%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO177+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 09:53:49 AM UTC 2026
% Result : Theorem 0.36s 0.48s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 19 unt; 4 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 215 ( 77 ~; 109 |; 15 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 89 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
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,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f36,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(f37,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)],[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(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f48,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(f49,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,[],[f48]) ).
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] :
( ~ 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,[],[f37]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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)],[f77]) ).
fof(f80,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,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,[],[f49]) ).
fof(f91,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(f93,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f95,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f115,plain,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f116,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK3))
| apart_point_and_line(sK1,line_connecting(sK2,sK3)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
~ apart_point_and_line(sK3,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f121,definition,
( spl4_1
<=> apart_point_and_line(sK1,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f123,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK3))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl4_2
<=> apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f127,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK3))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f117,f125,f121]) ).
fof(f371,definition,
( spl4_3
<=> apart_point_and_line(sK3,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f372,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK2,sK3))
| spl4_3 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f373,plain,
( apart_point_and_line(sK3,line_connecting(sK2,sK3))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f378,definition,
( spl4_5
<=> apart_point_and_line(sK2,line_connecting(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f379,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK2,sK3))
| spl4_5 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f380,plain,
( apart_point_and_line(sK2,line_connecting(sK2,sK3))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f424,plain,
( ! [X0] :
( distinct_lines(line_connecting(sK2,sK3),X0)
| apart_point_and_line(sK1,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f123,f91]) ).
fof(f427,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,[],[f424,f89]) ).
fof(f431,plain,
( ~ distinct_points(sK2,sK3)
| ~ spl4_3 ),
inference(resolution,[],[f373,f86]) ).
fof(f434,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f431,f115]) ).
fof(f435,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f452,plain,
( ~ distinct_points(sK2,sK3)
| ~ spl4_5 ),
inference(resolution,[],[f380,f85]) ).
fof(f455,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f452,f115]) ).
fof(f456,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f575,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,[],[f427,f115]) ).
fof(f606,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,[],[f575,f372]) ).
fof(f615,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_5 ),
inference(forward_subsumption_resolution,[],[f606,f379]) ).
fof(f654,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_1
| spl4_3
| spl4_5 ),
inference(resolution,[],[f615,f118]) ).
fof(f658,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_1
| spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f654,f119]) ).
fof(f659,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_1
| spl4_3
| spl4_5 ),
inference(resolution,[],[f658,f86]) ).
fof(f662,plain,
( $false
| ~ spl4_1
| spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f659,f116]) ).
fof(f663,plain,
( ~ spl4_1
| spl4_3
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f662]) ).
fof(f665,plain,
( ! [X0] :
( distinct_lines(line_connecting(sK2,sK3),X0)
| apart_point_and_line(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f127,f91]) ).
fof(f671,plain,
( ! [X0,X1] :
( apart_point_and_line(sK0,X0)
| distinct_lines(X0,X1)
| distinct_lines(line_connecting(sK2,sK3),X1) )
| ~ spl4_2 ),
inference(resolution,[],[f665,f83]) ).
fof(f708,plain,
( ! [X0] :
( distinct_lines(X0,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f671,f80]) ).
fof(f855,plain,
( ! [X0] :
( convergent_lines(X0,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f708,f93]) ).
fof(f904,plain,
( ! [X0] : apart_point_and_line(sK0,parallel_through_point(line_connecting(sK2,sK3),X0))
| ~ spl4_2 ),
inference(resolution,[],[f855,f94]) ).
fof(f923,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f904,f95]) ).
fof(f926,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f923]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
~ spl4_3,
inference(sat_conversion,[],[f435]) ).
cnf(s15,plain,
~ spl4_5,
inference(sat_conversion,[],[f456]) ).
cnf(s18,plain,
( ~ spl4_1
| spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f663]) ).
cnf(s29,plain,
~ spl4_2,
inference(sat_conversion,[],[f926]) ).
cnf(s31,plain,
~ spl4_1,
inference(rat,[],[s18,s15,s14]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s29,s31]) ).
fof(f927,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO177+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n016.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 07:29:17 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.42 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
% 0.36/0.48 % (2290261)Will run a generic schedule for satisfiability detection.
% 0.36/0.48 % (2290272)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1127946337:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.48 % (2290267)% WARNING: option uhcvi not known.
% 0.36/0.48 % (2290266)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2500087014_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.48 % (2290268)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2539104555:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.48 % (2290269)dis+10_1_sil=32000:sp=arity:random_seed=2457260884:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.48 % (2290270)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2002468207:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.48 % (2290271)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=114505611:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.48 % (2290267)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3446439804:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.48 % TRYING [1]
% 0.36/0.48 % TRYING [2]
% 0.36/0.48 % TRYING [3]
% 0.36/0.48 % TRYING [4]
% 0.36/0.48 % TRYING [5]
% 0.36/0.48 % TRYING [6]
% 0.36/0.48 % (2290269) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2290261-2290269"...
% 0.36/0.48 % (2290269)...printing done.
% 0.36/0.48 % (2290269)Refutation found. Thanks to Tanya!
% 0.36/0.48 % SZS status Theorem for theBenchmark
% 0.36/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.48 % (2290269)------------------------------
% 0.36/0.48 % (2290269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.48 % (2290269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.48 % (2290269)CaDiCaL version: 2.1.3
% 0.36/0.48 % (2290269)Termination reason: Refutation
% 0.36/0.48 % (2290269)Time elapsed: 0.019 s
% 0.36/0.48 % (2290269)Peak memory usage: 12 MB
% 0.36/0.48 % (2290269)Instructions burned: 28 (million)
% 0.36/0.48 % (2290261)Success in time 0.058 s
% 0.36/0.48 % Vampire exiting
%------------------------------------------------------------------------------