%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:51:18 AM UTC 2026
% Result : Unsatisfiable 3.84s 1.42s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 15 unt; 3 def)
% Number of atoms : 63 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 22 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f19,negated_conjecture,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
fof(f20,plain,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(forward_subsumption_resolution,[],[f19,f4]) ).
fof(f22,definition,
( spl0_1
<=> equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f24,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f26,definition,
( spl0_2
<=> v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f28,plain,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f20,f26,f22]) ).
fof(f31,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X1,X0) ),
inference(resolution,[],[f2,f1]) ).
fof(f33,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| equidistant(X4,X5,X2,X3) ),
inference(resolution,[],[f2,f5]) ).
fof(f35,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f31]) ).
fof(f59,plain,
! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3),
inference(resolution,[],[f33,f1]) ).
fof(f65,plain,
! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(resolution,[],[f59,f32]) ).
fof(f85,plain,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,extension(X5,X4,X0,X1))
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[],[f65,f2]) ).
fof(f512,plain,
( ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| spl0_1 ),
inference(resolution,[],[f85,f24]) ).
fof(f534,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f512,f65]) ).
fof(f535,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f547,plain,
( equidistant(lower_dimension_point_1,lower_dimension_point_2,v,v)
| ~ spl0_2 ),
inference(superposition,[],[f65,f28]) ).
fof(f739,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_2 ),
inference(resolution,[],[f547,f3]) ).
fof(f748,definition,
( spl0_21
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f750,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f755,plain,
( spl0_21
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f739,f26,f748]) ).
fof(f758,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_21 ),
inference(superposition,[],[f12,f750]) ).
fof(f779,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f758,f35]) ).
fof(f780,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[],[f779]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f535]) ).
cnf(s12,plain,
( ~ spl0_2
| spl0_21 ),
inference(sat_conversion,[],[f755]) ).
cnf(s15,plain,
~ spl0_21,
inference(sat_conversion,[],[f780]) ).
cnf(s17,plain,
~ spl0_2,
inference(rat,[],[s12,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s17,s2]) ).
fof(f785,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 06:45:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.84/1.42 % (2274594)Input is clausal, will run a generic CNF schedule.
% 3.84/1.42 % (2274599)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=2548553133:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.84/1.42 % (2274602)lrs+10_1_sil=8000:sp=occurrence:random_seed=2523508549:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.84/1.42 % (2274600)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=574255877:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.84/1.42 % (2274601)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3492396482:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.84/1.42 % (2274605)dis-21_1_sil=8000:lcm=predicate:random_seed=3699584679:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.84/1.42 % (2274603)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=832209984:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.84/1.42 % (2274605)Refutation not found, incomplete strategy
% 3.84/1.42 % (2274605)------------------------------
% 3.84/1.42 % (2274605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.42 % (2274605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.42 % (2274605)CaDiCaL version: 2.1.3
% 3.84/1.42 % (2274605)Termination reason: Refutation not found, incomplete strategy
% 3.84/1.42 % (2274605)Time elapsed: 0.006 s
% 3.84/1.42 % (2274605)Peak memory usage: 88 MB
% 3.84/1.42 % (2274605)Instructions burned: 7 (million)
% 3.84/1.42 % (2274604)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1672148326:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.84/1.42 % (2274602)First to succeed.
% 3.84/1.42 % (2274602)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2274594"
% 3.84/1.42 % (2274603)Also succeeded, but the first one will report.
% 3.84/1.42 % (2274604)Instruction limit reached!
% 3.84/1.42 % (2274604)------------------------------
% 3.84/1.42 % (2274604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.42 % (2274604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.42 % (2274604)CaDiCaL version: 2.1.3
% 3.84/1.42 % (2274604)Termination reason: Instruction limit
% 3.84/1.42 % (2274604)Termination phase: Saturation
% 3.84/1.42 % (2274604)Time elapsed: 0.121 s
% 3.84/1.42 % (2274604)Peak memory usage: 89 MB
% 3.84/1.42 % (2274604)Instructions burned: 181 (million)
% 3.84/1.42 % (2274605)------------------------------
% 3.84/1.42 % (2274605)------------------------------
% 3.84/1.42 % (2274602)Refutation found. Thanks to Tanya!
% 3.84/1.42 % SZS status Unsatisfiable for theBenchmark
% 3.84/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.42 % (2274602)------------------------------
% 3.84/1.42 % (2274602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.42 % (2274602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.42 % (2274602)CaDiCaL version: 2.1.3
% 3.84/1.42 % (2274602)Termination reason: Refutation
% 3.84/1.42 % (2274602)Time elapsed: 0.037 s
% 3.84/1.42 % (2274602)Peak memory usage: 90 MB
% 3.84/1.42 % (2274602)Instructions burned: 50 (million)
% 3.84/1.42 % (2274602)------------------------------
% 3.84/1.42 % (2274602)------------------------------
% 3.84/1.42 % (2274594)Success in time 0.479 s
% 3.84/1.42 % Vampire exiting
%------------------------------------------------------------------------------