%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO178+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:51:49 AM UTC 2026
% Result : Theorem 2.52s 1.34s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 29 ~; 21 |; 10 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X2,X0)
| ~ distinct_points(X2,X1) )
& distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X2,X0)
| ~ distinct_points(X2,X1) )
& distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f44,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f60,plain,
( ( ~ distinct_points(sK2,sK0)
| ~ distinct_points(sK2,sK1) )
& distinct_points(sK0,sK1)
& apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
fof(f61,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f60]) ).
fof(f62,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f63,plain,
( ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f64,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
! [X2,X0,X1] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X2,X1))
| distinct_points(X0,X1)
| ~ distinct_points(X2,X1) ),
inference(resolution,[],[f66,f64]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X1,X2))
| distinct_points(X0,X1)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f66,f65]) ).
fof(f108,plain,
( distinct_points(sK2,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f79,f61]) ).
fof(f112,plain,
distinct_points(sK2,sK1),
inference(forward_subsumption_resolution,[],[f108,f62]) ).
fof(f113,plain,
( distinct_points(sK2,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f80,f61]) ).
fof(f117,plain,
distinct_points(sK2,sK0),
inference(forward_subsumption_resolution,[],[f113,f62]) ).
fof(f119,plain,
~ distinct_points(sK2,sK0),
inference(resolution,[],[f112,f63]) ).
fof(f122,plain,
$false,
inference(forward_subsumption_resolution,[],[f119,f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO178+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:27:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.52/1.34 % (2491912)Detected formulas, will run a generic FOF schedule.
% 2.52/1.34 % (2491921)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3767299662:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.52/1.34 % (2491921)First to succeed.
% 2.52/1.34 % (2491921)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2491912"
% 2.52/1.34 % (2491919)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=15496696:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.52/1.34 % (2491923)dis-21_1_sil=8000:lcm=predicate:random_seed=2333197397: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)
% 2.52/1.34 % (2491918)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=1441073370:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.52/1.34 % (2491920)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2720433984:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.52/1.34 % (2491917)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=2027087531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.52/1.34 % (2491922)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3875884614:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.52/1.34 % (2491920)Also succeeded, but the first one will report.
% 2.52/1.34 % (2491923)Also succeeded, but the first one will report.
% 2.52/1.34 % (2491922)Also succeeded, but the first one will report.
% 2.52/1.34 % (2491921)Refutation found. Thanks to Tanya!
% 2.52/1.34 % SZS status Theorem for theBenchmark
% 2.52/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.34 % (2491921)------------------------------
% 2.52/1.34 % (2491921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.34 % (2491921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.34 % (2491921)CaDiCaL version: 2.1.3
% 2.52/1.34 % (2491921)Termination reason: Refutation
% 2.52/1.34 % (2491921)Time elapsed: 0.002 s
% 2.52/1.34 % (2491921)Peak memory usage: 88 MB
% 2.52/1.34 % (2491921)Instructions burned: 2 (million)
% 2.52/1.34 % (2491921)------------------------------
% 2.52/1.34 % (2491921)------------------------------
% 2.52/1.34 % (2491912)Success in time 0.274 s
% 2.52/1.34 % Vampire exiting
%------------------------------------------------------------------------------