TSTP Solution File: GEO202+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO202+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:16:04 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 14 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 233 ( 81 ~; 107 |; 26 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 109 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f421,plain,
$false,
inference(avatar_sat_refutation,[],[f245,f293,f316,f337,f352,f354,f400,f420]) ).
fof(f420,plain,
spl3_7,
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f416,plain,
( $false
| spl3_7 ),
inference(resolution,[],[f399,f38]) ).
fof(f38,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
& convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f35]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ( distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
& convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2] :
( distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X1,X2] :
( distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f399,plain,
( ~ distinct_points(sK0,sK2)
| spl3_7 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f397,plain,
( spl3_7
<=> distinct_points(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f400,plain,
( ~ spl3_7
| spl3_6
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f371,f234,f334,f397]) ).
fof(f334,plain,
( spl3_6
<=> distinct_points(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f234,plain,
( spl3_2
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f371,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK2)
| ~ spl3_2 ),
inference(resolution,[],[f236,f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X1)
& distinct_points(X2,X0) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X1)
& distinct_points(X2,X0) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
fof(f236,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f354,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f353,plain,
( $false
| ~ spl3_6 ),
inference(resolution,[],[f336,f43]) ).
fof(f43,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f336,plain,
( distinct_points(sK0,sK0)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f352,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f348,plain,
( $false
| spl3_5 ),
inference(resolution,[],[f332,f37]) ).
fof(f37,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f332,plain,
( ~ distinct_points(sK0,sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f330,plain,
( spl3_5
<=> distinct_points(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f337,plain,
( ~ spl3_5
| spl3_6
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f318,f242,f334,f330]) ).
fof(f242,plain,
( spl3_4
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f318,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f244,f52]) ).
fof(f244,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f316,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f314,plain,
( $false
| spl3_3 ),
inference(resolution,[],[f240,f39]) ).
fof(f39,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f36]) ).
fof(f240,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| spl3_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f238,plain,
( spl3_3
<=> convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f293,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f291,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f290,f39]) ).
fof(f290,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| spl3_1 ),
inference(resolution,[],[f273,f44]) ).
fof(f44,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f273,plain,
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| spl3_1 ),
inference(resolution,[],[f260,f42]) ).
fof(f42,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f260,plain,
( ! [X0] :
( distinct_lines(X0,line_connecting(sK0,sK1))
| ~ distinct_lines(X0,line_connecting(sK0,sK2)) )
| spl3_1 ),
inference(resolution,[],[f232,f48]) ).
fof(f48,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f232,plain,
( ~ distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1))
| spl3_1 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f230,plain,
( spl3_1
<=> distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f245,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f184,f242,f238,f234,f230]) ).
fof(f184,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1)) ),
inference(resolution,[],[f171,f40]) ).
fof(f40,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ distinct_points(intersection_point(X1,X0),X2)
| apart_point_and_line(X2,X1)
| ~ convergent_lines(X1,X0)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[],[f129,f43]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( distinct_points(X3,intersection_point(X2,X1))
| ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ convergent_lines(X2,X1)
| apart_point_and_line(X0,X1)
| ~ distinct_points(X3,X0) ),
inference(resolution,[],[f110,f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,intersection_point(X1,X2))
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X1)
| apart_point_and_line(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f103,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X1)
| ~ distinct_points(X0,intersection_point(X1,X2))
| ~ convergent_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(resolution,[],[f73,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f47,f43]) ).
fof(f47,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X2)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X3,X2)
| ~ distinct_lines(X2,X0)
| ~ distinct_points(X3,intersection_point(X0,X1))
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f54,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f46,f43]) ).
fof(f46,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f54,plain,
! [X2,X3,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)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,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)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1,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)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( 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(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X3,X4] :
( ( distinct_lines(X3,X4)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X4)
| apart_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO202+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 21:57:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (5754)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (5759)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38 % (5755)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38 % (5756)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (5758)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38 % (5757)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.38 % (5760)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38 % (5761)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.38 TRYING [5]
% 0.15/0.39 % (5757)First to succeed.
% 0.15/0.39 TRYING [6]
% 0.15/0.39 TRYING [6]
% 0.15/0.39 % (5757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5754"
% 0.15/0.39 TRYING [6]
% 0.15/0.39 % (5757)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (5757)------------------------------
% 0.15/0.39 % (5757)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (5757)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (5757)Memory used [KB]: 974
% 0.15/0.39 % (5757)Time elapsed: 0.016 s
% 0.15/0.39 % (5757)Instructions burned: 25 (million)
% 0.15/0.39 % (5754)Success in time 0.032 s
%------------------------------------------------------------------------------