%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV177+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 : n003.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 01:08:19 PM UTC 2026
% Result : Theorem 2.42s 0.99s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 10 unt; 2 def)
% Number of atoms : 261 ( 59 equ)
% Maximal formula atoms : 37 ( 10 avg)
% Number of connectives : 347 ( 112 ~; 101 |; 104 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( leq(n0,pv40)
& leq(n0,pv45)
& leq(pv40,n4)
& leq(pv45,n135299)
& gt(loopcounter,n1)
& ! [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 ) ) )
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,n4) )
=> a_select2(rhoold_init,X9) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0061) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv40)
& leq(n0,pv45)
& leq(pv40,n4)
& leq(pv45,n135299)
& gt(loopcounter,n1)
& ! [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 ) ) )
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,n4) )
=> a_select2(rhoold_init,X9) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f143,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(n0,X9)
& leq(X9,n4) )
& leq(n0,pv40)
& leq(n0,pv45)
& leq(pv40,n4)
& leq(pv45,n135299)
& gt(loopcounter,n1)
& ! [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(f144,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(n0,X9)
& leq(X9,n4) )
& leq(n0,pv40)
& leq(n0,pv45)
& leq(pv40,n4)
& leq(pv45,n135299)
& gt(loopcounter,n1)
& ! [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,[],[f143]) ).
fof(f197,plain,
( ? [X0] :
( init != a_select2(rhoold_init,X0)
& leq(n0,X0)
& leq(X0,n4) )
& leq(n0,pv40)
& leq(n0,pv45)
& leq(pv40,n4)
& leq(pv45,n135299)
& gt(loopcounter,n1)
& ! [X1] :
( ! [X2] :
( init = a_select3(q_init,X1,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
| ~ leq(n0,X1)
| ~ leq(X1,n135299) )
& ! [X3] :
( init = a_select2(rho_init,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
& ! [X4] :
( init = a_select2(mu_init,X4)
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv40)) )
& ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(n0,X5)
| ~ leq(X5,pred(pv40)) )
& ! [X6] :
( init = a_select3(center_init,X6,n0)
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
& ( ! [X7] :
( init = a_select2(muold_init,X7)
| ~ leq(n0,X7)
| ~ leq(X7,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X8] :
( init = a_select2(rhoold_init,X8)
| ~ leq(n0,X8)
| ~ leq(X8,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X9] :
( init = a_select2(sigmaold_init,X9)
| ~ leq(n0,X9)
| ~ leq(X9,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(rectify,[],[f144]) ).
fof(f198,plain,
( init != a_select2(rhoold_init,sK31)
& leq(n0,sK31)
& leq(sK31,n4)
& leq(n0,pv40)
& leq(n0,pv45)
& leq(pv40,n4)
& leq(pv45,n135299)
& gt(loopcounter,n1)
& ! [X1] :
( ! [X2] :
( init = a_select3(q_init,X1,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
| ~ leq(n0,X1)
| ~ leq(X1,n135299) )
& ! [X3] :
( init = a_select2(rho_init,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
& ! [X4] :
( init = a_select2(mu_init,X4)
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv40)) )
& ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(n0,X5)
| ~ leq(X5,pred(pv40)) )
& ! [X6] :
( init = a_select3(center_init,X6,n0)
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
& ( ! [X7] :
( init = a_select2(muold_init,X7)
| ~ leq(n0,X7)
| ~ leq(X7,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X8] :
( init = a_select2(rhoold_init,X8)
| ~ leq(n0,X8)
| ~ leq(X8,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X9] :
( init = a_select2(sigmaold_init,X9)
| ~ leq(n0,X9)
| ~ leq(X9,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f310,plain,
! [X8] :
( init = a_select2(rhoold_init,X8)
| ~ leq(n0,X8)
| ~ leq(X8,n4)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f317,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f198]) ).
fof(f322,plain,
leq(sK31,n4),
inference(cnf_transformation,[],[f198]) ).
fof(f323,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f324,plain,
init != a_select2(rhoold_init,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f368,definition,
( spl32_1
<=> gt(loopcounter,n1) ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f376,definition,
( spl32_3
<=> ! [X8] :
( init = a_select2(rhoold_init,X8)
| ~ leq(X8,n4)
| ~ leq(n0,X8) ) ),
introduced(definition,[new_symbols(definition,[spl32_3])],[avatar_definition]) ).
fof(f377,plain,
( ! [X8] :
( init = a_select2(rhoold_init,X8)
| ~ leq(X8,n4)
| ~ leq(n0,X8) )
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( ~ spl32_1
| spl32_3 ),
inference(avatar_split_clause,[],[f310,f376,f368]) ).
fof(f383,plain,
spl32_1,
inference(avatar_split_clause,[],[f317,f368]) ).
fof(f384,plain,
( init != init
| ~ leq(sK31,n4)
| ~ leq(n0,sK31)
| ~ spl32_3 ),
inference(superposition,[],[f324,f377]) ).
fof(f385,plain,
( ~ leq(sK31,n4)
| ~ leq(n0,sK31)
| ~ spl32_3 ),
inference(trivial_inequality_removal,[],[f384]) ).
fof(f386,plain,
( ~ leq(n0,sK31)
| ~ spl32_3 ),
inference(forward_subsumption_resolution,[],[f385,f322]) ).
fof(f387,plain,
( $false
| ~ spl32_3 ),
inference(forward_subsumption_resolution,[],[f386,f323]) ).
fof(f388,plain,
~ spl32_3,
inference(avatar_contradiction_clause,[],[f387]) ).
cnf(s2,plain,
( ~ spl32_1
| spl32_3 ),
inference(sat_conversion,[],[f378]) ).
cnf(s4,plain,
spl32_1,
inference(sat_conversion,[],[f383]) ).
cnf(s5,plain,
~ spl32_3,
inference(sat_conversion,[],[f388]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s5,s4]) ).
fof(f389,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV177+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.26 % Computer : n003.cluster.edu
% 0.14/0.26 % Model : x86_64 x86_64
% 0.14/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.26 % Memory : 8046.5625MB
% 0.14/0.26 % OS : Linux 6.8.0-71-generic
% 0.14/0.26 % CPULimit : 300
% 0.14/0.26 % WCLimit : 300
% 0.14/0.26 % DateTime : Mon Sep 28 10:09:23 UTC 2026
% 0.14/0.27 % CPUTime :
% 0.14/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.30 Running first-order theorem proving
% 0.14/0.30 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
% 2.42/0.99 % (1486617)Detected formulas, will run a generic FOF schedule.
% 2.42/0.99 % (1486627)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3178947313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.42/0.99 % (1486627)First to succeed.
% 2.42/0.99 % (1486627)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1486617"
% 2.42/0.99 % (1486625)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3549200110:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.42/0.99 % (1486628)dis-21_1_sil=8000:lcm=predicate:random_seed=770480591: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)
% 2.42/0.99 % (1486623)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=2917022575:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.42/0.99 % (1486622)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=2390468187:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.42/0.99 % (1486624)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=2136146010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.42/0.99 % (1486626)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=356626765:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.42/0.99 % (1486626)Also succeeded, but the first one will report.
% 2.42/0.99 % (1486628)Also succeeded, but the first one will report.
% 2.42/0.99 % (1486625)Also succeeded, but the first one will report.
% 2.42/0.99 % (1486627)Refutation found. Thanks to Tanya!
% 2.42/0.99 % SZS status Theorem for theBenchmark
% 2.42/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/0.99 % (1486627)------------------------------
% 2.42/0.99 % (1486627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.99 % (1486627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.99 % (1486627)CaDiCaL version: 2.1.3
% 2.42/0.99 % (1486627)Termination reason: Refutation
% 2.42/0.99 % (1486627)Time elapsed: 0.004 s
% 2.42/0.99 % (1486627)Peak memory usage: 89 MB
% 2.42/0.99 % (1486627)Instructions burned: 11 (million)
% 2.42/0.99 % (1486627)------------------------------
% 2.42/0.99 % (1486627)------------------------------
% 2.42/0.99 % (1486617)Success in time 0.293 s
% 2.42/0.99 % Vampire exiting
%------------------------------------------------------------------------------