TSTP Solution File: GEO187+2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GEO187+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n016.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 23:31:33 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 16 unt; 0 def)
% Number of atoms : 223 ( 2 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 242 ( 95 ~; 96 |; 37 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 101 (; 89 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f171,plain,
$false,
inference(avatar_sat_refutation,[],[f70,f134,f141,f164,f170]) ).
fof(f170,plain,
( ~ spl6_1
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f169]) ).
fof(f169,plain,
( $false
| ~ spl6_1
| spl6_3 ),
inference(subsumption_resolution,[],[f65,f136]) ).
fof(f136,plain,
( ~ apart_point_and_line(sK2,sF4)
| spl6_3 ),
inference(resolution,[],[f130,f96]) ).
fof(f96,plain,
! [X1] :
( distinct_lines(X1,sF5)
| ~ apart_point_and_line(sK2,X1) ),
inference(resolution,[],[f94,f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586',ceq2) ).
fof(f94,plain,
~ apart_point_and_line(sK2,sF5),
inference(resolution,[],[f89,f45]) ).
fof(f45,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586',apart1) ).
fof(f89,plain,
! [X1] :
( distinct_points(X1,sK2)
| ~ apart_point_and_line(X1,sF5) ),
inference(subsumption_resolution,[],[f87,f39]) ).
fof(f39,plain,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
( ( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) )
& ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
& distinct_points(sK2,sK3)
& distinct_points(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f36]) ).
fof(f36,plain,
( ? [X0,X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) )
& ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( ( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) )
& ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
& distinct_points(sK2,sK3)
& distinct_points(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) )
& ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) )
& ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X0,X1,X2,X3] :
( ( ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X3,X4] :
( ( ~ apart_point_and_line(X1,line_connecting(X3,X4))
& ~ apart_point_and_line(X0,line_connecting(X3,X4))
& distinct_points(X3,X4)
& distinct_points(X0,X1) )
=> ( ~ apart_point_and_line(X4,line_connecting(X0,X1))
& ~ apart_point_and_line(X3,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1,X3,X4] :
( ( ~ apart_point_and_line(X1,line_connecting(X3,X4))
& ~ apart_point_and_line(X0,line_connecting(X3,X4))
& distinct_points(X3,X4)
& distinct_points(X0,X1) )
=> ( ~ apart_point_and_line(X4,line_connecting(X0,X1))
& ~ apart_point_and_line(X3,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586',con) ).
fof(f87,plain,
! [X1] :
( ~ apart_point_and_line(X1,sF5)
| distinct_points(X1,sK2)
| ~ distinct_points(sK2,sK3) ),
inference(superposition,[],[f52,f59]) ).
fof(f59,plain,
line_connecting(sK2,sK3) = sF5,
introduced(function_definition,[]) ).
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,[],[f29]) ).
fof(f29,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,[],[f28]) ).
fof(f28,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/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586',con1) ).
fof(f130,plain,
( ~ distinct_lines(sF4,sF5)
| spl6_3 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f128,plain,
( spl6_3
<=> distinct_lines(sF4,sF5) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f65,plain,
( apart_point_and_line(sK2,sF4)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f63,plain,
( spl6_1
<=> apart_point_and_line(sK2,sF4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f164,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f163]) ).
fof(f163,plain,
( $false
| ~ spl6_4 ),
inference(subsumption_resolution,[],[f160,f38]) ).
fof(f38,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f160,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl6_4 ),
inference(resolution,[],[f156,f45]) ).
fof(f156,plain,
( ! [X0] :
( distinct_points(X0,sK0)
| ~ distinct_points(X0,sK1) )
| ~ spl6_4 ),
inference(resolution,[],[f152,f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f26,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/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586',apart4) ).
fof(f152,plain,
( ~ distinct_points(sK1,sK0)
| ~ spl6_4 ),
inference(subsumption_resolution,[],[f149,f103]) ).
fof(f103,plain,
~ apart_point_and_line(sK1,sF4),
inference(resolution,[],[f101,f45]) ).
fof(f101,plain,
! [X0] :
( distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,sF4) ),
inference(subsumption_resolution,[],[f99,f38]) ).
fof(f99,plain,
! [X0] :
( ~ apart_point_and_line(X0,sF4)
| distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[],[f53,f57]) ).
fof(f57,plain,
line_connecting(sK0,sK1) = sF4,
introduced(function_definition,[]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f149,plain,
( ~ distinct_points(sK1,sK0)
| apart_point_and_line(sK1,sF4)
| ~ spl6_4 ),
inference(resolution,[],[f133,f60]) ).
fof(f60,plain,
~ apart_point_and_line(sK1,sF5),
inference(definition_folding,[],[f41,f59]) ).
fof(f41,plain,
~ apart_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f133,plain,
( ! [X1] :
( apart_point_and_line(X1,sF5)
| ~ distinct_points(X1,sK0)
| apart_point_and_line(X1,sF4) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f132,plain,
( spl6_4
<=> ! [X1] :
( apart_point_and_line(X1,sF5)
| ~ distinct_points(X1,sK0)
| apart_point_and_line(X1,sF4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f141,plain,
( ~ spl6_2
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f140,plain,
( $false
| ~ spl6_2
| spl6_3 ),
inference(subsumption_resolution,[],[f135,f69]) ).
fof(f69,plain,
( apart_point_and_line(sK3,sF4)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl6_2
<=> apart_point_and_line(sK3,sF4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f135,plain,
( ~ apart_point_and_line(sK3,sF4)
| spl6_3 ),
inference(resolution,[],[f130,f108]) ).
fof(f108,plain,
! [X1] :
( distinct_lines(X1,sF5)
| ~ apart_point_and_line(sK3,X1) ),
inference(resolution,[],[f106,f54]) ).
fof(f106,plain,
~ apart_point_and_line(sK3,sF5),
inference(resolution,[],[f102,f45]) ).
fof(f102,plain,
! [X1] :
( distinct_points(X1,sK3)
| ~ apart_point_and_line(X1,sF5) ),
inference(subsumption_resolution,[],[f100,f39]) ).
fof(f100,plain,
! [X1] :
( ~ apart_point_and_line(X1,sF5)
| distinct_points(X1,sK3)
| ~ distinct_points(sK2,sK3) ),
inference(superposition,[],[f53,f59]) ).
fof(f134,plain,
( ~ spl6_3
| spl6_4 ),
inference(avatar_split_clause,[],[f123,f132,f128]) ).
fof(f123,plain,
! [X1] :
( apart_point_and_line(X1,sF5)
| apart_point_and_line(X1,sF4)
| ~ distinct_lines(sF4,sF5)
| ~ distinct_points(X1,sK0) ),
inference(resolution,[],[f110,f91]) ).
fof(f91,plain,
~ apart_point_and_line(sK0,sF4),
inference(resolution,[],[f88,f45]) ).
fof(f88,plain,
! [X0] :
( distinct_points(X0,sK0)
| ~ apart_point_and_line(X0,sF4) ),
inference(subsumption_resolution,[],[f86,f38]) ).
fof(f86,plain,
! [X0] :
( ~ apart_point_and_line(X0,sF4)
| distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[],[f52,f57]) ).
fof(f110,plain,
! [X0,X1] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(X1,sF5)
| apart_point_and_line(X1,X0)
| ~ distinct_lines(X0,sF5)
| ~ distinct_points(X1,sK0) ),
inference(resolution,[],[f56,f61]) ).
fof(f61,plain,
~ apart_point_and_line(sK0,sF5),
inference(definition_folding,[],[f40,f59]) ).
fof(f40,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f56,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,[],[f35]) ).
fof(f35,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,[],[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(ennf_transformation,[],[f16]) ).
fof(f16,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/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586',cu1) ).
fof(f70,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f58,f67,f63]) ).
fof(f58,plain,
( apart_point_and_line(sK3,sF4)
| apart_point_and_line(sK2,sF4) ),
inference(definition_folding,[],[f42,f57,f57]) ).
fof(f42,plain,
( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO187+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n016.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 : Wed Aug 30 00:18:16 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_NEQ problem
% 0.15/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.qhe4HkevBd/Vampire---4.8_6586
% 0.21/0.35 % (6693)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (6698)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)
% 0.21/0.41 % (6695)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)
% 0.21/0.41 % (6696)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)
% 0.21/0.41 % (6697)dis-1_128_add=large:amm=sco:anc=all_dependent:bs=on:bsr=on:bce=on:cond=fast:fsr=off:gsp=on:gs=on:gsem=off:lcm=predicate:lma=on:nm=32:nwc=4.0:nicw=on:sac=on:sp=weighted_frequency_692 on Vampire---4 for (692ds/0Mi)
% 0.21/0.41 % (6699)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)
% 0.21/0.41 % (6694)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)
% 0.21/0.41 % (6700)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)
% 0.21/0.42 % (6698)First to succeed.
% 0.21/0.42 % (6699)Also succeeded, but the first one will report.
% 0.21/0.42 % (6698)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for Vampire---4
% 0.21/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42 % (6698)------------------------------
% 0.21/0.42 % (6698)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42 % (6698)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42 % (6698)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (6698)Memory used [KB]: 5500
% 0.21/0.42 % (6698)Time elapsed: 0.008 s
% 0.21/0.42 % (6698)------------------------------
% 0.21/0.42 % (6698)------------------------------
% 0.21/0.42 % (6693)Success in time 0.066 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------