%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV188+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 : n010.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 01:08:20 PM UTC 2026
% Result : Theorem 3.46s 1.14s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 216 ( 53 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 279 ( 100 ~; 90 |; 61 &)
% ( 1 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 79 ( 76 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f53,conjecture,
( ( ! [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,n4) )
=> a_select3(center_init,X3,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(muold_init,X4) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(rhoold_init,X5) = init ) )
& ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select2(sigmaold_init,X6) = init ) ) )
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,tptp_minus_1) )
=> a_select2(mu_init,X7) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0116) ).
fof(f54,negated_conjecture,
~ ( ( ! [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,n4) )
=> a_select3(center_init,X3,n0) = init )
& ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(muold_init,X4) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(rhoold_init,X5) = init ) )
& ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select2(sigmaold_init,X6) = init ) ) )
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,tptp_minus_1) )
=> a_select2(mu_init,X7) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f85,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f94,plain,
( ? [X7] :
( init != a_select2(mu_init,X7)
& leq(n0,X7)
& leq(X7,tptp_minus_1) )
& ! [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_select3(center_init,X3,n0) = init
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
& ( ! [X4] :
( a_select2(muold_init,X4) = init
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X5] :
( a_select2(rhoold_init,X5) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X6] :
( a_select2(sigmaold_init,X6) = init
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X7] :
( init != a_select2(mu_init,X7)
& leq(n0,X7)
& leq(X7,tptp_minus_1) )
& ! [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_select3(center_init,X3,n0) = init
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
& ( ! [X4] :
( a_select2(muold_init,X4) = init
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X5] :
( a_select2(rhoold_init,X5) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X6] :
( a_select2(sigmaold_init,X6) = init
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f99,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f103,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f104,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f103]) ).
fof(f117,plain,
( ? [X0] :
( init != a_select2(mu_init,X0)
& leq(n0,X0)
& leq(X0,tptp_minus_1) )
& ! [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_select3(center_init,X4,n0)
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
& ( ! [X5] :
( init = a_select2(muold_init,X5)
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X6] :
( init = a_select2(rhoold_init,X6)
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X7] :
( init = a_select2(sigmaold_init,X7)
| ~ leq(n0,X7)
| ~ leq(X7,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
( init != a_select2(mu_init,sK0)
& leq(n0,sK0)
& leq(sK0,tptp_minus_1)
& ! [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_select3(center_init,X4,n0)
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
& ( ! [X5] :
( init = a_select2(muold_init,X5)
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X6] :
( init = a_select2(rhoold_init,X6)
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n1) )
& ( ! [X7] :
( init = a_select2(sigmaold_init,X7)
| ~ leq(n0,X7)
| ~ leq(X7,n4) )
| ~ gt(loopcounter,n1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f120,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f127,plain,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f118]) ).
fof(f128,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f130,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f133,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f135,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f136,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f141,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f144,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f180,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f203,plain,
! [X0] : ~ leq(succ(X0),X0),
inference(resolution,[],[f180,f130]) ).
fof(f220,plain,
~ leq(n0,tptp_minus_1),
inference(superposition,[],[f203,f144]) ).
fof(f293,plain,
( ~ leq(sK0,n0)
| n0 = sK0 ),
inference(resolution,[],[f133,f128]) ).
fof(f322,plain,
! [X0] :
( ~ leq(sK0,X0)
| ~ leq(X0,n0)
| n0 = sK0 ),
inference(resolution,[],[f136,f293]) ).
fof(f323,plain,
( ~ leq(tptp_minus_1,n0)
| n0 = sK0 ),
inference(resolution,[],[f322,f127]) ).
fof(f329,plain,
( n0 = sK0
| ~ gt(n0,tptp_minus_1) ),
inference(resolution,[],[f323,f135]) ).
fof(f330,plain,
n0 = sK0,
inference(forward_subsumption_resolution,[],[f329,f141]) ).
fof(f351,plain,
~ leq(sK0,tptp_minus_1),
inference(superposition,[],[f220,f330]) ).
fof(f353,plain,
$false,
inference(forward_subsumption_resolution,[],[f351,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV188+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n010.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 10:08:32 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 3.46/1.14 % (1823504)Detected formulas, will run a generic FOF schedule.
% 3.46/1.14 % (1823510)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=2138398454:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.14 % (1823513)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3602667071:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.14 % (1823515)dis-21_1_sil=8000:lcm=predicate:random_seed=2292307583: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)
% 3.46/1.14 % (1823514)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1589100610:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.14 % (1823512)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3029015390:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.14 % (1823509)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=1127001316:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.14 % (1823511)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=770982473:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.14 % (1823513)First to succeed.
% 3.46/1.14 % (1823513)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1823504"
% 3.46/1.14 % (1823512)Also succeeded, but the first one will report.
% 3.46/1.14 % (1823515)Instruction limit reached!
% 3.46/1.14 % (1823515)------------------------------
% 3.46/1.14 % (1823515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.14 % (1823515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.14 % (1823515)CaDiCaL version: 2.1.3
% 3.46/1.14 % (1823515)Termination reason: Instruction limit
% 3.46/1.14 % (1823515)Termination phase: Saturation
% 3.46/1.14 % (1823515)Time elapsed: 0.077 s
% 3.46/1.14 % (1823515)Peak memory usage: 89 MB
% 3.46/1.14 % (1823515)Instructions burned: 129 (million)
% 3.46/1.14 % (1823514)Instruction limit reached!
% 3.46/1.14 % (1823514)------------------------------
% 3.46/1.14 % (1823514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.14 % (1823514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.14 % (1823514)CaDiCaL version: 2.1.3
% 3.46/1.14 % (1823514)Termination reason: Instruction limit
% 3.46/1.14 % (1823514)Termination phase: Saturation
% 3.46/1.14 % (1823514)Time elapsed: 0.093 s
% 3.46/1.14 % (1823514)Peak memory usage: 90 MB
% 3.46/1.14 % (1823514)Instructions burned: 140 (million)
% 3.46/1.14 % (1823523)lrs+10_1_sil=8000:sp=occurrence:random_seed=3161214032:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.46/1.14 % (1823524)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3409078522:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.46/1.14 % (1823524)Also succeeded, but the first one will report.
% 3.46/1.14 % (1823523)Also succeeded, but the first one will report.
% 3.46/1.14 % (1823513)Refutation found. Thanks to Tanya!
% 3.46/1.14 % SZS status Theorem for theBenchmark
% 3.46/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.14 % (1823513)------------------------------
% 3.46/1.14 % (1823513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.14 % (1823513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.14 % (1823513)CaDiCaL version: 2.1.3
% 3.46/1.14 % (1823513)Termination reason: Refutation
% 3.46/1.14 % (1823513)Time elapsed: 0.007 s
% 3.46/1.14 % (1823513)Peak memory usage: 88 MB
% 3.46/1.14 % (1823513)Instructions burned: 9 (million)
% 3.46/1.14 % (1823513)------------------------------
% 3.46/1.14 % (1823513)------------------------------
% 3.46/1.14 % (1823504)Success in time 0.412 s
% 3.46/1.14 % Vampire exiting
%------------------------------------------------------------------------------