%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:51:29 AM UTC 2026
% Result : Theorem 2.57s 1.32s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 4 unt; 1 def)
% Number of atoms : 59 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 20 |; 9 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 43 ( 33 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( open(X0)
<=> ? [X1] : end_point(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn) ).
fof(f13,axiom,
! [X0,X1] :
( end_point(X1,X0)
=> ? [X2] :
( end_point(X2,X0)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
fof(f17,conjecture,
! [X0] :
( open(X0)
=> ? [X1,X2] :
( X1 != X2
& end_point(X1,X0)
& end_point(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_2_7_1) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( open(X0)
=> ? [X1,X2] :
( X1 != X2
& end_point(X1,X0)
& end_point(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0] :
( open(X0)
=> ? [X1] : end_point(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f21,plain,
? [X0] :
( ! [X1,X2] :
( X1 = X2
| ~ end_point(X1,X0)
| ~ end_point(X2,X0) )
& open(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
( end_point(X2,X0)
& X1 != X2 )
| ~ end_point(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f34,plain,
! [X0] :
( ? [X1] : end_point(X1,X0)
| ~ open(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f41,plain,
( ! [X1,X2] :
( X1 = X2
| ~ end_point(X1,sK0)
| ~ end_point(X2,sK0) )
& open(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f46,plain,
! [X0,X1] :
( ( end_point(sK3(X0,X1),X0)
& sK3(X0,X1) != X1 )
| ~ end_point(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f26]) ).
fof(f52,plain,
! [X0] :
( end_point(sK7(X0),X0)
| ~ open(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f34]) ).
fof(f68,plain,
open(sK0),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
! [X2,X1] :
( X1 = X2
| ~ end_point(X1,sK0)
| ~ end_point(X2,sK0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f74,plain,
! [X0,X1] :
( sK3(X0,X1) != X1
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1] :
( end_point(sK3(X0,X1),X0)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f87,plain,
! [X0] :
( ~ open(X0)
| end_point(sK7(X0),X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f115,definition,
! [X0,X1] :
( sQ14_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ14_eqProxy])],[equality_proxy_definition]) ).
fof(f116,plain,
! [X2,X1] :
( sQ14_eqProxy(X1,X2)
| ~ end_point(X1,sK0)
| ~ end_point(X2,sK0) ),
inference(equality_proxy_replacement,[],[f69,f115]) ).
fof(f120,plain,
! [X0,X1] :
( ~ sQ14_eqProxy(sK3(X0,X1),X1)
| ~ end_point(X1,X0) ),
inference(equality_proxy_replacement,[],[f74,f115]) ).
fof(f129,plain,
end_point(sK7(sK0),sK0),
inference(resolution,[],[f87,f68]) ).
fof(f135,plain,
! [X0,X1] :
( ~ end_point(sK3(X1,X0),sK0)
| ~ end_point(X0,X1)
| ~ end_point(X0,sK0) ),
inference(resolution,[],[f120,f116]) ).
fof(f136,plain,
! [X0] :
( ~ end_point(X0,sK0)
| ~ end_point(X0,sK0)
| ~ end_point(X0,sK0) ),
inference(resolution,[],[f135,f75]) ).
fof(f137,plain,
! [X0] : ~ end_point(X0,sK0),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f139,plain,
$false,
inference(resolution,[],[f137,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:56:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.57/1.32 % (2475979)Detected formulas, will run a generic FOF schedule.
% 2.57/1.32 % (2475990)dis-21_1_sil=8000:lcm=predicate:random_seed=2033079883: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)
% 2.57/1.32 % (2475990)First to succeed.
% 2.57/1.32 % (2475990)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2475979"
% 2.57/1.32 % (2475985)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=1347071717:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.32 % (2475988)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=656014447:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.32 % (2475987)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2949587107:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.32 % (2475984)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=3990598709:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.32 % (2475986)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=2581941577:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.32 % (2475989)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2308085724:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.32 % (2475988)Also succeeded, but the first one will report.
% 2.57/1.32 % (2475987)Also succeeded, but the first one will report.
% 2.57/1.32 % (2475989)Also succeeded, but the first one will report.
% 2.57/1.32 % (2475990)Refutation found. Thanks to Tanya!
% 2.57/1.32 % SZS status Theorem for theBenchmark
% 2.57/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.32 % (2475990)------------------------------
% 2.57/1.32 % (2475990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.32 % (2475990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.32 % (2475990)CaDiCaL version: 2.1.3
% 2.57/1.32 % (2475990)Termination reason: Refutation
% 2.57/1.32 % (2475990)Time elapsed: 0.002 s
% 2.57/1.32 % (2475990)Peak memory usage: 88 MB
% 2.57/1.32 % (2475990)Instructions burned: 3 (million)
% 2.57/1.32 % (2475990)------------------------------
% 2.57/1.32 % (2475990)------------------------------
% 2.57/1.32 % (2475979)Success in time 0.273 s
% 2.57/1.32 % Vampire exiting
%------------------------------------------------------------------------------