%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:51:52 AM UTC 2026
% Result : Theorem 0.71s 1.01s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 11 unt; 2 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 191 ( 73 ~; 90 |; 19 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 78 !; 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(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(f15,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f31,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(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2] :
( apart_point_and_line(X0,line_connecting(X2,X1))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( apart_point_and_line(X0,line_connecting(X2,X1))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK1))
& distinct_points(sK0,sK1)
& distinct_points(sK0,sK2)
& distinct_points(sK1,sK2)
& ~ 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)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| ~ distinct_points(X1,X0) ),
inference(resolution,[],[f41,f38]) ).
fof(f60,plain,
! [X0] :
( distinct_lines(line_connecting(sK2,sK1),X0)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f50,f56]) ).
fof(f62,plain,
! [X2,X0,X1] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(X2,line_connecting(sK2,sK1))
| apart_point_and_line(X2,X1)
| ~ distinct_points(X0,X2)
| apart_point_and_line(X0,line_connecting(sK2,sK1))
| apart_point_and_line(X0,X1) ),
inference(resolution,[],[f48,f60]) ).
fof(f63,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,line_connecting(sK2,sK1))
| apart_point_and_line(X0,line_connecting(sK0,X1))
| ~ distinct_points(X2,X0)
| apart_point_and_line(X2,line_connecting(sK2,sK1))
| apart_point_and_line(X2,line_connecting(sK0,X1))
| ~ distinct_points(sK0,X1) ),
inference(resolution,[],[f62,f44]) ).
fof(f74,plain,
! [X0,X1] :
( apart_point_and_line(sK1,line_connecting(sK0,X0))
| ~ distinct_points(X1,sK1)
| apart_point_and_line(X1,line_connecting(sK2,sK1))
| apart_point_and_line(X1,line_connecting(sK0,X0))
| ~ distinct_points(sK0,X0)
| ~ distinct_points(sK2,sK1) ),
inference(resolution,[],[f63,f45]) ).
fof(f80,definition,
( spl3_1
<=> distinct_points(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f81,plain,
( distinct_points(sK2,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( ~ distinct_points(sK2,sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl3_2
<=> ! [X0,X1] :
( apart_point_and_line(sK1,line_connecting(sK0,X0))
| ~ distinct_points(sK0,X0)
| ~ distinct_points(X1,sK1)
| apart_point_and_line(X1,line_connecting(sK0,X0))
| apart_point_and_line(X1,line_connecting(sK2,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f85,plain,
( ! [X0,X1] :
( apart_point_and_line(sK1,line_connecting(sK0,X0))
| ~ distinct_points(sK0,X0)
| ~ distinct_points(X1,sK1)
| apart_point_and_line(X1,line_connecting(sK0,X0))
| apart_point_and_line(X1,line_connecting(sK2,sK1)) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f74,f84,f80]) ).
fof(f91,plain,
( ~ distinct_points(sK1,sK2)
| spl3_1 ),
inference(resolution,[],[f82,f57]) ).
fof(f93,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f91,f53]) ).
fof(f94,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f99,plain,
( ! [X0] :
( ~ distinct_points(sK0,sK1)
| ~ distinct_points(X0,sK1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK2,sK1))
| ~ distinct_points(sK0,sK1) )
| ~ spl3_2 ),
inference(resolution,[],[f85,f45]) ).
fof(f102,plain,
( ! [X0] :
( ~ distinct_points(sK0,sK1)
| ~ distinct_points(X0,sK1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK2,sK1)) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f103,plain,
( ! [X0] :
( apart_point_and_line(X0,line_connecting(sK2,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1) )
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f102,f55]) ).
fof(f109,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f103,f44]) ).
fof(f115,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK2,sK1)
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f116,plain,
( ~ distinct_points(sK2,sK1)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f115,f52]) ).
fof(f117,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f116,f81]) ).
fof(f118,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f117]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
spl3_1,
inference(sat_conversion,[],[f94]) ).
cnf(s4,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f118]) ).
cnf(s5,plain,
~ spl3_2,
inference(rat,[],[s4,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n004.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
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:29:07 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.71/1.01 % (3171222)Detected formulas, will run a generic FOF schedule.
% 0.71/1.01 % (3171230)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1519561444:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.71/1.01 % (3171227)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=1112515763:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.71/1.01 % (3171232)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=851938726:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.71/1.01 % (3171231)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1961270373:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.71/1.01 % (3171233)dis-21_1_sil=8000:lcm=predicate:random_seed=2359672730: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)
% 0.71/1.01 % (3171229)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=2157111786:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.71/1.01 % (3171228)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=3461213552:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.71/1.01 % (3171232)First to succeed.
% 0.71/1.01 % (3171232)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3171222"
% 0.71/1.01 % (3171231)Instruction limit reached!
% 0.71/1.01 % (3171231)------------------------------
% 0.71/1.01 % (3171231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.71/1.01 % (3171231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/1.01 % (3171231)CaDiCaL version: 2.1.3
% 0.71/1.01 % (3171231)Termination reason: Instruction limit
% 0.71/1.01 % (3171231)Termination phase: Saturation
% 0.71/1.01 % (3171231)Time elapsed: 0.046 s
% 0.71/1.01 % (3171231)Peak memory usage: 87 MB
% 0.71/1.01 % (3171231)Instructions burned: 120 (million)
% 0.71/1.01 % (3171233)Also succeeded, but the first one will report.
% 0.71/1.01 % (3171230)Instruction limit reached!
% 0.71/1.01 % (3171230)------------------------------
% 0.71/1.01 % (3171230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.71/1.01 % (3171230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/1.01 % (3171230)CaDiCaL version: 2.1.3
% 0.71/1.01 % (3171230)Termination reason: Instruction limit
% 0.71/1.01 % (3171230)Termination phase: Saturation
% 0.71/1.01 % (3171230)Time elapsed: 0.053 s
% 0.71/1.01 % (3171230)Peak memory usage: 88 MB
% 0.71/1.01 % (3171230)Instructions burned: 111 (million)
% 0.71/1.01 % (3171241)lrs+10_1_sil=8000:sp=occurrence:random_seed=3868732370:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.71/1.01 % (3171242)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2647270495:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.71/1.01 % (3171241)Also succeeded, but the first one will report.
% 0.71/1.01 % (3171242)Also succeeded, but the first one will report.
% 0.71/1.01 % (3171232)Refutation found. Thanks to Tanya!
% 0.71/1.01 % SZS status Theorem for theBenchmark
% 0.71/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.20 % (3171232)------------------------------
% 0.18/1.20 % (3171232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.20 % (3171232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.20 % (3171232)CaDiCaL version: 2.1.3
% 0.18/1.20 % (3171232)Termination reason: Refutation
% 0.18/1.20 % (3171232)Time elapsed: 0.005 s
% 0.18/1.20 % (3171232)Peak memory usage: 89 MB
% 0.18/1.20 % (3171232)Instructions burned: 6 (million)
% 0.18/1.20 % (3171232)------------------------------
% 0.18/1.20 % (3171232)------------------------------
% 0.18/1.20 % (3171222)Success in time 0.392 s
% 0.18/1.20 % Vampire exiting
%------------------------------------------------------------------------------