%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO180+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 : n006.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 2.41s 1.22s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 52 ( 18 ~; 21 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
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,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( 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(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X0,line_connecting(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f40]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X0,line_connecting(X2,X1))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X0,line_connecting(X2,X1))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK2,sK1))
& 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)],[f77]) ).
fof(f80,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f95,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f116,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f122,plain,
! [X0] :
( distinct_lines(line_connecting(sK0,sK1),X0)
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f91,f116]) ).
fof(f152,plain,
! [X0,X1] :
( distinct_lines(line_connecting(sK0,sK1),X1)
| distinct_lines(X0,X1)
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f83,f122]) ).
fof(f161,plain,
! [X0] :
( distinct_lines(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f152,f80]) ).
fof(f169,plain,
! [X0] :
( convergent_lines(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f161,f93]) ).
fof(f171,plain,
! [X0] : apart_point_and_line(sK2,parallel_through_point(line_connecting(sK0,sK1),X0)),
inference(resolution,[],[f169,f94]) ).
fof(f173,plain,
$false,
inference(resolution,[],[f171,f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO180+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 07:25:41 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
% 2.41/1.22 % (2653799)Detected formulas, will run a generic FOF schedule.
% 2.41/1.22 % (2653809)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=259435890:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.41/1.22 % (2653809)First to succeed.
% 2.41/1.22 % (2653809)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2653799"
% 2.41/1.22 % (2653806)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=4041827250:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.41/1.22 % (2653808)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3376718801:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.41/1.22 % (2653804)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=1404950395:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.41/1.22 % (2653805)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=11182139:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.41/1.22 % (2653807)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3086189338:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.41/1.22 % (2653810)dis-21_1_sil=8000:lcm=predicate:random_seed=453609091: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)
% 2.41/1.22 % (2653810)Also succeeded, but the first one will report.
% 2.41/1.22 % (2653807)Instruction limit reached!
% 2.41/1.22 % (2653807)------------------------------
% 2.41/1.22 % (2653807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.22 % (2653807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.22 % (2653807)CaDiCaL version: 2.1.3
% 2.41/1.22 % (2653807)Termination reason: Instruction limit
% 2.41/1.22 % (2653807)Termination phase: Saturation
% 2.41/1.22 % (2653807)Time elapsed: 0.054 s
% 2.41/1.22 % (2653807)Peak memory usage: 88 MB
% 2.41/1.22 % (2653807)Instructions burned: 110 (million)
% 2.41/1.22 % (2653808)Instruction limit reached!
% 2.41/1.22 % (2653808)------------------------------
% 2.41/1.22 % (2653808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.22 % (2653808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.22 % (2653808)CaDiCaL version: 2.1.3
% 2.41/1.22 % (2653808)Termination reason: Instruction limit
% 2.41/1.22 % (2653808)Termination phase: Saturation
% 2.41/1.22 % (2653808)Time elapsed: 0.067 s
% 2.41/1.22 % (2653808)Peak memory usage: 88 MB
% 2.41/1.22 % (2653808)Instructions burned: 120 (million)
% 2.41/1.22 % (2653809)Refutation found. Thanks to Tanya!
% 2.41/1.22 % SZS status Theorem for theBenchmark
% 2.41/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/1.22 % (2653809)------------------------------
% 2.41/1.22 % (2653809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.22 % (2653809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.22 % (2653809)CaDiCaL version: 2.1.3
% 2.41/1.22 % (2653809)Termination reason: Refutation
% 2.41/1.22 % (2653809)Time elapsed: 0.002 s
% 2.41/1.22 % (2653809)Peak memory usage: 88 MB
% 2.41/1.22 % (2653809)Instructions burned: 4 (million)
% 2.41/1.22 % (2653809)------------------------------
% 2.41/1.22 % (2653809)------------------------------
% 2.41/1.22 % (2653799)Success in time 0.267 s
% 2.41/1.22 % Vampire exiting
%------------------------------------------------------------------------------