TSTP Solution File: GEO203+3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GEO203+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n012.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 : Wed Aug 30 23:31:46 EDT 2023
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 66 ( 23 unt; 0 def)
% Number of atoms : 159 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 155 ( 62 ~; 59 |; 21 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 114 (; 105 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f701,plain,
$false,
inference(avatar_sat_refutation,[],[f612,f627,f700]) ).
fof(f700,plain,
~ spl8_18,
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f695,plain,
( $false
| ~ spl8_18 ),
inference(resolution,[],[f579,f148]) ).
fof(f148,plain,
distinct_points(sF5,sF6),
inference(definition_folding,[],[f105,f145,f144]) ).
fof(f144,plain,
intersection_point(sK2,sK3) = sF5,
introduced(function_definition,[]) ).
fof(f145,plain,
intersection_point(sK2,sK4) = sF6,
introduced(function_definition,[]) ).
fof(f105,plain,
distinct_points(intersection_point(sK2,sK3),intersection_point(sK2,sK4)),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( ~ equal_lines(line_connecting(intersection_point(sK2,sK3),intersection_point(sK2,sK4)),sK2)
& distinct_points(intersection_point(sK2,sK3),intersection_point(sK2,sK4))
& convergent_lines(sK2,sK4)
& convergent_lines(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f53,f97]) ).
fof(f97,plain,
( ? [X0,X1,X2] :
( ~ equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> ( ~ equal_lines(line_connecting(intersection_point(sK2,sK3),intersection_point(sK2,sK4)),sK2)
& distinct_points(intersection_point(sK2,sK3),intersection_point(sK2,sK4))
& convergent_lines(sK2,sK4)
& convergent_lines(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
? [X0,X1,X2] :
( ~ equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ~ equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',con) ).
fof(f579,plain,
( ! [X90] : ~ distinct_points(X90,sF6)
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f578,plain,
( spl8_18
<=> ! [X90] : ~ distinct_points(X90,sF6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f627,plain,
~ spl8_11,
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f621,plain,
( $false
| ~ spl8_11 ),
inference(resolution,[],[f469,f152]) ).
fof(f152,plain,
distinct_lines(sF7,sK2),
inference(resolution,[],[f124,f147]) ).
fof(f147,plain,
~ equal_lines(sF7,sK2),
inference(definition_folding,[],[f106,f146,f145,f144]) ).
fof(f146,plain,
line_connecting(sF5,sF6) = sF7,
introduced(function_definition,[]) ).
fof(f106,plain,
~ equal_lines(line_connecting(intersection_point(sK2,sK3),intersection_point(sK2,sK4)),sK2),
inference(cnf_transformation,[],[f98]) ).
fof(f124,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',ax2) ).
fof(f469,plain,
( ! [X22] : ~ distinct_lines(X22,sK2)
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f468,plain,
( spl8_11
<=> ! [X22] : ~ distinct_lines(X22,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f612,plain,
( spl8_18
| spl8_11 ),
inference(avatar_split_clause,[],[f611,f468,f578]) ).
fof(f611,plain,
! [X111,X110] :
( ~ distinct_lines(X110,sK2)
| ~ distinct_points(X111,sF6) ),
inference(subsumption_resolution,[],[f610,f362]) ).
fof(f362,plain,
! [X3,X4] : ~ apart_point_and_line(X3,X4),
inference(resolution,[],[f190,f241]) ).
fof(f241,plain,
! [X10,X11] : ~ distinct_lines(X10,parallel_through_point(X10,X11)),
inference(resolution,[],[f235,f115]) ).
fof(f115,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',p1) ).
fof(f235,plain,
! [X2,X1] : ~ convergent_lines(X1,parallel_through_point(X1,X2)),
inference(resolution,[],[f209,f151]) ).
fof(f151,plain,
! [X2,X1] : ~ distinct_lines(parallel_through_point(X1,X2),X1),
inference(resolution,[],[f115,f113]) ).
fof(f113,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',cp1) ).
fof(f209,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f131,f109]) ).
fof(f109,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',apart3) ).
fof(f131,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',ceq3) ).
fof(f190,plain,
! [X2,X0,X1] :
( distinct_lines(X0,parallel_through_point(X1,X2))
| ~ apart_point_and_line(X2,X0) ),
inference(resolution,[],[f130,f111]) ).
fof(f111,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',cp2) ).
fof(f130,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',ceq2) ).
fof(f610,plain,
! [X111,X110] :
( apart_point_and_line(X111,X110)
| ~ distinct_lines(X110,sK2)
| ~ distinct_points(X111,sF6) ),
inference(subsumption_resolution,[],[f609,f362]) ).
fof(f609,plain,
! [X111,X110] :
( apart_point_and_line(X111,sK2)
| apart_point_and_line(X111,X110)
| ~ distinct_lines(X110,sK2)
| ~ distinct_points(X111,sF6) ),
inference(subsumption_resolution,[],[f427,f362]) ).
fof(f427,plain,
! [X111,X110] :
( apart_point_and_line(sF6,X110)
| apart_point_and_line(X111,sK2)
| apart_point_and_line(X111,X110)
| ~ distinct_lines(X110,sK2)
| ~ distinct_points(X111,sF6) ),
inference(resolution,[],[f143,f166]) ).
fof(f166,plain,
~ apart_point_and_line(sF6,sK2),
inference(subsumption_resolution,[],[f164,f104]) ).
fof(f104,plain,
convergent_lines(sK2,sK4),
inference(cnf_transformation,[],[f98]) ).
fof(f164,plain,
( ~ apart_point_and_line(sF6,sK2)
| ~ convergent_lines(sK2,sK4) ),
inference(superposition,[],[f118,f145]) ).
fof(f118,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',ci3) ).
fof(f143,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,[],[f92]) ).
fof(f92,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,[],[f91]) ).
fof(f91,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,[],[f50]) ).
fof(f50,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,[],[f11]) ).
fof(f11,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/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368',cu1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO203+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 19:27:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_NEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.7xBR5okyhp/Vampire---4.8_11368
% 0.14/0.36 % (11482)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (11485)lrs+11_4:3_aac=none:add=off:amm=off:anc=none:bd=preordered:bs=on:bce=on:flr=on:fsd=off:fsr=off:fde=none:nwc=2.5:sims=off:sp=reverse_arity:tgt=full:stl=188_1106 on Vampire---4 for (1106ds/0Mi)
% 0.21/0.42 % (11488)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_415 on Vampire---4 for (415ds/0Mi)
% 0.21/0.42 % (11484)dis-1002_1_av=off:bsr=on:cond=on:flr=on:fsr=off:gsp=on:nwc=2.0:sims=off_1218 on Vampire---4 for (1218ds/0Mi)
% 0.21/0.42 % (11483)lrs-1_7_acc=on:amm=off:anc=all:bs=on:bsr=on:cond=fast:flr=on:fsr=off:gsp=on:lcm=reverse:lma=on:msp=off:nm=0:nwc=1.2:sp=frequency:stl=188_1354 on Vampire---4 for (1354ds/0Mi)
% 0.21/0.42 % (11487)ott-1010_5_add=off:amm=off:anc=none:bce=on:cond=fast:flr=on:lma=on:nm=2:nwc=1.1:sp=occurrence:tgt=ground_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.43 % (11489)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.21/0.44 % (11487)First to succeed.
% 0.21/0.44 % (11487)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for Vampire---4
% 0.21/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.44 % (11487)------------------------------
% 0.21/0.44 % (11487)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44 % (11487)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44 % (11487)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (11487)Memory used [KB]: 5756
% 0.21/0.44 % (11487)Time elapsed: 0.017 s
% 0.21/0.44 % (11487)------------------------------
% 0.21/0.44 % (11487)------------------------------
% 0.21/0.44 % (11482)Success in time 0.078 s
% 0.21/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------