%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO190+2 : 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 09:53:54 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 18 unt; 6 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 205 ( 74 ~; 100 |; 18 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 77 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(f9,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/GEO008+0.ax',cu1) ).
fof(f11,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/GEO008+0.ax',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X2,line_connecting(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X2,line_connecting(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0,X1,X2] :
( apart_point_and_line(X2,line_connecting(X1,X0))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( apart_point_and_line(X2,line_connecting(X1,X0))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1)
| distinct_points(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1)
| distinct_points(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(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) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
apart_point_and_line(sK2,line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f60,plain,
! [X0] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(resolution,[],[f37,f51]) ).
fof(f67,plain,
! [X0] :
( ~ distinct_lines(line_connecting(sK1,sK0),X0)
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f56,f52]) ).
fof(f76,definition,
( spl3_2
<=> distinct_points(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f77,plain,
( distinct_points(sK1,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( ~ distinct_points(sK1,sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f82,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f55,f51]) ).
fof(f87,plain,
( distinct_points(sK0,sK0)
| spl3_2 ),
inference(resolution,[],[f60,f78]) ).
fof(f91,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f87,f34]) ).
fof(f92,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f111,plain,
! [X0] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f82,f67]) ).
fof(f113,definition,
( spl3_3
<=> apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f115,plain,
( apart_point_and_line(sK0,line_connecting(sK1,sK0))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f117,definition,
( spl3_4
<=> apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f119,plain,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f121,definition,
( spl3_5
<=> ! [X0] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f122,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( spl3_3
| spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f111,f121,f117,f113]) ).
fof(f128,plain,
( ~ distinct_points(sK1,sK0)
| distinct_points(sK1,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f119,f41]) ).
fof(f132,plain,
( distinct_points(sK1,sK1)
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f128,f77]) ).
fof(f133,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f132,f34]) ).
fof(f134,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f178,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_5 ),
inference(resolution,[],[f122,f48]) ).
fof(f184,definition,
( spl3_6
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f186,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f188,definition,
( spl3_7
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f190,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( spl3_6
| spl3_7
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f178,f121,f188,f184]) ).
fof(f213,plain,
( ~ distinct_points(sK0,sK1)
| distinct_points(sK0,sK0)
| ~ spl3_6 ),
inference(resolution,[],[f186,f41]) ).
fof(f217,plain,
( distinct_points(sK0,sK0)
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f213,f51]) ).
fof(f218,plain,
( $false
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f217,f34]) ).
fof(f219,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f267,plain,
( ~ distinct_points(sK0,sK1)
| distinct_points(sK1,sK1)
| ~ spl3_7 ),
inference(resolution,[],[f190,f40]) ).
fof(f270,plain,
( distinct_points(sK1,sK1)
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f267,f60]) ).
fof(f271,plain,
( $false
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f270,f34]) ).
fof(f272,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f274,plain,
( ~ distinct_points(sK1,sK0)
| distinct_points(sK0,sK0)
| ~ spl3_3 ),
inference(resolution,[],[f115,f40]) ).
fof(f277,plain,
( distinct_points(sK0,sK0)
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f274,f60]) ).
fof(f278,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f277,f34]) ).
fof(f279,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f92]) ).
cnf(s3,plain,
( spl3_3
| spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f123]) ).
cnf(s4,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f134]) ).
cnf(s5,plain,
( ~ spl3_5
| spl3_6
| spl3_7 ),
inference(sat_conversion,[],[f191]) ).
cnf(s7,plain,
~ spl3_6,
inference(sat_conversion,[],[f219]) ).
cnf(s8,plain,
~ spl3_7,
inference(sat_conversion,[],[f272]) ).
cnf(s9,plain,
~ spl3_3,
inference(sat_conversion,[],[f279]) ).
cnf(s11,plain,
~ spl3_5,
inference(rat,[],[s5,s8,s7]) ).
cnf(s12,plain,
spl3_4,
inference(rat,[],[s3,s11,s9]) ).
cnf(s13,plain,
~ spl3_2,
inference(rat,[],[s4,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s13]) ).
fof(f280,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO190+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 07:29:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.46 % (3172532)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3172542)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1604829840:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3172538)% WARNING: option uhcvi not known.
% 0.16/0.46 % (3172537)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=767292211_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (3172539)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2852607770:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (3172540)dis+10_1_sil=32000:sp=arity:random_seed=4154329807:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3172541)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=54171964:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (3172543)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2076826351:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (3172538)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4238695775:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % TRYING [5]
% 0.16/0.46 % TRYING [6]
% 0.16/0.46 % TRYING [7]
% 0.16/0.46 % TRYING [8]
% 0.16/0.46 % (3172538) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3172532-3172538"...
% 0.16/0.46 % (3172540) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3172532-3172540"...
% 0.16/0.46 % (3172538)...printing done.
% 0.16/0.46 % TRYING [9]
% 0.16/0.46 % (3172540)...printing done.
% 0.16/0.46 % (3172538)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (3172538)------------------------------
% 0.16/0.46 % (3172538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (3172538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (3172538)CaDiCaL version: 2.1.3
% 0.16/0.46 % (3172538)Termination reason: Refutation
% 0.16/0.46 % (3172538)Time elapsed: 0.008 s
% 0.16/0.46 % (3172538)Peak memory usage: 12 MB
% 0.16/0.46 % (3172538)Instructions burned: 11 (million)
% 0.16/0.46 % (3172532)Success in time 0.041 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------