%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV167+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 3.72s 1.29s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 255 ( 77 equ)
% Maximal formula atoms : 36 ( 9 avg)
% Number of connectives : 336 ( 107 ~; 99 |; 100 &)
% ( 1 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 74 ( 71 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
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/sandbox2/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(f94,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(f95,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,[],[f94]) ).
fof(f100,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f101,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f100]) ).
fof(f117,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,[],[f95]) ).
fof(f118,plain,
( init != a_select2(mu_init,sK0)
& leq(n0,sK0)
& leq(sK0,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,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f127,plain,
! [X4] :
( init = a_select2(mu_init,X4)
| ~ leq(n0,X4)
| ~ leq(X4,pred(pv40)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f133,plain,
a_select2(mu_init,pv40) = init,
inference(cnf_transformation,[],[f118]) ).
fof(f134,plain,
leq(sK0,pv40),
inference(cnf_transformation,[],[f118]) ).
fof(f135,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f136,plain,
init != a_select2(mu_init,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f140,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f145,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f195,plain,
( init != init
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv40)) ),
inference(superposition,[],[f136,f127]) ).
fof(f196,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv40)) ),
inference(trivial_inequality_removal,[],[f195]) ).
fof(f197,plain,
~ leq(sK0,pred(pv40)),
inference(forward_subsumption_resolution,[],[f196,f135]) ).
fof(f227,plain,
~ gt(pv40,sK0),
inference(resolution,[],[f140,f197]) ).
fof(f379,plain,
( ~ leq(sK0,pv40)
| pv40 = sK0 ),
inference(resolution,[],[f145,f227]) ).
fof(f381,plain,
pv40 = sK0,
inference(forward_subsumption_resolution,[],[f379,f134]) ).
fof(f385,plain,
init = a_select2(mu_init,sK0),
inference(superposition,[],[f133,f381]) ).
fof(f393,plain,
$false,
inference(forward_subsumption_resolution,[],[f385,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV167+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % 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 10:03:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 3.72/1.29 % (3900663)Detected formulas, will run a generic FOF schedule.
% 3.72/1.29 % (3900674)dis-21_1_sil=8000:lcm=predicate:random_seed=762908027: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)
% 3.72/1.29 % (3900672)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1048234470:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.72/1.29 % (3900668)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=3071198799:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.72/1.29 % (3900673)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1586386038:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.72/1.29 % (3900670)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=542881241:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.72/1.29 % (3900671)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1681684612:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.72/1.29 % (3900669)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=248529081:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.72/1.29 % (3900674)Instruction limit reached!
% 3.72/1.29 % (3900674)------------------------------
% 3.72/1.29 % (3900674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.29 % (3900674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.29 % (3900674)CaDiCaL version: 2.1.3
% 3.72/1.29 % (3900674)Termination reason: Instruction limit
% 3.72/1.29 % (3900674)Termination phase: Saturation
% 3.72/1.29 % (3900674)Time elapsed: 0.043 s
% 3.72/1.29 % (3900674)Peak memory usage: 89 MB
% 3.72/1.29 % (3900674)Instructions burned: 132 (million)
% 3.72/1.29 % (3900672)First to succeed.
% 3.72/1.29 % (3900672)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3900663"
% 3.72/1.29 % (3900671)Instruction limit reached!
% 3.72/1.29 % (3900671)------------------------------
% 3.72/1.29 % (3900671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.29 % (3900671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.29 % (3900671)CaDiCaL version: 2.1.3
% 3.72/1.29 % (3900671)Termination reason: Instruction limit
% 3.72/1.29 % (3900671)Termination phase: Saturation
% 3.72/1.29 % (3900671)Time elapsed: 0.069 s
% 3.72/1.29 % (3900671)Peak memory usage: 89 MB
% 3.72/1.29 % (3900671)Instructions burned: 109 (million)
% 3.72/1.29 % (3900673)Instruction limit reached!
% 3.72/1.29 % (3900673)------------------------------
% 3.72/1.29 % (3900673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.29 % (3900673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.29 % (3900673)CaDiCaL version: 2.1.3
% 3.72/1.29 % (3900673)Termination reason: Instruction limit
% 3.72/1.29 % (3900673)Termination phase: Saturation
% 3.72/1.29 % (3900673)Time elapsed: 0.090 s
% 3.72/1.29 % (3900673)Peak memory usage: 90 MB
% 3.72/1.29 % (3900673)Instructions burned: 139 (million)
% 3.72/1.29 % (3900682)lrs+10_1_sil=8000:sp=occurrence:random_seed=1825850762:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.72/1.29 % (3900682)Also succeeded, but the first one will report.
% 3.72/1.29 % (3900683)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1308992577:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.72/1.29 % (3900683)Also succeeded, but the first one will report.
% 3.72/1.29 % (3900684)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1124675409:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.72/1.29 % (3900672)Refutation found. Thanks to Tanya!
% 3.72/1.29 % SZS status Theorem for theBenchmark
% 3.72/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.29 % (3900672)------------------------------
% 3.72/1.29 % (3900672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.29 % (3900672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.29 % (3900672)CaDiCaL version: 2.1.3
% 3.72/1.29 % (3900672)Termination reason: Refutation
% 3.72/1.29 % (3900672)Time elapsed: 0.008 s
% 3.72/1.29 % (3900672)Peak memory usage: 88 MB
% 3.72/1.29 % (3900672)Instructions burned: 11 (million)
% 3.72/1.29 % (3900672)------------------------------
% 3.72/1.29 % (3900672)------------------------------
% 3.72/1.29 % (3900663)Success in time 0.444 s
% 3.72/1.29 % Vampire exiting
%------------------------------------------------------------------------------