%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:51:52 AM UTC 2026
% Result : Theorem 3.64s 1.49s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 12 unt; 2 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 32 ~; 51 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',apart5) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) )
=> ( incident_point_and_line(X2,line_connecting(X0,X1))
& incident_point_and_line(X3,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) )
=> ( incident_point_and_line(X2,line_connecting(X0,X1))
& incident_point_and_line(X3,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f40]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X2,line_connecting(X0,X1))
| ~ incident_point_and_line(X3,line_connecting(X0,X1)) )
& distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X2,line_connecting(X0,X1))
| ~ incident_point_and_line(X3,line_connecting(X0,X1)) )
& distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) )
& ( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f79,plain,
( ( ~ incident_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK3,line_connecting(sK0,sK1)) )
& distinct_points(sK0,sK1)
& distinct_points(sK2,sK3)
& incident_point_and_line(sK0,line_connecting(sK2,sK3))
& incident_point_and_line(sK1,line_connecting(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f81,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f122,plain,
( ~ incident_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK3,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f124,definition,
( spl4_1
<=> incident_point_and_line(sK3,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f126,plain,
( ~ incident_point_and_line(sK3,line_connecting(sK0,sK1))
| spl4_1 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f128,definition,
( spl4_2
<=> incident_point_and_line(sK2,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f130,plain,
( ~ incident_point_and_line(sK2,line_connecting(sK0,sK1))
| spl4_2 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f122,f128,f124]) ).
fof(f132,plain,
( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| spl4_1 ),
inference(resolution,[],[f117,f126]) ).
fof(f139,plain,
( ! [X0] :
( distinct_lines(line_connecting(sK0,sK1),X0)
| apart_point_and_line(sK3,X0) )
| spl4_1 ),
inference(resolution,[],[f92,f132]) ).
fof(f142,plain,
( ! [X0,X1] :
( distinct_lines(line_connecting(sK0,sK1),X1)
| distinct_lines(X0,X1)
| apart_point_and_line(sK3,X0) )
| spl4_1 ),
inference(resolution,[],[f139,f84]) ).
fof(f147,plain,
( ! [X0] :
( distinct_lines(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK3,X0) )
| spl4_1 ),
inference(resolution,[],[f142,f81]) ).
fof(f154,plain,
( ! [X0] :
( convergent_lines(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK3,X0) )
| spl4_1 ),
inference(resolution,[],[f147,f94]) ).
fof(f159,plain,
( ! [X0] : apart_point_and_line(sK3,parallel_through_point(line_connecting(sK0,sK1),X0))
| spl4_1 ),
inference(resolution,[],[f154,f95]) ).
fof(f163,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f159,f96]) ).
fof(f167,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f163]) ).
fof(f168,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| spl4_2 ),
inference(resolution,[],[f130,f117]) ).
fof(f169,plain,
( ! [X0] :
( distinct_lines(line_connecting(sK0,sK1),X0)
| apart_point_and_line(sK2,X0) )
| spl4_2 ),
inference(resolution,[],[f168,f92]) ).
fof(f173,plain,
( ! [X0,X1] :
( distinct_lines(line_connecting(sK0,sK1),X1)
| distinct_lines(X0,X1)
| apart_point_and_line(sK2,X0) )
| spl4_2 ),
inference(resolution,[],[f169,f84]) ).
fof(f181,plain,
( ! [X0] :
( distinct_lines(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,X0) )
| spl4_2 ),
inference(resolution,[],[f173,f81]) ).
fof(f188,plain,
( ! [X0] :
( convergent_lines(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,X0) )
| spl4_2 ),
inference(resolution,[],[f181,f94]) ).
fof(f192,plain,
( ! [X0] : apart_point_and_line(sK2,parallel_through_point(line_connecting(sK0,sK1),X0))
| spl4_2 ),
inference(resolution,[],[f188,f95]) ).
fof(f195,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f192,f96]) ).
fof(f199,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f195]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f131]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f167]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f199]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f200,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 07:28:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.48/1.30 % (3170796)Detected formulas, will run a generic FOF schedule.
% 2.48/1.30 % (3170807)dis-21_1_sil=8000:lcm=predicate:random_seed=1423882876: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)
% 2.48/1.30 % (3170807)Instruction limit reached!
% 2.48/1.30 % (3170807)------------------------------
% 2.48/1.30 % (3170807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.30 % (3170807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.30 % (3170807)CaDiCaL version: 2.1.3
% 2.48/1.30 % (3170807)Termination reason: Instruction limit
% 2.48/1.30 % (3170807)Termination phase: Saturation
% 2.48/1.30 % (3170807)Time elapsed: 0.038 s
% 2.48/1.30 % (3170807)Peak memory usage: 88 MB
% 2.48/1.30 % (3170807)Instructions burned: 132 (million)
% 2.48/1.30 % (3170805)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=958397604:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.48/1.30 % (3170802)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=1105672682:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.48/1.30 % (3170804)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1255866585:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.48/1.30 % (3170803)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=3325017403:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.48/1.30 % (3170801)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=444939378:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.48/1.30 % (3170806)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2780156696:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.48/1.30 % (3170806)First to succeed.
% 2.48/1.30 % (3170806)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3170796"
% 2.48/1.30 % (3170804)Instruction limit reached!
% 2.48/1.30 % (3170804)------------------------------
% 2.48/1.30 % (3170804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.30 % (3170804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.30 % (3170804)CaDiCaL version: 2.1.3
% 2.48/1.30 % (3170804)Termination reason: Instruction limit
% 2.48/1.30 % (3170804)Termination phase: Saturation
% 2.48/1.30 % (3170804)Time elapsed: 0.055 s
% 2.48/1.30 % (3170804)Peak memory usage: 88 MB
% 2.48/1.30 % (3170804)Instructions burned: 109 (million)
% 2.48/1.30 % (3170805)Instruction limit reached!
% 2.48/1.30 % (3170805)------------------------------
% 2.48/1.30 % (3170805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.30 % (3170805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.30 % (3170805)CaDiCaL version: 2.1.3
% 2.48/1.30 % (3170805)Termination reason: Instruction limit
% 2.48/1.30 % (3170805)Termination phase: Saturation
% 2.48/1.30 % (3170805)Time elapsed: 0.067 s
% 2.48/1.30 % (3170805)Peak memory usage: 87 MB
% 2.48/1.30 % (3170805)Instructions burned: 120 (million)
% 2.48/1.30 % (3170815)lrs+10_1_sil=8000:sp=occurrence:random_seed=3381063393:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.48/1.30 % (3170815)Also succeeded, but the first one will report.
% 2.48/1.30 % (3170816)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3918272966:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.48/1.30 % (3170816)Refutation not found, incomplete strategy
% 2.48/1.30 % (3170816)------------------------------
% 2.48/1.30 % (3170816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.30 % (3170816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.30 % (3170816)CaDiCaL version: 2.1.3
% 2.48/1.30 % (3170816)Termination reason: Refutation not found, incomplete strategy
% 2.48/1.30 % (3170816)Time elapsed: 0.003 s
% 2.48/1.30 % (3170816)Peak memory usage: 88 MB
% 2.48/1.30 % (3170816)Instructions burned: 3 (million)
% 2.48/1.30 % (3170817)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3892278045:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.48/1.30 % (3170817)Refutation not found, incomplete strategy
% 2.48/1.30 % (3170817)------------------------------
% 3.64/1.49 % (3170817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.49 % (3170817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.49 % (3170817)CaDiCaL version: 2.1.3
% 3.64/1.49 % (3170817)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.49 % (3170817)Time elapsed: 0.002 s
% 3.64/1.49 % (3170817)Peak memory usage: 88 MB
% 3.64/1.49 % (3170817)Instructions burned: 1 (million)
% 3.64/1.49 % (3170806)Refutation found. Thanks to Tanya!
% 3.64/1.49 % SZS status Theorem for theBenchmark
% 3.64/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.49 % (3170806)------------------------------
% 3.64/1.49 % (3170806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.49 % (3170806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.49 % (3170806)CaDiCaL version: 2.1.3
% 3.64/1.50 % (3170806)Termination reason: Refutation
% 3.64/1.50 % (3170806)Time elapsed: 0.005 s
% 3.64/1.50 % (3170806)Peak memory usage: 89 MB
% 3.64/1.50 % (3170806)Instructions burned: 5 (million)
% 3.64/1.50 % (3170806)------------------------------
% 3.64/1.50 % (3170806)------------------------------
% 3.64/1.50 % (3170796)Success in time 0.433 s
% 3.64/1.50 % Vampire exiting
%------------------------------------------------------------------------------