%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV166+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 2.68s 1.16s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 14 unt; 5 def)
% Number of atoms : 279 ( 63 equ)
% Maximal formula atoms : 36 ( 7 avg)
% Number of connectives : 363 ( 123 ~; 109 |; 98 &)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 62 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( n0 != pv90
& leq(n0,pv40)
& leq(pv40,n4)
& 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/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0006) ).
fof(f54,negated_conjecture,
~ ( ( n0 != pv90
& leq(n0,pv40)
& leq(pv40,n4)
& 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(f100,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(n0,X9)
& leq(X9,n4) )
& n0 != pv90
& leq(n0,pv40)
& leq(pv40,n4)
& 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(f101,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(n0,X9)
& leq(X9,n4) )
& n0 != pv90
& leq(n0,pv40)
& leq(pv40,n4)
& 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,[],[f100]) ).
fof(f153,plain,
( ? [X0] :
( init != a_select2(rhoold_init,X0)
& leq(n0,X0)
& leq(X0,n4) )
& n0 != pv90
& leq(n0,pv40)
& leq(pv40,n4)
& 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,[],[f101]) ).
fof(f154,plain,
( init != a_select2(rhoold_init,sK3)
& leq(n0,sK3)
& leq(sK3,n4)
& n0 != pv90
& leq(n0,pv40)
& leq(pv40,n4)
& 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,[sK3]),skolemize(X0,sK3)],[f153]) ).
fof(f182,plain,
! [X8] :
( init = a_select2(rhoold_init,X8)
| ~ leq(n0,X8)
| ~ leq(X8,n4)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f154]) ).
fof(f193,plain,
leq(sK3,n4),
inference(cnf_transformation,[],[f154]) ).
fof(f194,plain,
leq(n0,sK3),
inference(cnf_transformation,[],[f154]) ).
fof(f195,plain,
init != a_select2(rhoold_init,sK3),
inference(cnf_transformation,[],[f154]) ).
fof(f358,definition,
! [X0,X1] :
( sQ25_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ25_eqProxy])],[equality_proxy_definition]) ).
fof(f359,plain,
~ sQ25_eqProxy(init,a_select2(rhoold_init,sK3)),
inference(equality_proxy_replacement,[],[f195,f358]) ).
fof(f367,plain,
! [X8] :
( sQ25_eqProxy(init,a_select2(rhoold_init,X8))
| ~ leq(n0,X8)
| ~ leq(X8,n4)
| ~ gt(loopcounter,n1) ),
inference(equality_proxy_replacement,[],[f182,f358]) ).
fof(f446,definition,
( spl26_1
<=> gt(loopcounter,n1) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f447,plain,
( ~ gt(loopcounter,n1)
| spl26_1 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f453,definition,
( spl26_3
<=> ! [X8] :
( sQ25_eqProxy(init,a_select2(rhoold_init,X8))
| ~ leq(X8,n4)
| ~ leq(n0,X8) ) ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f454,plain,
( ! [X8] :
( sQ25_eqProxy(init,a_select2(rhoold_init,X8))
| ~ leq(X8,n4)
| ~ leq(n0,X8) )
| ~ spl26_3 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f455,plain,
( ~ spl26_1
| spl26_3 ),
inference(avatar_split_clause,[],[f367,f453,f446]) ).
fof(f460,plain,
( $false
| spl26_1 ),
inference(resolution,[],[f447,f189]) ).
fof(f461,plain,
spl26_1,
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f462,plain,
( ~ leq(sK3,n4)
| ~ leq(n0,sK3)
| ~ spl26_3 ),
inference(resolution,[],[f359,f454]) ).
fof(f464,definition,
( spl26_5
<=> leq(n0,sK3) ),
introduced(definition,[new_symbols(definition,[spl26_5])],[avatar_definition]) ).
fof(f465,plain,
( ~ leq(n0,sK3)
| spl26_5 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f467,definition,
( spl26_6
<=> leq(sK3,n4) ),
introduced(definition,[new_symbols(definition,[spl26_6])],[avatar_definition]) ).
fof(f468,plain,
( ~ leq(sK3,n4)
| spl26_6 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f469,plain,
( ~ spl26_5
| ~ spl26_6
| ~ spl26_3 ),
inference(avatar_split_clause,[],[f462,f453,f467,f464]) ).
fof(f470,plain,
( $false
| spl26_5 ),
inference(resolution,[],[f465,f194]) ).
fof(f471,plain,
spl26_5,
inference(avatar_contradiction_clause,[],[f470]) ).
fof(f472,plain,
( $false
| spl26_6 ),
inference(resolution,[],[f468,f193]) ).
fof(f473,plain,
spl26_6,
inference(avatar_contradiction_clause,[],[f472]) ).
cnf(s2,plain,
( ~ spl26_1
| spl26_3 ),
inference(sat_conversion,[],[f455]) ).
cnf(s4,plain,
spl26_1,
inference(sat_conversion,[],[f461]) ).
cnf(s5,plain,
( ~ spl26_3
| ~ spl26_5
| ~ spl26_6 ),
inference(sat_conversion,[],[f469]) ).
cnf(s6,plain,
spl26_5,
inference(sat_conversion,[],[f471]) ).
cnf(s7,plain,
spl26_6,
inference(sat_conversion,[],[f473]) ).
cnf(s8,plain,
~ spl26_3,
inference(rat,[],[s5,s7,s6]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s8,s4]) ).
fof(f474,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV166+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n014.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 10:03:46 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.68/1.16 % (1681667)Detected formulas, will run a generic FOF schedule.
% 2.68/1.16 % (1681678)dis-21_1_sil=8000:lcm=predicate:random_seed=4281601207: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)
% 2.68/1.16 % (1681678)First to succeed.
% 2.68/1.16 % (1681678)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1681667"
% 2.68/1.16 % (1681673)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=976944315:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.16 % (1681672)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=760802946:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.16 % (1681674)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=4018680199:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.16 % (1681676)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=142790323:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.16 % (1681675)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1875420256:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.16 % (1681676)Also succeeded, but the first one will report.
% 2.68/1.16 % (1681677)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2703298066:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.16 % (1681677)Also succeeded, but the first one will report.
% 2.68/1.16 % (1681675)Also succeeded, but the first one will report.
% 2.68/1.16 % (1681678)Refutation found. Thanks to Tanya!
% 2.68/1.16 % SZS status Theorem for theBenchmark
% 2.68/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.16 % (1681678)------------------------------
% 2.68/1.16 % (1681678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (1681678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (1681678)CaDiCaL version: 2.1.3
% 2.68/1.16 % (1681678)Termination reason: Refutation
% 2.68/1.16 % (1681678)Time elapsed: 0.004 s
% 2.68/1.16 % (1681678)Peak memory usage: 89 MB
% 2.68/1.16 % (1681678)Instructions burned: 11 (million)
% 2.68/1.16 % (1681678)------------------------------
% 2.68/1.16 % (1681678)------------------------------
% 2.68/1.16 % (1681667)Success in time 0.288 s
% 2.68/1.16 % Vampire exiting
%------------------------------------------------------------------------------