%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO198+2 : 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 : n020.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 09:53:57 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 19 unt; 5 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 200 ( 71 ~; 95 |; 21 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 84 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
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/sandbox/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
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(f23,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
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(f27,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,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,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
distinct_lines(sK0,sK2),
inference(resolution,[],[f48,f50]) ).
fof(f63,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK2),X0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f46,f53]) ).
fof(f76,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f83,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f45,f54]) ).
fof(f92,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK1)
| distinct_points(X0,X1)
| distinct_points(intersection_point(sK0,sK2),X1) ),
inference(resolution,[],[f63,f38]) ).
fof(f170,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0,sK2))
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f92,f35]) ).
fof(f251,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f252,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK0)
| spl3_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f255,definition,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f256,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK2)
| spl3_5 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl3_6
<=> ! [X0] :
( apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f260,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f275,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_4 ),
inference(resolution,[],[f253,f79]) ).
fof(f280,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f275,f50]) ).
fof(f281,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f306,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_5 ),
inference(resolution,[],[f257,f76]) ).
fof(f311,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f306,f50]) ).
fof(f312,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f358,plain,
! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK2)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f170,f83]) ).
fof(f362,plain,
( ! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK2)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0) )
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f358,f252]) ).
fof(f363,plain,
( ! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0) )
| spl3_4
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f362,f256]) ).
fof(f364,plain,
( spl3_6
| spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f363,f255,f251,f259]) ).
fof(f520,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_6 ),
inference(resolution,[],[f260,f49]) ).
fof(f529,definition,
( spl3_13
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f531,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f533,definition,
( spl3_14
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f535,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f536,plain,
( spl3_13
| spl3_14
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f520,f259,f533,f529]) ).
fof(f544,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_13 ),
inference(resolution,[],[f531,f79]) ).
fof(f549,plain,
( $false
| ~ spl3_13 ),
inference(forward_subsumption_resolution,[],[f544,f52]) ).
fof(f550,plain,
~ spl3_13,
inference(avatar_contradiction_clause,[],[f549]) ).
fof(f564,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_14 ),
inference(resolution,[],[f535,f76]) ).
fof(f569,plain,
( $false
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f564,f52]) ).
fof(f570,plain,
~ spl3_14,
inference(avatar_contradiction_clause,[],[f569]) ).
cnf(s8,plain,
~ spl3_4,
inference(sat_conversion,[],[f281]) ).
cnf(s9,plain,
~ spl3_5,
inference(sat_conversion,[],[f312]) ).
cnf(s13,plain,
( spl3_4
| spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f364]) ).
cnf(s14,plain,
( ~ spl3_6
| spl3_13
| spl3_14 ),
inference(sat_conversion,[],[f536]) ).
cnf(s16,plain,
~ spl3_13,
inference(sat_conversion,[],[f550]) ).
cnf(s19,plain,
~ spl3_14,
inference(sat_conversion,[],[f570]) ).
cnf(s20,plain,
~ spl3_6,
inference(rat,[],[s14,s19,s16]) ).
cnf(s21,plain,
( spl3_4
| spl3_5 ),
inference(rat,[],[s13,s20]) ).
cnf(s22,plain,
spl3_4,
inference(rat,[],[s21,s9]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s8,s22]) ).
fof(f571,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:34:05 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.48 % (3070635)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3070644)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1155862736:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3070641)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3070640)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1412186890_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3070641)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2539561449:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3070642)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3937253745:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3070643)dis+10_1_sil=32000:sp=arity:random_seed=2248848649:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3070645)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=218997546:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3070646)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1694276346:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % TRYING [6]
% 0.17/0.48 % (3070643) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3070635-3070643"...
% 0.17/0.48 % (3070643)...printing done.
% 0.17/0.48 % (3070643)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3070643)------------------------------
% 0.17/0.48 % (3070643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3070643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3070643)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3070643)Termination reason: Refutation
% 0.17/0.48 % (3070643)Time elapsed: 0.012 s
% 0.17/0.48 % (3070643)Peak memory usage: 12 MB
% 0.17/0.48 % (3070643)Instructions burned: 18 (million)
% 0.17/0.48 % (3070635)Success in time 0.049 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------