%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 09:53:19 AM UTC 2026
% Result : Unsatisfiable 0.36s 0.49s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 55 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 33 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X4,X5)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X1,X2,X3)
| ~ between(X2,X3,X5)
| X0 = X1
| equidistant(X4,X6,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
fof(f19,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_x) ).
fof(f21,axiom,
equidistant(v,w,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v_to_x) ).
fof(f22,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
fof(f23,negated_conjecture,
w != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_is_x) ).
fof(f26,plain,
! [X0,X1] :
( ~ equidistant(v,w,X0,X1)
| equidistant(v,x,X0,X1) ),
inference(resolution,[],[f2,f21]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X1,X0,X2,X3) ),
inference(resolution,[],[f2,f1]) ).
fof(f71,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[],[f27,f1]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( ~ equidistant(v,x,X0,X1)
| ~ equidistant(u,X2,X3,X4)
| ~ equidistant(v,X2,X0,X4)
| ~ equidistant(u,v,X3,X0)
| ~ between(X3,X0,X1)
| u = v
| equidistant(x,X2,X1,X4) ),
inference(resolution,[],[f6,f20]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X4] :
( ~ between(X3,X0,X1)
| ~ equidistant(u,X2,X3,X4)
| ~ equidistant(v,X2,X0,X4)
| ~ equidistant(u,v,X3,X0)
| ~ equidistant(v,x,X0,X1)
| equidistant(x,X2,X1,X4) ),
inference(forward_subsumption_resolution,[],[f88,f22]) ).
fof(f97,plain,
equidistant(v,x,v,w),
inference(resolution,[],[f71,f26]) ).
fof(f392,plain,
! [X0,X1] :
( ~ equidistant(u,X0,u,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,v,u,v)
| ~ equidistant(v,x,v,w)
| equidistant(x,X0,w,X1) ),
inference(resolution,[],[f91,f19]) ).
fof(f409,plain,
! [X0,X1] :
( ~ equidistant(u,X0,u,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(v,x,v,w)
| equidistant(x,X0,w,X1) ),
inference(forward_subsumption_resolution,[],[f392,f71]) ).
fof(f422,plain,
! [X0,X1] :
( ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,X0,u,X1)
| equidistant(x,X0,w,X1) ),
inference(forward_subsumption_resolution,[],[f409,f97]) ).
fof(f1134,plain,
! [X0] :
( ~ equidistant(u,X0,u,X0)
| equidistant(x,X0,w,X0) ),
inference(resolution,[],[f422,f71]) ).
fof(f1137,plain,
! [X0] : equidistant(x,X0,w,X0),
inference(forward_subsumption_resolution,[],[f1134,f71]) ).
fof(f1150,plain,
w = x,
inference(resolution,[],[f1137,f3]) ).
fof(f1154,plain,
$false,
inference(forward_subsumption_resolution,[],[f1150,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 06:36:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.49 % (3629389)Will run a generic schedule for satisfiability detection.
% 0.36/0.49 % (3629400)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=635724157:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.36/0.49 % (3629395)% WARNING: option uhcvi not known.
% 0.36/0.49 % (3629395)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2655388349:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.36/0.49 % (3629399)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1487092156:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.36/0.49 % (3629396)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2824526437:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.36/0.49 % (3629397)dis+10_1_sil=32000:sp=arity:random_seed=65971282:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.36/0.49 % (3629398)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=370582787:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.36/0.49 % (3629394)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3890155381_2999 on theBenchmark for (2999ds/0Mi)
% 0.36/0.49 % TRYING [1]
% 0.36/0.49 % TRYING [2]
% 0.36/0.49 % TRYING [3]
% 0.36/0.49 % (3629399) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3629389-3629399"...
% 0.36/0.49 % (3629399)...printing done.
% 0.36/0.49 % TRYING [4]
% 0.36/0.49 % (3629399)Refutation found. Thanks to Tanya!
% 0.36/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.36/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.49 % (3629399)------------------------------
% 0.36/0.49 % (3629399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.49 % (3629399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.49 % (3629399)CaDiCaL version: 2.1.3
% 0.36/0.49 % (3629399)Termination reason: Refutation
% 0.36/0.49 % (3629399)Time elapsed: 0.034 s
% 0.36/0.49 % (3629399)Peak memory usage: 12 MB
% 0.36/0.49 % (3629399)Instructions burned: 51 (million)
% 0.36/0.49 % (3629389)Success in time 0.068 s
% 0.36/0.49 % Vampire exiting
%------------------------------------------------------------------------------