%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO204+2 : 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 : n015.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 09:51:59 AM UTC 2026
% Result : Theorem 2.43s 1.28s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 197 ( 75 ~; 102 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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,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/sandbox2/benchmark/theBenchmark.p',con1) ).
fof(f9,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,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( distinct_points(X0,X2)
& ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( distinct_points(X0,X2)
& ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& ~ distinct_points(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& ~ distinct_points(X1,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f19]) ).
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,[],[f9]) ).
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(f29,plain,
( ( ~ distinct_points(sK0,sK2)
| distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) )
& distinct_points(sK0,sK1)
& ~ distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f30,plain,
~ distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f31,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f32,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,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,[],[f28]) ).
fof(f42,plain,
! [X0] :
( distinct_points(X0,sK2)
| ~ distinct_points(X0,sK1) ),
inference(resolution,[],[f35,f30]) ).
fof(f46,plain,
~ distinct_points(sK2,sK1),
inference(resolution,[],[f42,f36]) ).
fof(f47,plain,
! [X0] :
( distinct_points(X0,sK1)
| ~ distinct_points(X0,sK2) ),
inference(resolution,[],[f46,f35]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4] :
( apart_point_and_line(X0,line_connecting(X1,X2))
| apart_point_and_line(X3,X4)
| apart_point_and_line(X0,X4)
| ~ distinct_points(X0,X3)
| ~ distinct_lines(X4,line_connecting(X1,X2))
| distinct_points(X3,X1)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f41,f34]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| ~ distinct_points(X2,X0)
| ~ distinct_lines(X1,line_connecting(X3,X4))
| distinct_points(X0,X3)
| ~ distinct_points(X3,X4)
| distinct_points(X2,X4)
| ~ distinct_points(X3,X4) ),
inference(resolution,[],[f58,f33]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] :
( ~ distinct_lines(X1,line_connecting(X3,X4))
| apart_point_and_line(X2,X1)
| ~ distinct_points(X2,X0)
| apart_point_and_line(X0,X1)
| distinct_points(X0,X3)
| ~ distinct_points(X3,X4)
| distinct_points(X2,X4) ),
inference(duplicate_literal_removal,[],[f72]) ).
fof(f103,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2)
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f73,f32]) ).
fof(f113,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0,sK1))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2) ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f115,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f113,f34]) ).
fof(f121,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2)
| ~ distinct_points(sK0,sK1) ),
inference(duplicate_literal_removal,[],[f115]) ).
fof(f127,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,X1)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f121,f47]) ).
fof(f141,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2)
| distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f127,f33]) ).
fof(f153,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK2)
| distinct_points(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f141,f47]) ).
fof(f154,plain,
! [X0,X1] :
( distinct_points(X1,sK0)
| ~ distinct_points(X0,X1)
| ~ distinct_points(sK0,sK2)
| distinct_points(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f153,f47]) ).
fof(f155,plain,
! [X0] :
( distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK2)
| ~ distinct_points(X0,sK0) ),
inference(resolution,[],[f154,f36]) ).
fof(f167,plain,
( ~ distinct_points(sK1,sK0)
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f155,f36]) ).
fof(f181,plain,
! [X0] :
( distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK2)
| ~ distinct_points(X0,sK1) ),
inference(resolution,[],[f167,f35]) ).
fof(f198,plain,
( ~ distinct_points(sK0,sK2)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f181,f36]) ).
fof(f202,plain,
~ distinct_points(sK0,sK2),
inference(forward_subsumption_resolution,[],[f198,f47]) ).
fof(f214,plain,
~ distinct_points(sK0,sK1),
inference(resolution,[],[f202,f42]) ).
fof(f216,plain,
$false,
inference(forward_subsumption_resolution,[],[f214,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 07:39:00 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.43/1.28 % (1321426)Detected formulas, will run a generic FOF schedule.
% 2.43/1.28 % (1321434)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1558109134:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.43/1.28 % (1321434)Instruction limit reached!
% 2.43/1.28 % (1321434)------------------------------
% 2.43/1.28 % (1321434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.28 % (1321434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.28 % (1321434)CaDiCaL version: 2.1.3
% 2.43/1.28 % (1321434)Termination reason: Instruction limit
% 2.43/1.28 % (1321434)Termination phase: Saturation
% 2.43/1.28 % (1321434)Time elapsed: 0.031 s
% 2.43/1.28 % (1321434)Peak memory usage: 88 MB
% 2.43/1.28 % (1321434)Instructions burned: 123 (million)
% 2.43/1.28 % (1321436)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=728563473:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.43/1.28 % (1321435)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2495433453:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.43/1.28 % (1321431)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=963474119:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.43/1.28 % (1321432)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=3566313755:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.43/1.28 % (1321433)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=1140692262:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.43/1.28 % (1321435)First to succeed.
% 2.43/1.28 % (1321435)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1321426"
% 2.43/1.28 % (1321437)dis-21_1_sil=8000:lcm=predicate:random_seed=1454760563: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)
% 2.43/1.28 % (1321437)Also succeeded, but the first one will report.
% 2.43/1.28 % (1321436)Instruction limit reached!
% 2.43/1.28 % (1321436)------------------------------
% 2.43/1.28 % (1321436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.28 % (1321436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.28 % (1321436)CaDiCaL version: 2.1.3
% 2.43/1.28 % (1321436)Termination reason: Instruction limit
% 2.43/1.28 % (1321436)Termination phase: Saturation
% 2.43/1.28 % (1321436)Time elapsed: 0.046 s
% 2.43/1.28 % (1321436)Peak memory usage: 89 MB
% 2.43/1.28 % (1321436)Instructions burned: 140 (million)
% 2.43/1.28 % (1321446)lrs+10_1_sil=32000:urr=on:br=off:random_seed=751269451:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.43/1.28 % (1321446)Also succeeded, but the first one will report.
% 2.43/1.28 % (1321439)lrs+10_1_sil=8000:sp=occurrence:random_seed=1592349171:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.43/1.28 % (1321439)Also succeeded, but the first one will report.
% 2.43/1.28 % (1321435)Refutation found. Thanks to Tanya!
% 2.43/1.28 % SZS status Theorem for theBenchmark
% 2.43/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.48 % (1321435)------------------------------
% 3.49/1.48 % (1321435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.48 % (1321435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.48 % (1321435)CaDiCaL version: 2.1.3
% 3.49/1.48 % (1321435)Termination reason: Refutation
% 3.49/1.48 % (1321435)Time elapsed: 0.007 s
% 3.49/1.48 % (1321435)Peak memory usage: 88 MB
% 3.49/1.48 % (1321435)Instructions burned: 10 (million)
% 3.49/1.48 % (1321435)------------------------------
% 3.49/1.48 % (1321435)------------------------------
% 3.49/1.48 % (1321426)Success in time 0.414 s
% 3.49/1.48 % Vampire exiting
%------------------------------------------------------------------------------