % (3662660)Time elapsed: 0.073 s
% 3.94/1.55 % (3662660)Peak memory usage: 91 MB
% 3.94/1.55 % (3662660)Instructions burned: 131 (million)
% 3.94/1.55 % (3662668)lrs+10_1_sil=8000:sp=occurrence:random_seed=3922626499:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.94/1.55 % (3662669)lrs+10_1_sil=32000:urr=on:br=off:random_seed=276687528:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.94/1.55 % (3662657)------------------------------
% 3.94/1.55 % (3662657)------------------------------
% 3.94/1.55 % (3662669)Also succeeded, but the first one will report.
% 3.94/1.55 % (3662659)Refutation found. Thanks to Tanya!
% 3.94/1.55 % SZS status Theorem for theBenchmark
% 3.94/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.55 % (3662659)------------------------------
% 3.94/1.55 % (3662659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.55 % (3662659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.55 % (3662659)CaDiCaL version: 2.1.3
% 3.94/1.55 % (3662659)Termination reason: Refutation
% 3.94/1.55 % (3662659)Time elapsed: 0.039 s
% 3.94/1.55 % (3662659)Peak memory usage: 90 MB
% 3.94/1.55 % (3662659)Instructions burned: 60 (million)
% 3.94/1.55 % (3662659)------------------------------
% 3.94/1.55 % (3662659)------------------------------
% 3.94/1.55 % (3662649)Success in time 0.476 s
% 3.94/1.55 % Vampire exiting
%------------------------------------------------------------------------------