%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO193+1 : 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 : n011.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 2.40s 1.18s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 12 unt; 2 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 55 ~; 79 |; 17 &)
% ( 2 <=>; 9 =>; 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 : 85 ( 0 sgn 79 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(X2,X1),X0) ) ),
file('/export/starexec/sandbox/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(X2,X1),X0) ) ),
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(X2,X1),X0)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X2,X1),X0)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ~ apart_point_and_line(intersection_point(sK2,sK1),sK0)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,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(f53,plain,
convergent_lines(sK2,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK1),X0)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f49,f55]) ).
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,sK2)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X0)
| ~ convergent_lines(X0,X2)
| apart_point_and_line(intersection_point(sK0,sK1),X2)
| apart_point_and_line(intersection_point(sK0,sK1),X0) ),
inference(resolution,[],[f68,f58]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ convergent_lines(sK2,X0)
| apart_point_and_line(intersection_point(sK2,X0),X2)
| ~ convergent_lines(X2,X1)
| apart_point_and_line(intersection_point(sK0,sK1),X1)
| apart_point_and_line(intersection_point(sK0,sK1),X2)
| apart_point_and_line(intersection_point(sK2,X0),X1) ),
inference(resolution,[],[f83,f46]) ).
fof(f181,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0,sK1),X1)
| ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK2,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK2,sK1),X1) ),
inference(resolution,[],[f95,f53]) ).
fof(f377,plain,
! [X0] :
( ~ convergent_lines(X0,sK1)
| apart_point_and_line(intersection_point(sK2,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK2,sK1),sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f181,f47]) ).
fof(f382,plain,
! [X0] :
( ~ convergent_lines(X0,sK1)
| apart_point_and_line(intersection_point(sK2,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK2,sK1),sK1) ),
inference(forward_subsumption_resolution,[],[f377,f54]) ).
fof(f385,definition,
( spl3_8
<=> apart_point_and_line(intersection_point(sK2,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f387,plain,
( apart_point_and_line(intersection_point(sK2,sK1),sK1)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f389,definition,
( spl3_9
<=> ! [X0] :
( ~ convergent_lines(X0,sK1)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK2,sK1),X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f390,plain,
( ! [X0] :
( ~ convergent_lines(X0,sK1)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK2,sK1),X0) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f391,plain,
( spl3_8
| spl3_9 ),
inference(avatar_split_clause,[],[f382,f389,f385]) ).
fof(f393,plain,
( ~ convergent_lines(sK2,sK1)
| ~ spl3_8 ),
inference(resolution,[],[f387,f47]) ).
fof(f396,plain,
( $false
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f393,f53]) ).
fof(f397,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f396]) ).
fof(f487,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK2,sK1),sK0)
| ~ spl3_9 ),
inference(resolution,[],[f390,f54]) ).
fof(f492,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f487,f56]) ).
fof(f496,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_9 ),
inference(resolution,[],[f492,f46]) ).
fof(f499,plain,
( $false
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f496,f54]) ).
fof(f500,plain,
~ spl3_9,
inference(avatar_contradiction_clause,[],[f499]) ).
cnf(s7,plain,
( spl3_8
| spl3_9 ),
inference(sat_conversion,[],[f391]) ).
cnf(s8,plain,
~ spl3_8,
inference(sat_conversion,[],[f397]) ).
cnf(s12,plain,
~ spl3_9,
inference(sat_conversion,[],[f500]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s7,s12,s8]) ).
fof(f501,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO193+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:30:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.40/1.18 % (2065602)Detected formulas, will run a generic FOF schedule.
% 2.40/1.18 % (2065695)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3078888752:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.40/1.18 % (2065695)First to succeed.
% 2.40/1.18 % (2065695)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2065602"
% 2.40/1.18 % (2065692)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=2179384193:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.40/1.18 % (2065691)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=3415300417:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.40/1.18 % (2065693)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=794955236:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.40/1.18 % (2065694)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=515481917:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.40/1.18 % (2065690)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=2967132375:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.40/1.18 % (2065693)Refutation not found, incomplete strategy
% 2.40/1.18 % (2065693)------------------------------
% 2.40/1.18 % (2065693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.18 % (2065693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.18 % (2065693)CaDiCaL version: 2.1.3
% 2.40/1.18 % (2065693)Termination reason: Refutation not found, incomplete strategy
% 2.40/1.18 % (2065693)Time elapsed: 0.001 s
% 2.40/1.18 % (2065693)Peak memory usage: 87 MB
% 2.40/1.18 % (2065694)Refutation not found, incomplete strategy
% 2.40/1.18 % (2065694)------------------------------
% 2.40/1.18 % (2065694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.18 % (2065694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.18 % (2065694)CaDiCaL version: 2.1.3
% 2.40/1.18 % (2065694)Termination reason: Refutation not found, incomplete strategy
% 2.40/1.18 % (2065694)Time elapsed: 0.001 s
% 2.40/1.18 % (2065694)Peak memory usage: 87 MB
% 2.40/1.18 % (2065696)dis-21_1_sil=8000:lcm=predicate:random_seed=1280326521: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)
% 2.40/1.18 % (2065696)Instruction limit reached!
% 2.40/1.18 % (2065696)------------------------------
% 2.40/1.18 % (2065696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.18 % (2065696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.18 % (2065696)CaDiCaL version: 2.1.3
% 2.40/1.18 % (2065696)Termination reason: Instruction limit
% 2.40/1.18 % (2065696)Termination phase: Saturation
% 2.40/1.18 % (2065696)Time elapsed: 0.069 s
% 2.40/1.18 % (2065696)Peak memory usage: 89 MB
% 2.40/1.18 % (2065696)Instructions burned: 131 (million)
% 2.40/1.18 % (2065695)Refutation found. Thanks to Tanya!
% 2.40/1.18 % SZS status Theorem for theBenchmark
% 2.40/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.37 % (2065695)------------------------------
% 2.85/1.37 % (2065695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.37 % (2065695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.37 % (2065695)CaDiCaL version: 2.1.3
% 2.85/1.37 % (2065695)Termination reason: Refutation
% 2.85/1.37 % (2065695)Time elapsed: 0.020 s
% 2.85/1.37 % (2065695)Peak memory usage: 89 MB
% 2.85/1.37 % (2065695)Instructions burned: 38 (million)
% 2.85/1.37 % (2065695)------------------------------
% 2.85/1.37 % (2065695)------------------------------
% 2.85/1.37 % (2065602)Success in time 0.32 s
% 2.85/1.37 % Vampire exiting
%------------------------------------------------------------------------------