%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO029-3 : 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 : n017.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 09:51:15 AM UTC 2026
% Result : Unsatisfiable 3.51s 1.39s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 14 unt; 4 def)
% Number of atoms : 69 ( 5 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 66 ( 32 ~; 30 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f26,axiom,
! [X2,X3,X0,X1] :
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
fof(f28,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
fof(f43,axiom,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X0,X1,X3)
| ~ equidistant(X1,X2,X1,X3)
| X0 = X1
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
fof(f44,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f45,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_extensions) ).
fof(f53,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( sQ0_eqProxy(X2,X3)
| ~ between(X0,X1,X3)
| ~ equidistant(X1,X2,X1,X3)
| sQ0_eqProxy(X0,X1)
| ~ between(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f43,f53,f53]) ).
fof(f59,plain,
~ sQ0_eqProxy(u,v),
inference(equality_proxy_replacement,[],[f44,f53]) ).
fof(f60,plain,
~ sQ0_eqProxy(extension(u,v,u,v),extension(u,v,v,u)),
inference(equality_proxy_replacement,[],[f45,f53]) ).
fof(f180,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ equidistant(X1,extension(u,v,u,v),X1,extension(u,v,v,u))
| ~ between(X0,X1,extension(u,v,v,u))
| ~ between(X0,X1,extension(u,v,u,v)) ),
inference(resolution,[],[f58,f60]) ).
fof(f248,plain,
( ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,v,u))
| ~ between(u,v,extension(u,v,u,v)) ),
inference(resolution,[],[f180,f59]) ).
fof(f261,definition,
( spl1_4
<=> between(u,v,extension(u,v,u,v)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f262,plain,
( ~ between(u,v,extension(u,v,u,v))
| spl1_4 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f264,definition,
( spl1_5
<=> between(u,v,extension(u,v,v,u)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f265,plain,
( ~ between(u,v,extension(u,v,v,u))
| spl1_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,definition,
( spl1_6
<=> equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f268,plain,
( ~ equidistant(v,extension(u,v,u,v),v,extension(u,v,v,u))
| spl1_6 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f269,plain,
( ~ spl1_4
| ~ spl1_5
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f248,f267,f264,f261]) ).
fof(f278,plain,
( ! [X0,X1] :
( ~ equidistant(X0,X1,v,extension(u,v,v,u))
| ~ equidistant(v,extension(u,v,u,v),X0,X1) )
| spl1_6 ),
inference(resolution,[],[f268,f28]) ).
fof(f376,plain,
( ~ equidistant(u,v,v,extension(u,v,v,u))
| spl1_6 ),
inference(resolution,[],[f278,f5]) ).
fof(f393,plain,
( ~ equidistant(v,extension(u,v,v,u),v,u)
| spl1_6 ),
inference(resolution,[],[f376,f26]) ).
fof(f457,plain,
( $false
| spl1_6 ),
inference(resolution,[],[f393,f5]) ).
fof(f468,plain,
spl1_6,
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f469,plain,
( $false
| spl1_4 ),
inference(resolution,[],[f262,f4]) ).
fof(f470,plain,
spl1_4,
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f471,plain,
( $false
| spl1_5 ),
inference(resolution,[],[f265,f4]) ).
fof(f472,plain,
spl1_5,
inference(avatar_contradiction_clause,[],[f471]) ).
cnf(s2,plain,
( ~ spl1_4
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f269]) ).
cnf(s3,plain,
spl1_6,
inference(sat_conversion,[],[f468]) ).
cnf(s4,plain,
spl1_4,
inference(sat_conversion,[],[f470]) ).
cnf(s5,plain,
spl1_5,
inference(sat_conversion,[],[f472]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s3,s5,s4]) ).
fof(f473,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO029-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 06:32:35 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.51/1.39 % (2188588)Input is clausal, will run a generic CNF schedule.
% 3.51/1.39 % (2188595)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1588231482:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.51/1.39 % (2188596)lrs+10_1_sil=8000:sp=occurrence:random_seed=2500762070:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.51/1.39 % (2188598)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=890475358:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.51/1.39 % (2188593)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=1038111667:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.51/1.39 % (2188594)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2734432646:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.51/1.39 % (2188599)dis-21_1_sil=8000:lcm=predicate:random_seed=1323683998: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)
% 3.51/1.39 % (2188597)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1302452153:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.51/1.39 % (2188599)First to succeed.
% 3.51/1.39 % (2188599)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2188588"
% 3.51/1.39 % (2188597)Instruction limit reached!
% 3.51/1.39 % (2188597)------------------------------
% 3.51/1.39 % (2188597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2188597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2188597)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2188597)Termination reason: Instruction limit
% 3.51/1.39 % (2188597)Termination phase: Saturation
% 3.51/1.39 % (2188597)Time elapsed: 0.063 s
% 3.51/1.39 % (2188597)Peak memory usage: 88 MB
% 3.51/1.39 % (2188597)Instructions burned: 115 (million)
% 3.51/1.39 % (2188596)Instruction limit reached!
% 3.51/1.39 % (2188596)------------------------------
% 3.51/1.39 % (2188596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2188596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2188596)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2188596)Termination reason: Instruction limit
% 3.51/1.39 % (2188596)Termination phase: Saturation
% 3.51/1.39 % (2188596)Time elapsed: 0.069 s
% 3.51/1.39 % (2188596)Peak memory usage: 88 MB
% 3.51/1.39 % (2188596)Instructions burned: 108 (million)
% 3.51/1.39 % (2188598)Instruction limit reached!
% 3.51/1.39 % (2188598)------------------------------
% 3.51/1.39 % (2188598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2188598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2188598)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2188598)Termination reason: Instruction limit
% 3.51/1.39 % (2188598)Termination phase: Saturation
% 3.51/1.39 % (2188598)Time elapsed: 0.100 s
% 3.51/1.39 % (2188598)Peak memory usage: 89 MB
% 3.51/1.39 % (2188598)Instructions burned: 181 (million)
% 3.51/1.39 % (2188608)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1640761694:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.51/1.39 % (2188607)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2643171819:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.51/1.39 % (2188607)Refutation not found, incomplete strategy
% 3.51/1.39 % (2188607)------------------------------
% 3.51/1.39 % (2188607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2188607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2188607)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2188607)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.39 % (2188607)Time elapsed: 0.002 s
% 3.51/1.39 % (2188607)Peak memory usage: 88 MB
% 3.51/1.39 % (2188607)Instructions burned: 1 (million)
% 3.51/1.39 % (2188608)Also succeeded, but the first one will report.
% 3.51/1.39 % (2188599)Refutation found. Thanks to Tanya!
% 3.51/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.39 % (2188599)------------------------------
% 3.51/1.39 % (2188599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.39 % (2188599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.39 % (2188599)CaDiCaL version: 2.1.3
% 3.51/1.39 % (2188599)Termination reason: Refutation
% 3.51/1.39 % (2188599)Time elapsed: 0.008 s
% 3.51/1.39 % (2188599)Peak memory usage: 89 MB
% 3.51/1.39 % (2188599)Instructions burned: 11 (million)
% 3.51/1.39 % (2188599)------------------------------
% 3.51/1.39 % (2188599)------------------------------
% 3.51/1.39 % (2188588)Success in time 0.435 s
% 3.51/1.39 % Vampire exiting
%------------------------------------------------------------------------------