%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO198+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 09:51:56 AM UTC 2026
% Result : Theorem 0.53s 0.96s
% Output : Refutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 12 unt; 2 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 57 ~; 75 |; 19 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 84 ( 0 sgn 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK2),X0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f49,f56]) ).
fof(f62,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f51,f40]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X2,X3)
| apart_point_and_line(X2,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X1) ),
inference(resolution,[],[f62,f48]) ).
fof(f83,plain,
! [X2,X0,X1] :
( apart_point_and_line(X1,sK1)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X0)
| ~ convergent_lines(X0,X2)
| apart_point_and_line(intersection_point(sK0,sK2),X2)
| apart_point_and_line(intersection_point(sK0,sK2),X0) ),
inference(resolution,[],[f68,f58]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,sK1)
| apart_point_and_line(intersection_point(X0,sK1),X2)
| ~ convergent_lines(X2,X1)
| apart_point_and_line(intersection_point(sK0,sK2),X1)
| apart_point_and_line(intersection_point(sK0,sK2),X2)
| apart_point_and_line(intersection_point(X0,sK1),X1) ),
inference(resolution,[],[f83,f47]) ).
fof(f166,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0,sK2),X1)
| ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X1) ),
inference(resolution,[],[f95,f55]) ).
fof(f265,plain,
! [X0] :
( ~ convergent_lines(X0,sK2)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ convergent_lines(sK0,sK2) ),
inference(resolution,[],[f166,f47]) ).
fof(f270,plain,
! [X0] :
( ~ convergent_lines(X0,sK2)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| ~ convergent_lines(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f265,f52]) ).
fof(f272,plain,
! [X0] :
( ~ convergent_lines(X0,sK2)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0) ),
inference(forward_subsumption_resolution,[],[f270,f53]) ).
fof(f274,definition,
( spl3_1
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f276,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f281,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
inference(resolution,[],[f272,f53]) ).
fof(f286,definition,
( spl3_3
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f288,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f289,plain,
( spl3_3
| spl3_1 ),
inference(avatar_split_clause,[],[f281,f274,f286]) ).
fof(f305,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f276,f46]) ).
fof(f308,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f305,f55]) ).
fof(f309,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f336,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_3 ),
inference(resolution,[],[f288,f46]) ).
fof(f339,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f336,f53]) ).
fof(f340,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f339]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f289]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f309]) ).
cnf(s6,plain,
~ spl3_3,
inference(sat_conversion,[],[f340]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s6,s4]) ).
fof(f341,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 07:31:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.53/0.96 % (1074566)Detected formulas, will run a generic FOF schedule.
% 0.53/0.96 % (1074576)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=969254522:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.53/0.96 % (1074575)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2122259735:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.53/0.96 % (1074573)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=1601382921:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.53/0.96 % (1074577)dis-21_1_sil=8000:lcm=predicate:random_seed=3385953135: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)
% 0.53/0.96 % (1074571)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=3557134388:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.53/0.96 % (1074574)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3332890869:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.53/0.96 % (1074572)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=3366885144:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.53/0.96 % (1074574)Refutation not found, incomplete strategy
% 0.53/0.96 % (1074574)------------------------------
% 0.53/0.96 % (1074574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/0.96 % (1074574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.96 % (1074574)CaDiCaL version: 2.1.3
% 0.53/0.96 % (1074574)Termination reason: Refutation not found, incomplete strategy
% 0.53/0.96 % (1074574)Time elapsed: 0.001 s
% 0.53/0.96 % (1074574)Peak memory usage: 87 MB
% 0.53/0.96 % (1074575)Refutation not found, incomplete strategy
% 0.53/0.96 % (1074575)------------------------------
% 0.53/0.96 % (1074575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/0.96 % (1074575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.96 % (1074575)CaDiCaL version: 2.1.3
% 0.53/0.96 % (1074575)Termination reason: Refutation not found, incomplete strategy
% 0.53/0.96 % (1074575)Time elapsed: 0.001 s
% 0.53/0.96 % (1074575)Peak memory usage: 88 MB
% 0.53/0.96 % (1074576)First to succeed.
% 0.53/0.96 % (1074576)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1074566"
% 0.53/0.96 % (1074577)Instruction limit reached!
% 0.53/0.96 % (1074577)------------------------------
% 0.53/0.96 % (1074577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.53/0.96 % (1074577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.96 % (1074577)CaDiCaL version: 2.1.3
% 0.53/0.96 % (1074577)Termination reason: Instruction limit
% 0.53/0.96 % (1074577)Termination phase: Saturation
% 0.53/0.96 % (1074577)Time elapsed: 0.068 s
% 0.53/0.96 % (1074577)Peak memory usage: 89 MB
% 0.53/0.96 % (1074577)Instructions burned: 129 (million)
% 0.53/0.96 % (1074585)lrs+10_1_sil=8000:sp=occurrence:random_seed=2268619328:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.53/0.96 % (1074576)Refutation found. Thanks to Tanya!
% 0.53/0.96 % SZS status Theorem for theBenchmark
% 0.53/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.87/1.06 % (1074576)------------------------------
% 2.87/1.06 % (1074576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.06 % (1074576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.06 % (1074576)CaDiCaL version: 2.1.3
% 2.87/1.06 % (1074576)Termination reason: Refutation
% 2.87/1.06 % (1074576)Time elapsed: 0.017 s
% 2.87/1.06 % (1074576)Peak memory usage: 89 MB
% 2.87/1.06 % (1074576)Instructions burned: 28 (million)
% 2.87/1.06 % (1074576)------------------------------
% 2.87/1.06 % (1074576)------------------------------
% 2.87/1.06 % (1074566)Success in time 0.368 s
% 2.87/1.06 % Vampire exiting
%------------------------------------------------------------------------------