%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV178+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 : n001.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 2.68s 1.19s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 228 ( 58 equ)
% Maximal formula atoms : 35 ( 14 avg)
% Number of connectives : 313 ( 101 ~; 92 |; 92 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 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 : 61 ( 58 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( 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(sigmaold_init,X9) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0066) ).
fof(f54,negated_conjecture,
~ ( ( 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(sigmaold_init,X9) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,plain,
( ? [X9] :
( init != a_select2(sigmaold_init,X9)
& leq(n0,X9)
& leq(X9,n4) )
& 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(f95,plain,
( ? [X9] :
( init != a_select2(sigmaold_init,X9)
& leq(n0,X9)
& leq(X9,n4) )
& 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,[],[f94]) ).
fof(f117,plain,
( ? [X0] :
( init != a_select2(sigmaold_init,X0)
& leq(n0,X0)
& leq(X0,n4) )
& 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,[],[f95]) ).
fof(f118,plain,
( init != a_select2(sigmaold_init,sK0)
& leq(n0,sK0)
& leq(sK0,n4)
& 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,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f122,plain,
! [X9] :
( init = a_select2(sigmaold_init,X9)
| ~ leq(n0,X9)
| ~ leq(X9,n4)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f130,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f118]) ).
fof(f133,plain,
leq(sK0,n4),
inference(cnf_transformation,[],[f118]) ).
fof(f134,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f135,plain,
init != a_select2(sigmaold_init,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f194,plain,
! [X9] :
( init = a_select2(sigmaold_init,X9)
| ~ leq(n0,X9)
| ~ leq(X9,n4) ),
inference(forward_subsumption_resolution,[],[f122,f130]) ).
fof(f195,plain,
( init != init
| ~ leq(n0,sK0)
| ~ leq(sK0,n4) ),
inference(superposition,[],[f135,f194]) ).
fof(f196,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,n4) ),
inference(trivial_inequality_removal,[],[f195]) ).
fof(f197,plain,
~ leq(sK0,n4),
inference(forward_subsumption_resolution,[],[f196,f134]) ).
fof(f198,plain,
$false,
inference(forward_subsumption_resolution,[],[f197,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV178+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n001.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 10:11:48 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running first-order theorem proving
% 0.09/0.26 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
% 2.68/1.19 % (262214)Detected formulas, will run a generic FOF schedule.
% 2.68/1.19 % (262223)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1634093745:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.19 % (262223)First to succeed.
% 2.68/1.19 % (262223)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-262214"
% 2.68/1.19 % (262224)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1189109709:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.19 % (262219)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=2577784302:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.19 % (262225)dis-21_1_sil=8000:lcm=predicate:random_seed=2842439392: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)
% 2.68/1.19 % (262222)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3316303501:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.19 % (262220)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=2948708069:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.19 % (262221)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=3050015881:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.19 % (262225)Also succeeded, but the first one will report.
% 2.68/1.19 % (262224)Also succeeded, but the first one will report.
% 2.68/1.19 % (262222)Also succeeded, but the first one will report.
% 2.68/1.19 % (262223)Refutation found. Thanks to Tanya!
% 2.68/1.19 % SZS status Theorem for theBenchmark
% 2.68/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.19 % (262223)------------------------------
% 2.68/1.19 % (262223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.19 % (262223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.19 % (262223)CaDiCaL version: 2.1.3
% 2.68/1.19 % (262223)Termination reason: Refutation
% 2.68/1.19 % (262223)Time elapsed: 0.002 s
% 2.68/1.19 % (262223)Peak memory usage: 88 MB
% 2.68/1.19 % (262223)Instructions burned: 4 (million)
% 2.68/1.19 % (262223)------------------------------
% 2.68/1.19 % (262223)------------------------------
% 2.68/1.19 % (262214)Success in time 0.29 s
% 2.68/1.19 % Vampire exiting
%------------------------------------------------------------------------------