%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO181+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 : n020.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 09:51:50 AM UTC 2026
% Result : Theorem 2.64s 1.37s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 64 ~; 76 |; 7 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 86 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
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(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ci2) ).
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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X1,line_connecting(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X1,line_connecting(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,line_connecting(X0,X2))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,line_connecting(X0,X2))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(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(f45,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(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f54,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f60,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(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,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f62,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f60]) ).
fof(f63,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK2)),
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(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,[],[f46]) ).
fof(f68,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f69,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f73,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f81,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(f89,plain,
! [X2,X0,X1] :
( distinct_lines(X0,line_connecting(X1,X2))
| ~ apart_point_and_line(X2,X0)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f73,f64]) ).
fof(f104,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X0,X1)
| ~ distinct_points(X0,sK1)
| ~ distinct_lines(X1,line_connecting(sK0,sK2)) ),
inference(resolution,[],[f67,f63]) ).
fof(f119,plain,
! [X0] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0)
| ~ distinct_points(sK0,sK1)
| ~ distinct_lines(X0,line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f104,f65]) ).
fof(f121,plain,
! [X0] :
( ~ distinct_lines(X0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ distinct_points(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f119,f61]) ).
fof(f139,plain,
( distinct_points(sK2,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f81,f62]) ).
fof(f144,plain,
distinct_points(sK2,sK0),
inference(forward_subsumption_resolution,[],[f139,f61]) ).
fof(f156,plain,
! [X0] :
( ~ apart_point_and_line(sK2,X0)
| ~ distinct_points(sK0,sK2)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f89,f121]) ).
fof(f159,plain,
! [X0] :
( apart_point_and_line(sK1,X0)
| ~ distinct_points(sK0,sK2)
| apart_point_and_line(sK0,X0)
| ~ apart_point_and_line(sK2,X0) ),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f161,plain,
! [X0] :
( apart_point_and_line(sK0,line_connecting(X0,sK1))
| ~ distinct_points(sK0,sK2)
| ~ apart_point_and_line(sK2,line_connecting(X0,sK1))
| ~ distinct_points(X0,sK1) ),
inference(resolution,[],[f159,f64]) ).
fof(f179,plain,
( ~ distinct_points(sK0,sK2)
| ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f161,f65]) ).
fof(f180,plain,
( ~ distinct_points(sK0,sK2)
| ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK1) ),
inference(duplicate_literal_removal,[],[f179]) ).
fof(f183,plain,
( ~ distinct_points(sK0,sK2)
| ~ distinct_points(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f180,f62]) ).
fof(f184,plain,
~ distinct_points(sK0,sK2),
inference(forward_subsumption_resolution,[],[f183,f61]) ).
fof(f199,plain,
! [X0] :
( distinct_points(X0,sK2)
| ~ distinct_points(X0,sK0) ),
inference(resolution,[],[f184,f68]) ).
fof(f215,plain,
~ distinct_points(sK2,sK0),
inference(resolution,[],[f199,f69]) ).
fof(f217,plain,
$false,
inference(forward_subsumption_resolution,[],[f215,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO181+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 07:27:19 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 2.64/1.37 % (3068541)Detected formulas, will run a generic FOF schedule.
% 2.64/1.37 % (3068550)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1947529733:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.37 % (3068550)First to succeed.
% 2.64/1.37 % (3068550)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3068541"
% 2.64/1.37 % (3068548)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=1704680063:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.37 % (3068546)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=2825513521:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.37 % (3068547)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=228574374:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.37 % (3068551)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1564475674:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.37 % (3068549)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2453227311:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.37 % (3068551)Also succeeded, but the first one will report.
% 2.64/1.37 % (3068552)dis-21_1_sil=8000:lcm=predicate:random_seed=2143185116: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)
% 2.64/1.37 % (3068549)Instruction limit reached!
% 2.64/1.37 % (3068549)------------------------------
% 2.64/1.37 % (3068549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.37 % (3068549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.37 % (3068549)CaDiCaL version: 2.1.3
% 2.64/1.37 % (3068549)Termination reason: Instruction limit
% 2.64/1.37 % (3068549)Termination phase: Saturation
% 2.64/1.37 % (3068549)Time elapsed: 0.054 s
% 2.64/1.37 % (3068549)Peak memory usage: 88 MB
% 2.64/1.37 % (3068549)Instructions burned: 110 (million)
% 2.64/1.37 % (3068552)Instruction limit reached!
% 2.64/1.37 % (3068552)------------------------------
% 2.64/1.37 % (3068552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.37 % (3068552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.37 % (3068552)CaDiCaL version: 2.1.3
% 2.64/1.37 % (3068552)Termination reason: Instruction limit
% 2.64/1.37 % (3068552)Termination phase: Saturation
% 2.64/1.37 % (3068552)Time elapsed: 0.076 s
% 2.64/1.37 % (3068552)Peak memory usage: 89 MB
% 2.64/1.37 % (3068552)Instructions burned: 129 (million)
% 2.64/1.37 % (3068550)Refutation found. Thanks to Tanya!
% 2.64/1.37 % SZS status Theorem for theBenchmark
% 2.64/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.37 % (3068550)------------------------------
% 2.64/1.37 % (3068550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.37 % (3068550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.37 % (3068550)CaDiCaL version: 2.1.3
% 2.64/1.37 % (3068550)Termination reason: Refutation
% 2.64/1.37 % (3068550)Time elapsed: 0.003 s
% 2.64/1.37 % (3068550)Peak memory usage: 88 MB
% 2.64/1.37 % (3068550)Instructions burned: 7 (million)
% 2.64/1.37 % (3068550)------------------------------
% 2.64/1.37 % (3068550)------------------------------
% 2.64/1.37 % (3068541)Success in time 0.293 s
% 2.64/1.37 % Vampire exiting
%------------------------------------------------------------------------------