%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO026-3 : 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 3.73s 1.49s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 12 unt; 2 def)
% Number of atoms : 71 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 82 ( 40 ~; 40 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X1,X2,X3)
| ~ between(X0,X1,X4)
| ~ between(X2,X3,X5)
| X0 = X1
| equidistant(X4,X6,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f20,axiom,
! [X0,X1] : equidistant(X0,X1,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f43,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f44,axiom,
between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f45,axiom,
equidistant(v,w,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
fof(f46,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f47,negated_conjecture,
w != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_x) ).
fof(f178,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X3,X4,X5,X4)
| ~ equidistant(X0,X1,X0,X2)
| ~ equidistant(X3,X0,X5,X0)
| ~ between(X3,X0,X1)
| ~ between(X5,X0,X2)
| X0 = X3
| equidistant(X1,X4,X2,X4) ),
inference(resolution,[],[f6,f20]) ).
fof(f349,plain,
! [X2,X3,X0,X1,X4] :
( ~ equidistant(X0,X1,X0,X2)
| ~ equidistant(X3,X0,X3,X0)
| ~ between(X3,X0,X1)
| ~ between(X3,X0,X2)
| X0 = X3
| equidistant(X1,X4,X2,X4) ),
inference(resolution,[],[f178,f20]) ).
fof(f356,plain,
! [X2,X3,X0,X1,X4] :
( ~ equidistant(X0,X1,X0,X2)
| ~ between(X3,X0,X1)
| ~ between(X3,X0,X2)
| X0 = X3
| equidistant(X1,X4,X2,X4) ),
inference(forward_subsumption_resolution,[],[f349,f20]) ).
fof(f624,plain,
! [X0,X1] :
( ~ between(X0,v,w)
| ~ between(X0,v,x)
| v = X0
| equidistant(w,X1,x,X1) ),
inference(resolution,[],[f356,f45]) ).
fof(f633,definition,
( spl0_22
<=> ! [X0] :
( ~ between(X0,v,x)
| v = X0
| ~ between(X0,v,w) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f634,plain,
( ! [X0] :
( ~ between(X0,v,x)
| v = X0
| ~ between(X0,v,w) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f637,definition,
( spl0_23
<=> ! [X1] : equidistant(w,X1,x,X1) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f638,plain,
( ! [X1] : equidistant(w,X1,x,X1)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f639,plain,
( spl0_23
| spl0_22 ),
inference(avatar_split_clause,[],[f624,f633,f637]) ).
fof(f821,plain,
( w = x
| ~ spl0_23 ),
inference(resolution,[],[f638,f3]) ).
fof(f843,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f821,f47]) ).
fof(f844,plain,
~ spl0_23,
inference(avatar_contradiction_clause,[],[f843]) ).
fof(f879,plain,
( u = v
| ~ between(u,v,w)
| ~ spl0_22 ),
inference(resolution,[],[f634,f44]) ).
fof(f880,plain,
( ~ between(u,v,w)
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f879,f46]) ).
fof(f881,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f880,f43]) ).
fof(f882,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f881]) ).
cnf(s16,plain,
( spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f639]) ).
cnf(s41,plain,
~ spl0_23,
inference(sat_conversion,[],[f844]) ).
cnf(s43,plain,
~ spl0_22,
inference(sat_conversion,[],[f882]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s16,s41,s43]) ).
fof(f883,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 06:31:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.73/1.49 % (2187549)Input is clausal, will run a generic CNF schedule.
% 3.73/1.49 % (2187558)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4023507714:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.73/1.49 % (2187554)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=3523639957:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.73/1.49 % (2187560)dis-21_1_sil=8000:lcm=predicate:random_seed=1766377617: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)
% 3.73/1.49 % (2187557)lrs+10_1_sil=8000:sp=occurrence:random_seed=3085498764:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.73/1.49 % (2187556)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4131625688:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.73/1.49 % (2187555)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=411628568:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.73/1.49 % (2187559)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=260376171:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.73/1.49 % (2187558)Instruction limit reached!
% 3.73/1.49 % (2187558)------------------------------
% 3.73/1.49 % (2187558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2187558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2187558)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2187558)Termination reason: Instruction limit
% 3.73/1.49 % (2187558)Termination phase: Saturation
% 3.73/1.49 % (2187558)Time elapsed: 0.034 s
% 3.73/1.49 % (2187558)Peak memory usage: 88 MB
% 3.73/1.49 % (2187558)Instructions burned: 115 (million)
% 3.73/1.49 % (2187557)First to succeed.
% 3.73/1.49 % (2187557)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2187549"
% 3.73/1.49 % (2187560)Also succeeded, but the first one will report.
% 3.73/1.49 % (2187559)Instruction limit reached!
% 3.73/1.49 % (2187559)------------------------------
% 3.73/1.49 % (2187559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2187559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2187559)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2187559)Termination reason: Instruction limit
% 3.73/1.49 % (2187559)Termination phase: Saturation
% 3.73/1.49 % (2187559)Time elapsed: 0.106 s
% 3.73/1.49 % (2187559)Peak memory usage: 89 MB
% 3.73/1.49 % (2187559)Instructions burned: 181 (million)
% 3.73/1.49 % (2187568)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=3690177319:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.73/1.49 % (2187568)Also succeeded, but the first one will report.
% 3.73/1.49 % (2187557)Refutation found. Thanks to Tanya!
% 3.73/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.73/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.73/1.49 % (2187557)------------------------------
% 3.73/1.49 % (2187557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.73/1.49 % (2187557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/1.49 % (2187557)CaDiCaL version: 2.1.3
% 3.73/1.49 % (2187557)Termination reason: Refutation
% 3.73/1.49 % (2187557)Time elapsed: 0.020 s
% 3.73/1.49 % (2187557)Peak memory usage: 89 MB
% 3.73/1.49 % (2187557)Instructions burned: 27 (million)
% 3.73/1.49 % (2187557)------------------------------
% 3.73/1.49 % (2187557)------------------------------
% 3.73/1.49 % (2187549)Success in time 0.448 s
% 3.73/1.49 % Vampire exiting
%------------------------------------------------------------------------------