%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:51:54 AM UTC 2026
% Result : Theorem 2.45s 1.23s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 12 unt; 2 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 57 ~; 57 |; 10 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 73 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X0,X2)
& distinct_lines(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X0,X2)
& distinct_lines(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ( ~ distinct_lines(X0,X2)
| ~ distinct_lines(X1,X2) )
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ( ~ distinct_lines(X0,X2)
| ~ distinct_lines(X1,X2) )
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ( ~ distinct_lines(sK0,sK2)
| ~ distinct_lines(sK1,sK2) )
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
( ~ distinct_lines(sK0,sK2)
| ~ distinct_lines(sK1,sK2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,definition,
( spl3_1
<=> distinct_lines(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f55,plain,
( ~ distinct_lines(sK1,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl3_2
<=> distinct_lines(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f59,plain,
( ~ distinct_lines(sK0,sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f51,f57,f53]) ).
fof(f87,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f35,f44]) ).
fof(f88,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f35,f43]) ).
fof(f113,plain,
! [X2,X0,X1] :
( distinct_lines(X2,X0)
| ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(resolution,[],[f87,f47]) ).
fof(f118,plain,
! [X2,X0,X1] :
( distinct_lines(X2,X1)
| ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(resolution,[],[f88,f47]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( distinct_lines(X0,X3)
| ~ apart_point_and_line(intersection_point(X0,X1),X2)
| ~ convergent_lines(X0,X1)
| distinct_lines(X2,X3) ),
inference(resolution,[],[f113,f39]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( distinct_lines(X1,X3)
| ~ apart_point_and_line(intersection_point(X0,X1),X2)
| ~ convergent_lines(X0,X1)
| distinct_lines(X2,X3) ),
inference(resolution,[],[f118,f39]) ).
fof(f232,plain,
( ! [X0,X1] :
( distinct_lines(X1,sK2)
| ~ convergent_lines(X0,sK1)
| ~ apart_point_and_line(intersection_point(X0,sK1),X1) )
| spl3_1 ),
inference(resolution,[],[f153,f55]) ).
fof(f415,plain,
( ! [X0] :
( ~ apart_point_and_line(intersection_point(X0,sK1),sK2)
| ~ convergent_lines(X0,sK1) )
| spl3_1 ),
inference(resolution,[],[f232,f36]) ).
fof(f423,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_1 ),
inference(resolution,[],[f415,f50]) ).
fof(f427,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f423,f49]) ).
fof(f428,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f440,plain,
( ! [X0,X1] :
( distinct_lines(X1,sK2)
| ~ convergent_lines(sK0,X0)
| ~ apart_point_and_line(intersection_point(sK0,X0),X1) )
| spl3_2 ),
inference(resolution,[],[f59,f138]) ).
fof(f490,plain,
( ! [X0] :
( ~ apart_point_and_line(intersection_point(sK0,X0),sK2)
| ~ convergent_lines(sK0,X0) )
| spl3_2 ),
inference(resolution,[],[f440,f36]) ).
fof(f511,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_2 ),
inference(resolution,[],[f490,f50]) ).
fof(f515,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f511,f49]) ).
fof(f516,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f515]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
spl3_1,
inference(sat_conversion,[],[f428]) ).
cnf(s6,plain,
spl3_2,
inference(sat_conversion,[],[f516]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
fof(f517,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n016.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 07:35:17 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 2.45/1.22 % (2293242)Detected formulas, will run a generic FOF schedule.
% 2.45/1.22 % (2293252)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1327564674:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/1.22 % (2293252)First to succeed.
% 2.45/1.22 % (2293252)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2293242"
% 2.45/1.22 % (2293247)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=3318673207:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/1.22 % (2293250)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3996977635:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/1.22 % (2293248)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=820411801:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/1.22 % (2293253)dis-21_1_sil=8000:lcm=predicate:random_seed=892239457: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)
% 2.45/1.22 % (2293249)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=3197358239:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/1.22 % (2293251)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1794973168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/1.22 % (2293251)Also succeeded, but the first one will report.
% 2.45/1.22 % (2293253)Also succeeded, but the first one will report.
% 2.45/1.22 % (2293250)Instruction limit reached!
% 2.45/1.22 % (2293250)------------------------------
% 2.45/1.22 % (2293250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.22 % (2293250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.22 % (2293250)CaDiCaL version: 2.1.3
% 2.45/1.22 % (2293250)Termination reason: Instruction limit
% 2.45/1.22 % (2293250)Termination phase: Saturation
% 2.45/1.22 % (2293250)Time elapsed: 0.062 s
% 2.45/1.22 % (2293250)Peak memory usage: 88 MB
% 2.45/1.23 % (2293250)Instructions burned: 109 (million)
% 2.45/1.23 % (2293252)Refutation found. Thanks to Tanya!
% 2.45/1.23 % SZS status Theorem for theBenchmark
% 2.45/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/1.23 % (2293252)------------------------------
% 2.45/1.23 % (2293252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.23 % (2293252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.23 % (2293252)CaDiCaL version: 2.1.3
% 2.45/1.23 % (2293252)Termination reason: Refutation
% 2.45/1.23 % (2293252)Time elapsed: 0.011 s
% 2.45/1.23 % (2293252)Peak memory usage: 89 MB
% 2.45/1.23 % (2293252)Instructions burned: 26 (million)
% 2.45/1.23 % (2293252)------------------------------
% 2.45/1.23 % (2293252)------------------------------
% 2.45/1.23 % (2293242)Success in time 0.276 s
% 2.45/1.23 % Vampire exiting
%------------------------------------------------------------------------------