%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO177+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 09:53:48 AM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 14 unt; 5 def)
% Number of atoms : 233 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 234 ( 76 ~; 130 |; 15 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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))
& ( apart_point_and_line(X0,line_connecting(X2,X3))
| apart_point_and_line(X1,line_connecting(X2,X3)) )
& distinct_points(X0,X1)
& distinct_points(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))
& ( apart_point_and_line(X0,line_connecting(X2,X3))
| apart_point_and_line(X1,line_connecting(X2,X3)) )
& distinct_points(X0,X1)
& distinct_points(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))
& ( apart_point_and_line(sK0,line_connecting(sK2,sK3))
| apart_point_and_line(sK1,line_connecting(sK2,sK3)) )
& distinct_points(sK0,sK1)
& distinct_points(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] :
( ~ 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(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK3))
| apart_point_and_line(sK1,line_connecting(sK2,sK3)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
~ apart_point_and_line(sK3,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f58,definition,
( spl4_1
<=> apart_point_and_line(sK1,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f60,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl4_2
<=> apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f64,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK3))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f54,f62,f58]) ).
fof(f209,definition,
( spl4_3
<=> apart_point_and_line(sK3,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f210,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK2,sK3))
| spl4_3 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f211,plain,
( apart_point_and_line(sK3,line_connecting(sK2,sK3))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f221,definition,
( spl4_6
<=> apart_point_and_line(sK2,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f222,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK2,sK3))
| spl4_6 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f223,plain,
( apart_point_and_line(sK2,line_connecting(sK2,sK3))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f233,definition,
( spl4_9
<=> ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f234,plain,
( ! [X0] :
( apart_point_and_line(sK3,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,X0) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f237,plain,
( ~ distinct_points(sK2,sK3)
| ~ spl4_3 ),
inference(resolution,[],[f211,f45]) ).
fof(f240,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f237,f52]) ).
fof(f241,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f244,plain,
( ~ distinct_points(sK2,sK3)
| ~ spl4_6 ),
inference(resolution,[],[f223,f44]) ).
fof(f247,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f244,f52]) ).
fof(f248,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f249,plain,
( ! [X0] :
( distinct_lines(line_connecting(sK2,sK3),X0)
| apart_point_and_line(sK1,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f60,f50]) ).
fof(f252,plain,
( ! [X2,X0,X1] :
( ~ distinct_points(X1,X2)
| apart_point_and_line(X1,X0)
| apart_point_and_line(X2,line_connecting(sK2,sK3))
| apart_point_and_line(X2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X1,line_connecting(sK2,sK3)) )
| ~ spl4_1 ),
inference(resolution,[],[f249,f48]) ).
fof(f329,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK3,line_connecting(sK2,sK3))
| apart_point_and_line(sK3,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,line_connecting(sK2,sK3)) )
| ~ spl4_1 ),
inference(resolution,[],[f252,f52]) ).
fof(f352,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK3,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,line_connecting(sK2,sK3)) )
| ~ spl4_1
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f329,f210]) ).
fof(f356,plain,
( ! [X0] :
( apart_point_and_line(sK3,X0)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0) )
| ~ spl4_1
| spl4_3
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f352,f222]) ).
fof(f382,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_1
| spl4_3
| spl4_6 ),
inference(resolution,[],[f356,f55]) ).
fof(f386,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_1
| spl4_3
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f382,f56]) ).
fof(f387,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_1
| spl4_3
| spl4_6 ),
inference(resolution,[],[f386,f45]) ).
fof(f390,plain,
( $false
| ~ spl4_1
| spl4_3
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f387,f53]) ).
fof(f391,plain,
( ~ spl4_1
| spl4_3
| spl4_6 ),
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f393,plain,
( ! [X0] :
( distinct_lines(line_connecting(sK2,sK3),X0)
| apart_point_and_line(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f64,f50]) ).
fof(f397,plain,
( ! [X2,X0,X1] :
( ~ distinct_points(X1,X2)
| apart_point_and_line(X1,X0)
| apart_point_and_line(X2,line_connecting(sK2,sK3))
| apart_point_and_line(X2,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X1,line_connecting(sK2,sK3)) )
| ~ spl4_2 ),
inference(resolution,[],[f393,f48]) ).
fof(f489,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK3,line_connecting(sK2,sK3))
| apart_point_and_line(sK3,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,line_connecting(sK2,sK3)) )
| ~ spl4_2 ),
inference(resolution,[],[f397,f52]) ).
fof(f511,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK3,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,line_connecting(sK2,sK3)) )
| ~ spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f489,f210]) ).
fof(f517,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK3,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl4_2
| spl4_3
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f511,f222]) ).
fof(f518,plain,
( spl4_9
| ~ spl4_2
| spl4_3
| spl4_6 ),
inference(avatar_split_clause,[],[f517,f221,f209,f62,f233]) ).
fof(f521,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ spl4_9 ),
inference(resolution,[],[f234,f55]) ).
fof(f525,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f521,f56]) ).
fof(f526,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_9 ),
inference(resolution,[],[f525,f44]) ).
fof(f529,plain,
( $false
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f526,f53]) ).
fof(f530,plain,
~ spl4_9,
inference(avatar_contradiction_clause,[],[f529]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s8,plain,
~ spl4_3,
inference(sat_conversion,[],[f241]) ).
cnf(s9,plain,
~ spl4_6,
inference(sat_conversion,[],[f248]) ).
cnf(s11,plain,
( ~ spl4_1
| spl4_3
| spl4_6 ),
inference(sat_conversion,[],[f391]) ).
cnf(s18,plain,
( ~ spl4_2
| spl4_3
| spl4_6
| spl4_9 ),
inference(sat_conversion,[],[f518]) ).
cnf(s19,plain,
~ spl4_9,
inference(sat_conversion,[],[f530]) ).
cnf(s20,plain,
( ~ spl4_2
| spl4_3
| spl4_6 ),
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
~ spl4_2,
inference(rat,[],[s20,s9,s8]) ).
cnf(s22,plain,
~ spl4_1,
inference(rat,[],[s11,s9,s8]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s21,s22]) ).
fof(f531,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 07:24:15 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 % (2061082)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (2061089)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3959809424:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (2061088)% WARNING: option uhcvi not known.
% 0.18/0.48 % (2061087)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2567693010_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (2061088)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3350997367:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (2061090)dis+10_1_sil=32000:sp=arity:random_seed=3708147577:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (2061091)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1715379686:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (2061092)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=696965971:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (2061093)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4130312588:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % TRYING [4]
% 0.18/0.48 % TRYING [5]
% 0.18/0.48 % TRYING [6]
% 0.18/0.48 % (2061090) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2061082-2061090"...
% 0.18/0.48 % (2061088) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2061082-2061088"...
% 0.18/0.48 % (2061090)...printing done.
% 0.18/0.48 % (2061090)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (2061090)------------------------------
% 0.18/0.48 % (2061090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (2061090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (2061090)CaDiCaL version: 2.1.3
% 0.18/0.48 % (2061090)Termination reason: Refutation
% 0.18/0.48 % (2061090)Time elapsed: 0.012 s
% 0.18/0.48 % (2061090)Peak memory usage: 12 MB
% 0.18/0.48 % (2061090)Instructions burned: 16 (million)
% 0.18/0.48 % (2061082)Success in time 0.046 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------