%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV168+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 : n019.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 01:08:17 PM UTC 2026
% Result : Theorem 2.51s 0.91s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 16 unt; 5 def)
% Number of atoms : 204 ( 43 equ)
% Maximal formula atoms : 35 ( 5 avg)
% Number of connectives : 237 ( 71 ~; 67 |; 68 &)
% ( 5 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( a_select2(mu_init,pv40) = init
& leq(n0,pv40)
& leq(n0,pv46)
& leq(pv40,n4)
& leq(pv46,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,n135299) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,n4) )
=> a_select3(q_init,X0,X1) = init ) )
& ! [X2] :
( ( leq(n0,X2)
& leq(X2,n4) )
=> a_select2(rho_init,X2) = init )
& ! [X3] :
( ( leq(n0,X3)
& leq(X3,pred(pv40)) )
=> a_select2(mu_init,X3) = init )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,pred(pv40)) )
=> a_select2(sigma_init,X4) = init )
& ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(center_init,X5,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select2(muold_init,X6) = init ) )
& ( gt(loopcounter,n1)
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,n4) )
=> a_select2(rhoold_init,X7) = init ) )
& ( gt(loopcounter,n1)
=> ! [X8] :
( ( leq(n0,X8)
& leq(X8,n4) )
=> a_select2(sigmaold_init,X8) = init ) ) )
=> a_select3(q_init,pv46,pv40) = init ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0016) ).
fof(f54,negated_conjecture,
~ ( ( a_select2(mu_init,pv40) = init
& leq(n0,pv40)
& leq(n0,pv46)
& leq(pv40,n4)
& leq(pv46,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,n135299) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,n4) )
=> a_select3(q_init,X0,X1) = init ) )
& ! [X2] :
( ( leq(n0,X2)
& leq(X2,n4) )
=> a_select2(rho_init,X2) = init )
& ! [X3] :
( ( leq(n0,X3)
& leq(X3,pred(pv40)) )
=> a_select2(mu_init,X3) = init )
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,pred(pv40)) )
=> a_select2(sigma_init,X4) = init )
& ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(center_init,X5,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select2(muold_init,X6) = init ) )
& ( gt(loopcounter,n1)
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,n4) )
=> a_select2(rhoold_init,X7) = init ) )
& ( gt(loopcounter,n1)
=> ! [X8] :
( ( leq(n0,X8)
& leq(X8,n4) )
=> a_select2(sigmaold_init,X8) = init ) ) )
=> a_select3(q_init,pv46,pv40) = init ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f100,plain,
( init != a_select3(q_init,pv46,pv40)
& a_select2(mu_init,pv40) = init
& leq(n0,pv40)
& leq(n0,pv46)
& leq(pv40,n4)
& leq(pv46,n135299)
& ! [X0] :
( ! [X1] :
( a_select3(q_init,X0,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,n4) )
| ~ leq(n0,X0)
| ~ leq(X0,n135299) )
& ! [X2] :
( a_select2(rho_init,X2) = init
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
& ! [X3] :
( a_select2(mu_init,X3) = init
| ~ leq(n0,X3)
| ~ leq(X3,pred(pv40)) )
& ! [X4] :
( a_select2(sigma_init,X4) = init
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv40)) )
& ! [X5] :
( a_select3(center_init,X5,n0) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
& ( ! [X6] :
( a_select2(muold_init,X6) = init
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X7] :
( a_select2(rhoold_init,X7) = init
| ~ leq(n0,X7)
| ~ leq(X7,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X8] :
( a_select2(sigmaold_init,X8) = init
| ~ leq(n0,X8)
| ~ leq(X8,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f101,plain,
( init != a_select3(q_init,pv46,pv40)
& a_select2(mu_init,pv40) = init
& leq(n0,pv40)
& leq(n0,pv46)
& leq(pv40,n4)
& leq(pv46,n135299)
& ! [X0] :
( ! [X1] :
( a_select3(q_init,X0,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,n4) )
| ~ leq(n0,X0)
| ~ leq(X0,n135299) )
& ! [X2] :
( a_select2(rho_init,X2) = init
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
& ! [X3] :
( a_select2(mu_init,X3) = init
| ~ leq(n0,X3)
| ~ leq(X3,pred(pv40)) )
& ! [X4] :
( a_select2(sigma_init,X4) = init
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv40)) )
& ! [X5] :
( a_select3(center_init,X5,n0) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
& ( ! [X6] :
( a_select2(muold_init,X6) = init
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X7] :
( a_select2(rhoold_init,X7) = init
| ~ leq(n0,X7)
| ~ leq(X7,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X8] :
( a_select2(sigmaold_init,X8) = init
| ~ leq(n0,X8)
| ~ leq(X8,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(flattening,[],[f100]) ).
fof(f186,plain,
! [X0,X1] :
( init = a_select3(q_init,X0,X1)
| ~ leq(n0,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X0)
| ~ leq(X0,n135299) ),
inference(cnf_transformation,[],[f101]) ).
fof(f187,plain,
leq(pv46,n135299),
inference(cnf_transformation,[],[f101]) ).
fof(f188,plain,
leq(pv40,n4),
inference(cnf_transformation,[],[f101]) ).
fof(f189,plain,
leq(n0,pv46),
inference(cnf_transformation,[],[f101]) ).
fof(f190,plain,
leq(n0,pv40),
inference(cnf_transformation,[],[f101]) ).
fof(f192,plain,
init != a_select3(q_init,pv46,pv40),
inference(cnf_transformation,[],[f101]) ).
fof(f355,definition,
! [X0,X1] :
( sQ24_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ24_eqProxy])],[equality_proxy_definition]) ).
fof(f356,plain,
~ sQ24_eqProxy(init,a_select3(q_init,pv46,pv40)),
inference(equality_proxy_replacement,[],[f192,f355]) ).
fof(f358,plain,
! [X0,X1] :
( sQ24_eqProxy(init,a_select3(q_init,X0,X1))
| ~ leq(n0,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X0)
| ~ leq(X0,n135299) ),
inference(equality_proxy_replacement,[],[f186,f355]) ).
fof(f457,plain,
( ~ leq(n0,pv40)
| ~ leq(pv40,n4)
| ~ leq(n0,pv46)
| ~ leq(pv46,n135299) ),
inference(resolution,[],[f358,f356]) ).
fof(f459,definition,
( spl25_5
<=> leq(pv46,n135299) ),
introduced(definition,[new_symbols(definition,[spl25_5])],[avatar_definition]) ).
fof(f460,plain,
( ~ leq(pv46,n135299)
| spl25_5 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f462,definition,
( spl25_6
<=> leq(n0,pv46) ),
introduced(definition,[new_symbols(definition,[spl25_6])],[avatar_definition]) ).
fof(f463,plain,
( ~ leq(n0,pv46)
| spl25_6 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f465,definition,
( spl25_7
<=> leq(pv40,n4) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f466,plain,
( ~ leq(pv40,n4)
| spl25_7 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f468,definition,
( spl25_8
<=> leq(n0,pv40) ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
fof(f469,plain,
( ~ leq(n0,pv40)
| spl25_8 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f470,plain,
( ~ spl25_5
| ~ spl25_6
| ~ spl25_7
| ~ spl25_8 ),
inference(avatar_split_clause,[],[f457,f468,f465,f462,f459]) ).
fof(f471,plain,
( $false
| spl25_5 ),
inference(resolution,[],[f460,f187]) ).
fof(f472,plain,
spl25_5,
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f473,plain,
( $false
| spl25_6 ),
inference(resolution,[],[f463,f189]) ).
fof(f474,plain,
spl25_6,
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f475,plain,
( $false
| spl25_7 ),
inference(resolution,[],[f466,f188]) ).
fof(f476,plain,
spl25_7,
inference(avatar_contradiction_clause,[],[f475]) ).
fof(f477,plain,
( $false
| spl25_8 ),
inference(resolution,[],[f469,f190]) ).
fof(f478,plain,
spl25_8,
inference(avatar_contradiction_clause,[],[f477]) ).
cnf(s4,plain,
( ~ spl25_5
| ~ spl25_6
| ~ spl25_7
| ~ spl25_8 ),
inference(sat_conversion,[],[f470]) ).
cnf(s5,plain,
spl25_5,
inference(sat_conversion,[],[f472]) ).
cnf(s6,plain,
spl25_6,
inference(sat_conversion,[],[f474]) ).
cnf(s7,plain,
spl25_7,
inference(sat_conversion,[],[f476]) ).
cnf(s8,plain,
spl25_8,
inference(sat_conversion,[],[f478]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s4,s8,s7,s6,s5]) ).
fof(f479,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV168+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 10:04:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.51/0.91 % (3901540)Detected formulas, will run a generic FOF schedule.
% 2.51/0.91 % (3901551)dis-21_1_sil=8000:lcm=predicate:random_seed=3610184936: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)
% 2.51/0.91 % (3901551)First to succeed.
% 2.51/0.91 % (3901551)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3901540"
% 2.51/0.91 % (3901550)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1097730030:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/0.91 % (3901548)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3230697735:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/0.91 % (3901547)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=2458616354:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/0.91 % (3901545)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=1601913938:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/0.91 % (3901549)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2661530822:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/0.91 % (3901546)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=1171959030:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/0.91 % (3901549)Also succeeded, but the first one will report.
% 2.51/0.91 % (3901550)Also succeeded, but the first one will report.
% 2.51/0.91 % (3901548)Also succeeded, but the first one will report.
% 2.51/0.91 % (3901551)Refutation found. Thanks to Tanya!
% 2.51/0.91 % SZS status Theorem for theBenchmark
% 2.51/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/0.91 % (3901551)------------------------------
% 2.51/0.91 % (3901551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/0.91 % (3901551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.91 % (3901551)CaDiCaL version: 2.1.3
% 2.51/0.91 % (3901551)Termination reason: Refutation
% 2.51/0.91 % (3901551)Time elapsed: 0.004 s
% 2.51/0.91 % (3901551)Peak memory usage: 89 MB
% 2.51/0.91 % (3901551)Instructions burned: 11 (million)
% 2.51/0.91 % (3901551)------------------------------
% 2.51/0.91 % (3901551)------------------------------
% 2.51/0.91 % (3901540)Success in time 0.297 s
% 2.51/0.91 % Vampire exiting
%------------------------------------------------------------------------------