%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO189+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 : n015.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 09:53:53 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 17 unt; 5 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 67 ~; 92 |; 18 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 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(X1,line_connecting(X0,X2)) ),
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(X1,line_connecting(X0,X2)) ),
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(X1,line_connecting(X0,X2))
& 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(X1,line_connecting(X0,X2))
& 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(f50,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
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(f65,plain,
! [X0] :
( ~ distinct_lines(line_connecting(sK0,sK2),X0)
| apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f56,f52]) ).
fof(f70,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f55,f50]) ).
fof(f102,plain,
! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK2,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f70,f65]) ).
fof(f104,definition,
( spl3_1
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f106,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl3_2
<=> apart_point_and_line(sK2,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f110,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK2))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f112,definition,
( spl3_3
<=> ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f113,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( spl3_1
| spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f102,f112,f108,f104]) ).
fof(f119,plain,
( ~ distinct_points(sK0,sK2)
| distinct_points(sK2,sK2)
| ~ spl3_2 ),
inference(resolution,[],[f110,f40]) ).
fof(f122,plain,
( distinct_points(sK2,sK2)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f119,f50]) ).
fof(f124,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f122,f34]) ).
fof(f125,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f124]) ).
fof(f154,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_3 ),
inference(resolution,[],[f113,f48]) ).
fof(f161,definition,
( spl3_4
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f163,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl3_5
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f167,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl3_4
| spl3_5
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f154,f112,f165,f161]) ).
fof(f218,plain,
( ~ distinct_points(sK0,sK1)
| distinct_points(sK0,sK0)
| ~ spl3_4 ),
inference(resolution,[],[f163,f41]) ).
fof(f222,plain,
( distinct_points(sK0,sK0)
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f218,f51]) ).
fof(f223,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f222,f34]) ).
fof(f224,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f226,plain,
( ~ distinct_points(sK0,sK1)
| distinct_points(sK1,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f167,f40]) ).
fof(f229,plain,
( distinct_points(sK1,sK1)
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f226,f60]) ).
fof(f230,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f229,f34]) ).
fof(f231,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f230]) ).
fof(f232,plain,
( ~ distinct_points(sK0,sK2)
| distinct_points(sK0,sK0)
| ~ spl3_1 ),
inference(resolution,[],[f106,f41]) ).
fof(f236,plain,
( distinct_points(sK0,sK0)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f232,f50]) ).
fof(f237,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f236,f34]) ).
fof(f238,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f237]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f114]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f125]) ).
cnf(s3,plain,
( ~ spl3_3
| spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f168]) ).
cnf(s5,plain,
~ spl3_4,
inference(sat_conversion,[],[f224]) ).
cnf(s6,plain,
~ spl3_5,
inference(sat_conversion,[],[f231]) ).
cnf(s7,plain,
~ spl3_1,
inference(sat_conversion,[],[f238]) ).
cnf(s9,plain,
~ spl3_3,
inference(rat,[],[s3,s6,s5]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s9,s2,s7]) ).
fof(f239,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 07:33:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.10/0.44 % (1319708)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (1319713)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2076226647_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % TRYING [1]
% 0.10/0.44 % TRYING [2]
% 0.10/0.44 % TRYING [3]
% 0.10/0.44 % TRYING [4]
% 0.10/0.44 % TRYING [5]
% 0.10/0.44 % TRYING [6]
% 0.10/0.44 % TRYING [7]
% 0.10/0.44 % (1319714)% WARNING: option uhcvi not known.
% 0.10/0.44 % TRYING [8]
% 0.10/0.44 % TRYING [9]
% 0.10/0.44 % (1319717)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2393125195:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.44 % (1319719)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3704347389:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % TRYING [10]
% 0.10/0.44 % (1319715)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=896648530:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (1319716)dis+10_1_sil=32000:sp=arity:random_seed=175155869:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (1319718)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2917945144:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (1319714)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=348052988:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.44 % TRYING [11]
% 0.10/0.44 % TRYING [12]
% 0.10/0.44 % (1319714) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1319708-1319714"...
% 0.10/0.44 % TRYING [13]
% 0.10/0.44 % (1319714)...printing done.
% 0.10/0.44 % (1319716) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1319708-1319716"...
% 0.10/0.44 % (1319714)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1319714)------------------------------
% 0.10/0.45 % (1319714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1319714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1319714)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1319714)Termination reason: Refutation
% 0.10/0.45 % (1319714)Time elapsed: 0.007 s
% 0.10/0.45 % (1319714)Peak memory usage: 12 MB
% 0.10/0.45 % (1319714)Instructions burned: 9 (million)
% 0.10/0.45 % (1319708)Success in time 0.042 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------