%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV167+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 01:20:22 PM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 2 def)
% Number of atoms : 284 ( 83 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 358 ( 117 ~; 109 |; 100 &)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-3 aty)
% Number of variables : 79 ( 0 sgn 76 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(f53,conjecture,
( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [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,pv40) )
=> a_select2(mu_init,X9) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0011) ).
fof(f54,negated_conjecture,
~ ( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [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,pv40) )
=> a_select2(mu_init,X9) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f108,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f108]) ).
fof(f143,plain,
( ? [X9] :
( init != a_select2(mu_init,X9)
& leq(n0,X9)
& leq(X9,pv40) )
& a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [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(mu_init,X9)
& leq(n0,X9)
& leq(X9,pv40) )
& a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [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(f164,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f197,plain,
( ? [X0] :
( init != a_select2(mu_init,X0)
& leq(n0,X0)
& leq(X0,pv40) )
& a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [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(mu_init,sK31)
& leq(n0,sK31)
& leq(sK31,pv40)
& a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [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(f205,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f207,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f289,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f314,plain,
! [X4] :
( init = a_select2(mu_init,X4)
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv40)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f320,plain,
a_select2(mu_init,pv40) = init,
inference(cnf_transformation,[],[f198]) ).
fof(f321,plain,
leq(sK31,pv40),
inference(cnf_transformation,[],[f198]) ).
fof(f322,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f323,plain,
init != a_select2(mu_init,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f363,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f207,f289]) ).
fof(f384,plain,
! [X4] :
( ~ leq(n0,X4)
| init = a_select2(mu_init,X4)
| ~ leq(X4,minus(pv40,n1)) ),
inference(definition_unfolding,[],[f314,f289]) ).
fof(f426,plain,
a_select2(mu_init,pv40) != a_select2(mu_init,sK31),
inference(forward_demodulation,[],[f323,f320]) ).
fof(f545,plain,
( init = a_select2(mu_init,sK31)
| ~ leq(sK31,minus(pv40,n1)) ),
inference(resolution,[],[f384,f322]) ).
fof(f546,plain,
( a_select2(mu_init,pv40) = a_select2(mu_init,sK31)
| ~ leq(sK31,minus(pv40,n1)) ),
inference(forward_demodulation,[],[f545,f320]) ).
fof(f547,plain,
~ leq(sK31,minus(pv40,n1)),
inference(forward_subsumption_resolution,[],[f546,f426]) ).
fof(f1462,plain,
( gt(pv40,sK31)
| pv40 = sK31 ),
inference(resolution,[],[f205,f321]) ).
fof(f1465,definition,
( spl32_50
<=> pv40 = sK31 ),
introduced(definition,[new_symbols(definition,[spl32_50])],[avatar_definition]) ).
fof(f1467,plain,
( pv40 = sK31
| ~ spl32_50 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f1469,definition,
( spl32_51
<=> gt(pv40,sK31) ),
introduced(definition,[new_symbols(definition,[spl32_51])],[avatar_definition]) ).
fof(f1471,plain,
( gt(pv40,sK31)
| ~ spl32_51 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f1472,plain,
( spl32_50
| spl32_51 ),
inference(avatar_split_clause,[],[f1462,f1469,f1465]) ).
fof(f1583,plain,
( a_select2(mu_init,pv40) != a_select2(mu_init,pv40)
| ~ spl32_50 ),
inference(superposition,[],[f426,f1467]) ).
fof(f1599,plain,
( $false
| ~ spl32_50 ),
inference(trivial_inequality_removal,[],[f1583]) ).
fof(f1600,plain,
~ spl32_50,
inference(avatar_contradiction_clause,[],[f1599]) ).
fof(f1890,plain,
( leq(sK31,minus(pv40,n1))
| ~ spl32_51 ),
inference(resolution,[],[f1471,f363]) ).
fof(f1892,plain,
( $false
| ~ spl32_51 ),
inference(forward_subsumption_resolution,[],[f1890,f547]) ).
fof(f1893,plain,
~ spl32_51,
inference(avatar_contradiction_clause,[],[f1892]) ).
cnf(s36,plain,
( spl32_50
| spl32_51 ),
inference(sat_conversion,[],[f1472]) ).
cnf(s46,plain,
~ spl32_50,
inference(sat_conversion,[],[f1600]) ).
cnf(s56,plain,
~ spl32_51,
inference(sat_conversion,[],[f1893]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s36,s56,s46]) ).
fof(f1894,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV167+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 10:05:55 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.30 % (3275815)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (3275821)% WARNING: option uhcvi not known.
% 0.19/0.30 % (3275821)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1416042546:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (3275820)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1185655451_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (3275822)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2301169791:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (3275823)dis+10_1_sil=32000:sp=arity:random_seed=4161318220:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (3275824)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4166601756:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (3275826)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3812097446:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (3275825)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=929433491:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (3275825) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3275815-3275825"...
% 0.19/0.30 % (3275825)...printing done.
% 0.19/0.30 % (3275825)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (3275825)------------------------------
% 0.19/0.30 % (3275825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3275825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3275825)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3275825)Termination reason: Refutation
% 0.19/0.30 % (3275825)Time elapsed: 0.035 s
% 0.19/0.30 % (3275825)Peak memory usage: 13 MB
% 0.19/0.30 % (3275825)Instructions burned: 61 (million)
% 0.19/0.30 % (3275815)Success in time 0.073 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------