%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO227+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 : n018.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 09:52:08 AM UTC 2026
% Result : Theorem 3.58s 1.47s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 19 ~; 9 |; 4 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 36 ( 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
fof(f4,axiom,
! [X0,X1] :
( equally_directed_lines(X0,X1)
<=> ~ unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
fof(f5,axiom,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
<=> ~ unequally_directed_opposite_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_defns) ).
fof(f18,axiom,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
fof(f37,conjecture,
! [X0,X1] :
~ ( equally_directed_lines(X0,X1)
& equally_directed_opposite_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
~ ( equally_directed_lines(X0,X1)
& equally_directed_opposite_lines(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
=> ~ unequally_directed_opposite_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f40,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
=> unequally_directed_opposite_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f41,plain,
! [X0,X1] :
( equally_directed_lines(X0,X1)
=> ~ unequally_directed_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f42,plain,
? [X0,X1] :
( equally_directed_lines(X0,X1)
& equally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f43,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f50,plain,
( equally_directed_lines(sK0,sK1)
& equally_directed_opposite_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f42]) ).
fof(f51,plain,
equally_directed_opposite_lines(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
fof(f52,plain,
equally_directed_lines(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
fof(f54,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f55,plain,
! [X0,X1] :
( ~ equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f56,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f62,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f63,plain,
~ unequally_directed_lines(sK0,sK1),
inference(resolution,[],[f54,f52]) ).
fof(f65,plain,
~ unequally_directed_opposite_lines(sK0,sK1),
inference(resolution,[],[f55,f51]) ).
fof(f67,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(resolution,[],[f62,f56]) ).
fof(f82,plain,
unequally_directed_opposite_lines(sK0,sK1),
inference(resolution,[],[f67,f63]) ).
fof(f86,plain,
$false,
inference(forward_subsumption_resolution,[],[f82,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO227+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:48:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.58/1.47 % (2000222)Detected formulas, will run a generic FOF schedule.
% 3.58/1.47 % (2000288)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=3766037565:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.47 % (2000296)dis-21_1_sil=8000:lcm=predicate:random_seed=490064602: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)
% 3.58/1.47 % (2000289)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=1000367241:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.47 % (2000293)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2108090952:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.47 % (2000290)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=1042752198:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.47 % (2000291)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3374882722:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.47 % (2000295)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=955541593:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.47 % (2000291)Refutation not found, incomplete strategy
% 3.58/1.47 % (2000291)------------------------------
% 3.58/1.47 % (2000291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (2000291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (2000291)CaDiCaL version: 2.1.3
% 3.58/1.47 % (2000291)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.47 % (2000291)Time elapsed: 0.001 s
% 3.58/1.47 % (2000291)Peak memory usage: 86 MB
% 3.58/1.47 % (2000293)First to succeed.
% 3.58/1.47 % (2000296)Also succeeded, but the first one will report.
% 3.58/1.47 % (2000295)Also succeeded, but the first one will report.
% 3.58/1.47 % (2000293)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2000222"
% 3.58/1.47 % (2000291)------------------------------
% 3.58/1.47 % (2000291)------------------------------
% 3.58/1.47 % (2000293)Refutation found. Thanks to Tanya!
% 3.58/1.47 % SZS status Theorem for theBenchmark
% 3.58/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.47 % (2000293)------------------------------
% 3.58/1.47 % (2000293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (2000293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (2000293)CaDiCaL version: 2.1.3
% 3.58/1.47 % (2000293)Termination reason: Refutation
% 3.58/1.47 % (2000293)Time elapsed: 0.002 s
% 3.58/1.47 % (2000293)Peak memory usage: 88 MB
% 3.58/1.47 % (2000293)Instructions burned: 1 (million)
% 3.58/1.47 % (2000293)------------------------------
% 3.58/1.47 % (2000293)------------------------------
% 3.58/1.47 % (2000222)Success in time 0.422 s
% 3.58/1.47 % Vampire exiting
%------------------------------------------------------------------------------