%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO188+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 : n005.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 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 18 unt; 5 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 63 ~; 80 |; 19 &)
% ( 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 : 80 ( 0 sgn 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).
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] :
( ( 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(X0,line_connecting(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,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(X0,line_connecting(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
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] :
( apart_point_and_line(X0,line_connecting(X2,X1))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( apart_point_and_line(X0,line_connecting(X2,X1))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK1))
& distinct_points(sK0,sK1)
& distinct_points(sK0,sK2)
& distinct_points(sK1,sK2)
& ~ apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
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,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0] :
( distinct_points(sK2,X0)
| distinct_points(sK1,X0) ),
inference(resolution,[],[f41,f53]) ).
fof(f61,plain,
! [X0,X1] :
( distinct_points(sK1,X0)
| distinct_points(X0,X1)
| distinct_points(sK2,X1) ),
inference(resolution,[],[f57,f41]) ).
fof(f67,plain,
! [X0] :
( distinct_lines(line_connecting(sK2,sK1),X0)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f50,f56]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X2)
| apart_point_and_line(X2,line_connecting(sK2,sK1))
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,X1) ),
inference(resolution,[],[f48,f67]) ).
fof(f80,plain,
! [X0] :
( distinct_points(sK1,X0)
| distinct_points(X0,sK2) ),
inference(resolution,[],[f61,f38]) ).
fof(f89,plain,
! [X0,X1] :
( distinct_points(X0,sK2)
| distinct_points(X0,X1)
| distinct_points(sK1,X1) ),
inference(resolution,[],[f80,f41]) ).
fof(f126,plain,
! [X0] :
( distinct_points(X0,sK2)
| distinct_points(X0,sK1) ),
inference(resolution,[],[f89,f38]) ).
fof(f143,plain,
distinct_points(sK2,sK1),
inference(resolution,[],[f126,f38]) ).
fof(f174,plain,
! [X0] :
( apart_point_and_line(sK1,line_connecting(sK2,sK1))
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK2,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f76,f143]) ).
fof(f195,definition,
( spl3_2
<=> apart_point_and_line(sK2,line_connecting(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f197,plain,
( apart_point_and_line(sK2,line_connecting(sK2,sK1))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f208,definition,
( spl3_5
<=> apart_point_and_line(sK1,line_connecting(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f210,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK1))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl3_6
<=> ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f213,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( spl3_2
| spl3_6
| spl3_5 ),
inference(avatar_split_clause,[],[f174,f208,f212,f195]) ).
fof(f233,plain,
( ~ distinct_points(sK2,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f210,f45]) ).
fof(f236,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f233,f143]) ).
fof(f237,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f240,plain,
( ~ distinct_points(sK2,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f197,f44]) ).
fof(f243,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f240,f143]) ).
fof(f244,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f245,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_6 ),
inference(resolution,[],[f213,f52]) ).
fof(f251,definition,
( spl3_11
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f253,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f255,definition,
( spl3_12
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f257,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,plain,
( spl3_11
| spl3_12
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f245,f212,f255,f251]) ).
fof(f280,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_12 ),
inference(resolution,[],[f257,f44]) ).
fof(f283,plain,
( $false
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f280,f55]) ).
fof(f284,plain,
~ spl3_12,
inference(avatar_contradiction_clause,[],[f283]) ).
fof(f302,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_11 ),
inference(resolution,[],[f253,f45]) ).
fof(f305,plain,
( $false
| ~ spl3_11 ),
inference(forward_subsumption_resolution,[],[f302,f55]) ).
fof(f306,plain,
~ spl3_11,
inference(avatar_contradiction_clause,[],[f305]) ).
cnf(s5,plain,
( spl3_2
| spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f215]) ).
cnf(s11,plain,
~ spl3_5,
inference(sat_conversion,[],[f237]) ).
cnf(s12,plain,
~ spl3_2,
inference(sat_conversion,[],[f244]) ).
cnf(s13,plain,
( ~ spl3_6
| spl3_11
| spl3_12 ),
inference(sat_conversion,[],[f258]) ).
cnf(s14,plain,
~ spl3_12,
inference(sat_conversion,[],[f284]) ).
cnf(s15,plain,
~ spl3_11,
inference(sat_conversion,[],[f306]) ).
cnf(s16,plain,
~ spl3_6,
inference(rat,[],[s13,s14,s15]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s5,s16,s11,s12]) ).
fof(f307,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:29:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (3652159)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (3652164)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3870327700_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % TRYING [4]
% 0.11/0.46 % TRYING [5]
% 0.11/0.46 % TRYING [6]
% 0.11/0.46 % TRYING [7]
% 0.11/0.46 % (3652168)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2878963285:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (3652169)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1973718736:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (3652170)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1736955741:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (3652167)dis+10_1_sil=32000:sp=arity:random_seed=2374923213:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (3652165)% WARNING: option uhcvi not known.
% 0.11/0.46 % (3652166)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=205868359:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % TRYING [8]
% 0.11/0.46 % (3652165)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1458640766:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (3652167) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3652159-3652167"...
% 0.11/0.46 % (3652167)...printing done.
% 0.11/0.46 % (3652167)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (3652167)------------------------------
% 0.11/0.46 % (3652167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (3652167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (3652167)CaDiCaL version: 2.1.3
% 0.11/0.46 % (3652167)Termination reason: Refutation
% 0.11/0.46 % (3652167)Time elapsed: 0.007 s
% 0.11/0.46 % (3652167)Peak memory usage: 12 MB
% 0.11/0.46 % (3652167)Instructions burned: 10 (million)
% 0.11/0.46 % (3652159)Success in time 0.043 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------