%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO077-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:53:30 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.45s
% Output : Refutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 67 ( 21 unt; 2 def)
% Number of atoms : 245 ( 79 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 297 ( 119 ~; 176 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ line(X1)
| ~ line(X3)
| ~ on(X2,X1)
| X1 = X3
| ~ on(X0,X3)
| ~ on(X2,X3)
| ~ point(X0)
| ~ point(X2)
| ~ on(X0,X1)
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1D) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| ~ point(X1)
| ~ point(X2)
| X0 = X1
| X0 = X2
| X1 = X2
| on(X0,line_through_3_points(X0,X1,X2))
| ~ point(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10A) ).
fof(f32,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| ~ point(X1)
| ~ point(X2)
| X0 = X1
| X0 = X2
| X1 = X2
| on(X1,line_through_3_points(X0,X1,X2))
| ~ point(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10B) ).
fof(f33,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| ~ point(X1)
| ~ point(X2)
| X0 = X1
| X0 = X2
| X1 = X2
| on(X2,line_through_3_points(X0,X1,X2))
| ~ point(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10C) ).
fof(f34,axiom,
! [X2,X0,X1] :
( ~ collinear(X0,X1,X2)
| ~ point(X1)
| ~ point(X2)
| X0 = X1
| X0 = X2
| X1 = X2
| line(line_through_3_points(X0,X1,X2))
| ~ point(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10D) ).
fof(f36,axiom,
point(point1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1) ).
fof(f37,axiom,
point(point2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2) ).
fof(f38,axiom,
point(point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3) ).
fof(f39,axiom,
line(a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',line) ).
fof(f40,axiom,
on(point1,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_on_line) ).
fof(f41,axiom,
on(point2,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_on_line) ).
fof(f42,axiom,
~ on(point3,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3_not_on_line) ).
fof(f43,axiom,
point1 != point2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point2) ).
fof(f44,axiom,
point1 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point3) ).
fof(f45,axiom,
point2 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_not_point3) ).
fof(f46,negated_conjecture,
collinear(point1,point2,point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_points_noncollinear) ).
fof(f68,plain,
( ~ point(point2)
| ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| line(line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(resolution,[],[f34,f46]) ).
fof(f71,plain,
( ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| line(line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f68,f37]) ).
fof(f72,plain,
( point1 = point2
| point1 = point3
| point2 = point3
| line(line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f71,f38]) ).
fof(f73,plain,
( point1 = point3
| point2 = point3
| line(line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f72,f43]) ).
fof(f74,plain,
( point2 = point3
| line(line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f73,f44]) ).
fof(f75,plain,
( line(line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f74,f45]) ).
fof(f76,plain,
line(line_through_3_points(point1,point2,point3)),
inference(forward_subsumption_resolution,[],[f75,f36]) ).
fof(f90,plain,
( ~ point(point2)
| ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| on(point1,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(resolution,[],[f31,f46]) ).
fof(f99,plain,
( ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| on(point1,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f90,f37]) ).
fof(f100,plain,
( point1 = point2
| point1 = point3
| point2 = point3
| on(point1,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f99,f38]) ).
fof(f101,plain,
( point1 = point3
| point2 = point3
| on(point1,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f100,f43]) ).
fof(f102,plain,
( point2 = point3
| on(point1,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f101,f44]) ).
fof(f103,plain,
( on(point1,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f102,f45]) ).
fof(f104,plain,
on(point1,line_through_3_points(point1,point2,point3)),
inference(forward_subsumption_resolution,[],[f103,f36]) ).
fof(f105,plain,
( ~ point(point2)
| ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| on(point2,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(resolution,[],[f32,f46]) ).
fof(f114,plain,
( ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| on(point2,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f105,f37]) ).
fof(f115,plain,
( point1 = point2
| point1 = point3
| point2 = point3
| on(point2,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f114,f38]) ).
fof(f116,plain,
( point1 = point3
| point2 = point3
| on(point2,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f115,f43]) ).
fof(f117,plain,
( point2 = point3
| on(point2,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f116,f44]) ).
fof(f118,plain,
( on(point2,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f117,f45]) ).
fof(f119,plain,
on(point2,line_through_3_points(point1,point2,point3)),
inference(forward_subsumption_resolution,[],[f118,f36]) ).
fof(f120,plain,
( ~ point(point2)
| ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| on(point3,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(resolution,[],[f33,f46]) ).
fof(f129,plain,
( ~ point(point3)
| point1 = point2
| point1 = point3
| point2 = point3
| on(point3,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f120,f37]) ).
fof(f130,plain,
( point1 = point2
| point1 = point3
| point2 = point3
| on(point3,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f129,f38]) ).
fof(f131,plain,
( point1 = point3
| point2 = point3
| on(point3,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f130,f43]) ).
fof(f132,plain,
( point2 = point3
| on(point3,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f131,f44]) ).
fof(f133,plain,
( on(point3,line_through_3_points(point1,point2,point3))
| ~ point(point1) ),
inference(forward_subsumption_resolution,[],[f132,f45]) ).
fof(f134,plain,
on(point3,line_through_3_points(point1,point2,point3)),
inference(forward_subsumption_resolution,[],[f133,f36]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ line(X0)
| ~ on(X1,X0)
| line_through_3_points(point1,point2,point3) = X0
| ~ on(X2,line_through_3_points(point1,point2,point3))
| ~ on(X1,line_through_3_points(point1,point2,point3))
| ~ point(X2)
| ~ point(X1)
| ~ on(X2,X0)
| X1 = X2 ),
inference(resolution,[],[f5,f76]) ).
fof(f166,plain,
! [X0,X1] :
( ~ on(X0,a_line)
| a_line = line_through_3_points(point1,point2,point3)
| ~ on(X1,line_through_3_points(point1,point2,point3))
| ~ on(X0,line_through_3_points(point1,point2,point3))
| ~ point(X1)
| ~ point(X0)
| ~ on(X1,a_line)
| X0 = X1 ),
inference(resolution,[],[f141,f39]) ).
fof(f169,definition,
( spl0_1
<=> a_line = line_through_3_points(point1,point2,point3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f171,plain,
( a_line = line_through_3_points(point1,point2,point3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f173,definition,
( spl0_2
<=> ! [X0,X1] :
( ~ on(X0,a_line)
| X0 = X1
| ~ point(X0)
| ~ on(X0,line_through_3_points(point1,point2,point3))
| ~ on(X1,line_through_3_points(point1,point2,point3))
| ~ on(X1,a_line)
| ~ point(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f174,plain,
( ! [X0,X1] :
( ~ on(X0,line_through_3_points(point1,point2,point3))
| ~ on(X1,line_through_3_points(point1,point2,point3))
| ~ point(X0)
| ~ on(X0,a_line)
| X0 = X1
| ~ on(X1,a_line)
| ~ point(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f175,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f166,f173,f169]) ).
fof(f266,plain,
( ! [X0] :
( ~ on(X0,line_through_3_points(point1,point2,point3))
| ~ point(X0)
| ~ on(X0,a_line)
| point2 = X0
| ~ on(point2,a_line)
| ~ point(point2) )
| ~ spl0_2 ),
inference(resolution,[],[f174,f119]) ).
fof(f274,plain,
( ! [X0] :
( ~ on(X0,line_through_3_points(point1,point2,point3))
| ~ point(X0)
| ~ on(X0,a_line)
| point2 = X0
| ~ point(point2) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f266,f41]) ).
fof(f286,plain,
( ! [X0] :
( ~ on(X0,line_through_3_points(point1,point2,point3))
| ~ point(X0)
| ~ on(X0,a_line)
| point2 = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f274,f37]) ).
fof(f377,plain,
( on(point3,a_line)
| ~ spl0_1 ),
inference(superposition,[],[f134,f171]) ).
fof(f380,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f377,f42]) ).
fof(f381,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f560,plain,
( ~ point(point1)
| ~ on(point1,a_line)
| point1 = point2
| ~ spl0_2 ),
inference(resolution,[],[f286,f104]) ).
fof(f566,plain,
( ~ on(point1,a_line)
| point1 = point2
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f560,f36]) ).
fof(f568,plain,
( point1 = point2
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f566,f40]) ).
fof(f570,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f568,f43]) ).
fof(f571,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f570]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f381]) ).
cnf(s21,plain,
~ spl0_2,
inference(sat_conversion,[],[f571]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s21,s5]) ).
fof(f576,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO077-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 06:51:52 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.40 Running first-order model finding
% 0.03/0.40 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
% 0.03/0.45 % (3155544)Will run a generic schedule for satisfiability detection.
% 0.03/0.45 % (3155553)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1894173168:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.03/0.45 % (3155550)% WARNING: option uhcvi not known.
% 0.03/0.45 % (3155549)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3348330530_2999 on theBenchmark for (2999ds/0Mi)
% 0.03/0.45 % (3155554)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1068814743:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.03/0.45 % (3155550)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3732233418:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.03/0.45 % (3155551)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1186685749:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.03/0.45 % (3155552)dis+10_1_sil=32000:sp=arity:random_seed=2568100923:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.03/0.45 % (3155555)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=718805229:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.03/0.45 % Detected minimum model sizes of [3]
% 0.03/0.45 % Detected maximum model sizes of [max]
% 0.03/0.45 % TRYING [3]
% 0.03/0.45 % TRYING [4]
% 0.03/0.45 % (3155553) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3155544-3155553"...
% 0.03/0.45 % (3155553)...printing done.
% 0.03/0.45 % (3155555) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3155544-3155555"...
% 0.03/0.45 % (3155553)Refutation found. Thanks to Tanya!
% 0.03/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.03/0.45 % (3155553)------------------------------
% 0.03/0.45 % (3155553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.03/0.45 % (3155553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.03/0.45 % (3155553)CaDiCaL version: 2.1.3
% 0.03/0.45 % (3155553)Termination reason: Refutation
% 0.03/0.45 % (3155553)Time elapsed: 0.015 s
% 0.03/0.45 % (3155553)Peak memory usage: 12 MB
% 0.03/0.45 % (3155553)Instructions burned: 49 (million)
% 0.03/0.45 % (3155544)Success in time 0.042 s
% 0.03/0.45 % Vampire exiting
%------------------------------------------------------------------------------