%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV169+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 01:08:18 PM UTC 2026
% Result : Theorem 2.77s 1.17s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 10 unt; 3 def)
% Number of atoms : 148 ( 27 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 173 ( 51 ~; 45 |; 58 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( leq(n0,pv10)
& leq(n0,pv11)
& leq(n0,pv65)
& leq(pv10,n135299)
& leq(pv11,n4)
& leq(pv65,n4)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n135299)
& leq(X1,n4) )
=> ( ( X0 = pv10
& gt(pv11,X1) )
=> a_select3(q_init,X0,X1) = init ) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n135299)
& leq(X3,n4) )
=> ( gt(pv10,X2)
=> a_select3(q_init,X2,X3) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,pred(pv10)) )
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(q_init,X4,X5) = init ) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select3(center_init,X6,n0) = init ) )
=> a_select3(center_init,pv65,n0) = init ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0021) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv10)
& leq(n0,pv11)
& leq(n0,pv65)
& leq(pv10,n135299)
& leq(pv11,n4)
& leq(pv65,n4)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n135299)
& leq(X1,n4) )
=> ( ( X0 = pv10
& gt(pv11,X1) )
=> a_select3(q_init,X0,X1) = init ) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n135299)
& leq(X3,n4) )
=> ( gt(pv10,X2)
=> a_select3(q_init,X2,X3) = init ) )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,pred(pv10)) )
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(q_init,X4,X5) = init ) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select3(center_init,X6,n0) = init ) )
=> a_select3(center_init,pv65,n0) = init ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f100,plain,
( init != a_select3(center_init,pv65,n0)
& leq(n0,pv10)
& leq(n0,pv11)
& leq(n0,pv65)
& leq(pv10,n135299)
& leq(pv11,n4)
& leq(pv65,n4)
& ! [X0,X1] :
( a_select3(q_init,X0,X1) = init
| pv10 != X0
| ~ gt(pv11,X1)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n135299)
| ~ leq(X1,n4) )
& ! [X2,X3] :
( a_select3(q_init,X2,X3) = init
| ~ gt(pv10,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n135299)
| ~ leq(X3,n4) )
& ! [X4] :
( ! [X5] :
( a_select3(q_init,X4,X5) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv10)) )
& ! [X6] :
( a_select3(center_init,X6,n0) = init
| ~ leq(n0,X6)
| ~ leq(X6,n4) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f101,plain,
( init != a_select3(center_init,pv65,n0)
& leq(n0,pv10)
& leq(n0,pv11)
& leq(n0,pv65)
& leq(pv10,n135299)
& leq(pv11,n4)
& leq(pv65,n4)
& ! [X0,X1] :
( a_select3(q_init,X0,X1) = init
| pv10 != X0
| ~ gt(pv11,X1)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n135299)
| ~ leq(X1,n4) )
& ! [X2,X3] :
( a_select3(q_init,X2,X3) = init
| ~ gt(pv10,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n135299)
| ~ leq(X3,n4) )
& ! [X4] :
( ! [X5] :
( a_select3(q_init,X4,X5) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv10)) )
& ! [X6] :
( a_select3(center_init,X6,n0) = init
| ~ leq(n0,X6)
| ~ leq(X6,n4) ) ),
inference(flattening,[],[f100]) ).
fof(f170,plain,
! [X6] :
( init = a_select3(center_init,X6,n0)
| ~ leq(n0,X6)
| ~ leq(X6,n4) ),
inference(cnf_transformation,[],[f101]) ).
fof(f174,plain,
leq(pv65,n4),
inference(cnf_transformation,[],[f101]) ).
fof(f177,plain,
leq(n0,pv65),
inference(cnf_transformation,[],[f101]) ).
fof(f180,plain,
init != a_select3(center_init,pv65,n0),
inference(cnf_transformation,[],[f101]) ).
fof(f335,definition,
! [X0,X1] :
( sQ23_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ23_eqProxy])],[equality_proxy_definition]) ).
fof(f336,plain,
~ sQ23_eqProxy(init,a_select3(center_init,pv65,n0)),
inference(equality_proxy_replacement,[],[f180,f335]) ).
fof(f340,plain,
! [X6] :
( sQ23_eqProxy(init,a_select3(center_init,X6,n0))
| ~ leq(n0,X6)
| ~ leq(X6,n4) ),
inference(equality_proxy_replacement,[],[f170,f335]) ).
fof(f424,plain,
( ~ leq(n0,pv65)
| ~ leq(pv65,n4) ),
inference(resolution,[],[f340,f336]) ).
fof(f426,definition,
( spl24_4
<=> leq(pv65,n4) ),
introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition]) ).
fof(f427,plain,
( ~ leq(pv65,n4)
| spl24_4 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f429,definition,
( spl24_5
<=> leq(n0,pv65) ),
introduced(definition,[new_symbols(definition,[spl24_5])],[avatar_definition]) ).
fof(f430,plain,
( ~ leq(n0,pv65)
| spl24_5 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f431,plain,
( ~ spl24_4
| ~ spl24_5 ),
inference(avatar_split_clause,[],[f424,f429,f426]) ).
fof(f432,plain,
( $false
| spl24_4 ),
inference(resolution,[],[f427,f174]) ).
fof(f433,plain,
spl24_4,
inference(avatar_contradiction_clause,[],[f432]) ).
fof(f434,plain,
( $false
| spl24_5 ),
inference(resolution,[],[f430,f177]) ).
fof(f435,plain,
spl24_5,
inference(avatar_contradiction_clause,[],[f434]) ).
cnf(s4,plain,
( ~ spl24_4
| ~ spl24_5 ),
inference(sat_conversion,[],[f431]) ).
cnf(s5,plain,
spl24_4,
inference(sat_conversion,[],[f433]) ).
cnf(s6,plain,
spl24_5,
inference(sat_conversion,[],[f435]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s6,s5]) ).
fof(f436,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV169+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 10:04:54 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.77/1.17 % (2149830)Detected formulas, will run a generic FOF schedule.
% 2.77/1.17 % (2149841)dis-21_1_sil=8000:lcm=predicate:random_seed=1767614818: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)
% 2.77/1.17 % (2149841)First to succeed.
% 2.77/1.17 % (2149841)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2149830"
% 2.77/1.17 % (2149840)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2928606806:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.17 % (2149837)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=3959654788:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.17 % (2149838)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2293236452:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.17 % (2149839)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3715937930:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.17 % (2149835)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=261546744:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.17 % (2149836)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=1435933319:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.17 % (2149839)Also succeeded, but the first one will report.
% 2.77/1.17 % (2149840)Also succeeded, but the first one will report.
% 2.77/1.17 % (2149838)Also succeeded, but the first one will report.
% 2.77/1.17 % (2149841)Refutation found. Thanks to Tanya!
% 2.77/1.17 % SZS status Theorem for theBenchmark
% 2.77/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.17 % (2149841)------------------------------
% 2.77/1.17 % (2149841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.17 % (2149841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.17 % (2149841)CaDiCaL version: 2.1.3
% 2.77/1.17 % (2149841)Termination reason: Refutation
% 2.77/1.17 % (2149841)Time elapsed: 0.004 s
% 2.77/1.17 % (2149841)Peak memory usage: 89 MB
% 2.77/1.17 % (2149841)Instructions burned: 9 (million)
% 2.77/1.17 % (2149841)------------------------------
% 2.77/1.17 % (2149841)------------------------------
% 2.77/1.17 % (2149830)Success in time 0.301 s
% 2.77/1.17 % Vampire exiting
%------------------------------------------------------------------------------