%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO187+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:53:52 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 80 ( 17 unt; 7 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 248 ( 110 ~; 104 |; 21 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 69 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
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/Axioms/GEO006+0.ax',cu1) ).
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/Axioms/GEO006+0.ax',ceq2) ).
fof(f15,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_points(X2,X3)
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& ~ apart_point_and_line(X1,line_connecting(X2,X3)) )
=> ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& ~ apart_point_and_line(X3,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_points(X2,X3)
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& ~ apart_point_and_line(X1,line_connecting(X2,X3)) )
=> ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& ~ apart_point_and_line(X3,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
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(f31,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(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X2,line_connecting(X0,X1))
| apart_point_and_line(X3,line_connecting(X0,X1)) )
& distinct_points(X0,X1)
& distinct_points(X2,X3)
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& ~ apart_point_and_line(X1,line_connecting(X2,X3)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X2,line_connecting(X0,X1))
| apart_point_and_line(X3,line_connecting(X0,X1)) )
& distinct_points(X0,X1)
& distinct_points(X2,X3)
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& ~ apart_point_and_line(X1,line_connecting(X2,X3)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK3,line_connecting(sK0,sK1)) )
& distinct_points(sK0,sK1)
& distinct_points(sK2,sK3)
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
& ~ apart_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)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
~ apart_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK3,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f60,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2)
| ~ apart_point_and_line(X0,X3)
| ~ apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X1)
| distinct_lines(X2,X3) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f65,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X2)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f67,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ apart_point_and_line(sK3,line_connecting(sK0,sK1)) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f68,plain,
apart_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f69,plain,
apart_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f71,definition,
( spl4_1
<=> apart_point_and_line(sK3,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f73,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
| spl4_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl4_2
<=> apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f77,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
| spl4_2 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f67,f75,f71]) ).
fof(f89,definition,
( spl4_3
<=> distinct_points(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f91,plain,
( ~ distinct_points(sK0,sK1)
| spl4_3 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f105,plain,
( $false
| spl4_3 ),
inference(resolution,[],[f91,f55]) ).
fof(f107,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f258,plain,
! [X0,X1] :
( distinct_lines(X0,line_connecting(sK2,sK3))
| ~ apart_point_and_line(X1,line_connecting(sK2,sK3))
| ~ apart_point_and_line(X1,X0)
| ~ distinct_points(X1,sK1)
| ~ apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f63,f69]) ).
fof(f398,definition,
( spl4_17
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
fof(f400,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
| spl4_17 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f418,definition,
( spl4_22
<=> distinct_points(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
fof(f420,plain,
( ~ distinct_points(sK2,sK3)
| spl4_22 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f422,plain,
( $false
| spl4_22 ),
inference(resolution,[],[f420,f54]) ).
fof(f426,plain,
spl4_22,
inference(avatar_contradiction_clause,[],[f422]) ).
fof(f427,plain,
( ~ distinct_points(sK0,sK1)
| spl4_17 ),
inference(resolution,[],[f400,f59]) ).
fof(f430,plain,
( ~ spl4_3
| spl4_17 ),
inference(avatar_split_clause,[],[f427,f398,f89]) ).
fof(f456,plain,
( ! [X0] :
( ~ apart_point_and_line(sK2,X0)
| ~ distinct_lines(line_connecting(sK0,sK1),X0) )
| spl4_2 ),
inference(resolution,[],[f77,f65]) ).
fof(f458,plain,
( ! [X0] :
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,X0))
| ~ distinct_points(sK2,X0) )
| spl4_2 ),
inference(resolution,[],[f456,f59]) ).
fof(f481,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK2,sK3))
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ distinct_points(sK2,sK3) )
| spl4_2 ),
inference(resolution,[],[f258,f458]) ).
fof(f485,definition,
( spl4_24
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
fof(f487,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
| spl4_24 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f489,definition,
( spl4_25
<=> ! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK2,sK3))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition]) ).
fof(f490,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,line_connecting(sK2,sK3))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f491,plain,
( ~ spl4_22
| ~ spl4_24
| spl4_25
| spl4_2 ),
inference(avatar_split_clause,[],[f481,f75,f489,f485,f418]) ).
fof(f493,plain,
( ~ distinct_points(sK0,sK1)
| spl4_24 ),
inference(resolution,[],[f487,f60]) ).
fof(f496,plain,
( ~ spl4_3
| spl4_24 ),
inference(avatar_split_clause,[],[f493,f485,f89]) ).
fof(f535,plain,
( ! [X0] :
( ~ apart_point_and_line(sK3,X0)
| ~ distinct_lines(line_connecting(sK0,sK1),X0) )
| spl4_1 ),
inference(resolution,[],[f73,f65]) ).
fof(f542,plain,
( ! [X0] :
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(X0,sK3))
| ~ distinct_points(X0,sK3) )
| spl4_1 ),
inference(resolution,[],[f535,f60]) ).
fof(f556,plain,
( ! [X0] :
( ~ distinct_points(sK2,sK3)
| ~ apart_point_and_line(X0,line_connecting(sK2,sK3))
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1)) )
| spl4_1 ),
inference(resolution,[],[f542,f258]) ).
fof(f574,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_25 ),
inference(resolution,[],[f490,f68]) ).
fof(f583,plain,
( ~ spl4_17
| ~ spl4_3
| ~ spl4_25 ),
inference(avatar_split_clause,[],[f574,f489,f89,f398]) ).
fof(f584,plain,
( ~ spl4_24
| spl4_25
| ~ spl4_22
| spl4_1 ),
inference(avatar_split_clause,[],[f556,f71,f418,f489,f485]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f78]) ).
cnf(s4,plain,
spl4_3,
inference(sat_conversion,[],[f107]) ).
cnf(s19,plain,
spl4_22,
inference(sat_conversion,[],[f426]) ).
cnf(s20,plain,
( ~ spl4_3
| spl4_17 ),
inference(sat_conversion,[],[f430]) ).
cnf(s22,plain,
( spl4_2
| ~ spl4_22
| ~ spl4_24
| spl4_25 ),
inference(sat_conversion,[],[f491]) ).
cnf(s24,plain,
( ~ spl4_3
| spl4_24 ),
inference(sat_conversion,[],[f496]) ).
cnf(s28,plain,
( ~ spl4_3
| ~ spl4_17
| ~ spl4_25 ),
inference(sat_conversion,[],[f583]) ).
cnf(s29,plain,
( spl4_1
| ~ spl4_22
| ~ spl4_24
| spl4_25 ),
inference(sat_conversion,[],[f584]) ).
cnf(s31,plain,
spl4_24,
inference(rat,[],[s24,s4]) ).
cnf(s32,plain,
spl4_17,
inference(rat,[],[s20,s4]) ).
cnf(s33,plain,
~ spl4_25,
inference(rat,[],[s28,s4,s32]) ).
cnf(s35,plain,
spl4_1,
inference(rat,[],[s29,s31,s19,s33]) ).
cnf(s36,plain,
spl4_2,
inference(rat,[],[s22,s31,s19,s33]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s1,s36,s35]) ).
fof(f585,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 07:28:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 Running first-order model finding
% 0.13/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 % (3169878)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (3169888)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4219017579:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.44 % (3169884)% WARNING: option uhcvi not known.
% 0.13/0.44 % (3169883)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=899078261_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.44 % (3169884)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2571179266:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.44 % (3169885)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4109302059:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.44 % (3169889)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2384214612:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.44 % (3169886)dis+10_1_sil=32000:sp=arity:random_seed=2330154062:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.44 % (3169887)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1374810870:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.44 % TRYING [1]
% 0.13/0.44 % TRYING [2]
% 0.13/0.44 % TRYING [3]
% 0.13/0.44 % TRYING [4]
% 0.13/0.44 % TRYING [5]
% 0.13/0.44 % TRYING [6]
% 0.13/0.44 % (3169889) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3169878-3169889"...
% 0.13/0.44 % TRYING [7]
% 0.13/0.44 % (3169889)...printing done.
% 0.13/0.44 % (3169889)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (3169889)------------------------------
% 0.13/0.44 % (3169889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (3169889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (3169889)CaDiCaL version: 2.1.3
% 0.13/0.44 % (3169889)Termination reason: Refutation
% 0.13/0.44 % (3169889)Time elapsed: 0.015 s
% 0.13/0.44 % (3169889)Peak memory usage: 12 MB
% 0.13/0.44 % (3169889)Instructions burned: 22 (million)
% 0.13/0.44 % (3169878)Success in time 0.05 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------