%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO175+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:51:47 AM UTC 2026
% Result : Theorem 2.66s 1.36s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 61 ~; 60 |; 17 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 77 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f40,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) ),
inference(flattening,[],[f39]) ).
fof(f43,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,[],[f11]) ).
fof(f44,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,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f54,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f60,plain,
( ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK0,sK3)
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& distinct_points(sK0,intersection_point(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f40]) ).
fof(f61,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f60]) ).
fof(f62,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f60]) ).
fof(f64,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f60]) ).
fof(f65,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f60]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f70,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f71,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f73,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f75,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f76,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f89,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f76,f73]) ).
fof(f102,plain,
! [X0,X1] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,X1)
| ~ distinct_points(X0,sK0)
| ~ distinct_lines(X1,sK3) ),
inference(resolution,[],[f67,f64]) ).
fof(f108,plain,
! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2)
| ~ distinct_points(X0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f102,f65]) ).
fof(f114,plain,
! [X0] :
( apart_point_and_line(intersection_point(X0,sK3),sK2)
| ~ distinct_points(intersection_point(X0,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(X0,sK3) ),
inference(resolution,[],[f108,f70]) ).
fof(f126,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f114,f71]) ).
fof(f131,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f132,plain,
( ~ distinct_points(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(forward_subsumption_resolution,[],[f131,f75]) ).
fof(f144,plain,
! [X0] :
( ~ distinct_points(X0,intersection_point(sK2,sK3))
| distinct_points(X0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f132,f68]) ).
fof(f187,plain,
( distinct_points(sK0,sK0)
| ~ distinct_lines(sK2,sK3) ),
inference(resolution,[],[f144,f61]) ).
fof(f193,plain,
~ distinct_lines(sK2,sK3),
inference(forward_subsumption_resolution,[],[f187,f69]) ).
fof(f196,plain,
~ convergent_lines(sK3,sK2),
inference(resolution,[],[f193,f89]) ).
fof(f202,plain,
~ distinct_lines(sK3,sK2),
inference(resolution,[],[f196,f75]) ).
fof(f216,plain,
~ convergent_lines(sK2,sK3),
inference(resolution,[],[f202,f89]) ).
fof(f217,plain,
$false,
inference(forward_subsumption_resolution,[],[f216,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO175+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n019.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
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 07:24:04 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.66/1.36 % (2761414)Detected formulas, will run a generic FOF schedule.
% 2.66/1.36 % (2761423)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=639434790:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.36 % (2761423)First to succeed.
% 2.66/1.36 % (2761423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2761414"
% 2.66/1.36 % (2761419)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1338894888:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.36 % (2761421)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=711112067:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.36 % (2761425)dis-21_1_sil=8000:lcm=predicate:random_seed=3640836548:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.66/1.36 % (2761420)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1277772870:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.36 % (2761422)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=533816239:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.36 % (2761424)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1573981137:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.36 % (2761422)Refutation not found, incomplete strategy
% 2.66/1.36 % (2761422)------------------------------
% 2.66/1.36 % (2761422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.36 % (2761422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.36 % (2761422)CaDiCaL version: 2.1.3
% 2.66/1.36 % (2761422)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.36 % (2761422)Time elapsed: 0.001 s
% 2.66/1.36 % (2761422)Peak memory usage: 88 MB
% 2.66/1.36 % (2761424)Also succeeded, but the first one will report.
% 2.66/1.36 % (2761425)Instruction limit reached!
% 2.66/1.36 % (2761425)------------------------------
% 2.66/1.36 % (2761425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.36 % (2761425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.36 % (2761425)CaDiCaL version: 2.1.3
% 2.66/1.36 % (2761425)Termination reason: Instruction limit
% 2.66/1.36 % (2761425)Termination phase: Saturation
% 2.66/1.36 % (2761425)Time elapsed: 0.076 s
% 2.66/1.36 % (2761425)Peak memory usage: 89 MB
% 2.66/1.36 % (2761425)Instructions burned: 131 (million)
% 2.66/1.36 % (2761423)Refutation found. Thanks to Tanya!
% 2.66/1.36 % SZS status Theorem for theBenchmark
% 2.66/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.36 % (2761423)------------------------------
% 2.66/1.36 % (2761423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.36 % (2761423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.36 % (2761423)CaDiCaL version: 2.1.3
% 2.66/1.36 % (2761423)Termination reason: Refutation
% 2.66/1.36 % (2761423)Time elapsed: 0.003 s
% 2.66/1.36 % (2761423)Peak memory usage: 88 MB
% 2.66/1.36 % (2761423)Instructions burned: 5 (million)
% 2.66/1.36 % (2761423)------------------------------
% 2.66/1.36 % (2761423)------------------------------
% 2.66/1.36 % (2761414)Success in time 0.294 s
% 2.66/1.36 % Vampire exiting
%------------------------------------------------------------------------------