%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV181+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 : n009.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 3.59s 1.29s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 14 unt; 2 def)
% Number of atoms : 218 ( 45 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 266 ( 88 ~; 82 |; 70 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 61 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X0,X1)
& gt(X1,X2) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
fof(f53,conjecture,
( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X2,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X3] :
( ( leq(n0,X3)
& leq(X3,n4) )
=> a_select2(mu_init,X3) = init ) )
& ( gt(loopcounter,n0)
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init ) )
& ( gt(loopcounter,n0)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigma_init,X5) = init ) ) )
=> ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select2(muold_init,X6) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).
fof(f54,negated_conjecture,
~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,X2,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X3] :
( ( leq(n0,X3)
& leq(X3,n4) )
=> a_select2(mu_init,X3) = init ) )
& ( gt(loopcounter,n0)
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,n4) )
=> a_select2(rho_init,X4) = init ) )
& ( gt(loopcounter,n0)
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select2(sigma_init,X5) = init ) ) )
=> ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select2(muold_init,X6) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f91,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(f94,plain,
( ? [X6] :
( init != a_select2(muold_init,X6)
& leq(n0,X6)
& leq(X6,n4) )
& leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [X0] :
( ! [X1] :
( a_select3(q_init,X0,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,n4) )
| ~ leq(n0,X0)
| ~ leq(X0,n135299) )
& ! [X2] :
( a_select3(center_init,X2,n0) = init
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
& ( ! [X3] :
( a_select2(mu_init,X3) = init
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X4] :
( a_select2(rho_init,X4) = init
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X5] :
( a_select2(sigma_init,X5) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n0) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X6] :
( init != a_select2(muold_init,X6)
& leq(n0,X6)
& leq(X6,n4) )
& leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [X0] :
( ! [X1] :
( a_select3(q_init,X0,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,n4) )
| ~ leq(n0,X0)
| ~ leq(X0,n135299) )
& ! [X2] :
( a_select3(center_init,X2,n0) = init
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
& ( ! [X3] :
( a_select2(mu_init,X3) = init
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X4] :
( a_select2(rho_init,X4) = init
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X5] :
( a_select2(sigma_init,X5) = init
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n0) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f97,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(flattening,[],[f96]) ).
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(f109,plain,
( ? [X0] :
( init != a_select2(muold_init,X0)
& leq(n0,X0)
& leq(X0,n4) )
& leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [X1] :
( ! [X2] :
( init = a_select3(q_init,X1,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
| ~ leq(n0,X1)
| ~ leq(X1,n135299) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
& ( ! [X4] :
( init = a_select2(mu_init,X4)
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X5] :
( init = a_select2(rho_init,X5)
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X6] :
( init = a_select2(sigma_init,X6)
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n0) ) ),
inference(rectify,[],[f95]) ).
fof(f110,plain,
( init != a_select2(muold_init,sK0)
& leq(n0,sK0)
& leq(sK0,n4)
& leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [X1] :
( ! [X2] :
( init = a_select3(q_init,X1,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) )
| ~ leq(n0,X1)
| ~ leq(X1,n135299) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
& ( ! [X4] :
( init = a_select2(mu_init,X4)
| ~ leq(n0,X4)
| ~ leq(X4,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X5] :
( init = a_select2(rho_init,X5)
| ~ leq(n0,X5)
| ~ leq(X5,n4) )
| ~ gt(loopcounter,n0) )
& ( ! [X6] :
( init = a_select2(sigma_init,X6)
| ~ leq(n0,X6)
| ~ leq(X6,n4) )
| ~ gt(loopcounter,n0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f109]) ).
fof(f116,plain,
gt(n1,loopcounter),
inference(cnf_transformation,[],[f110]) ).
fof(f117,plain,
leq(n1,loopcounter),
inference(cnf_transformation,[],[f110]) ).
fof(f122,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f126,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f130,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f153,plain,
gt(succ(n0),loopcounter),
inference(forward_demodulation,[],[f116,f130]) ).
fof(f154,plain,
leq(succ(n0),loopcounter),
inference(forward_demodulation,[],[f117,f130]) ).
fof(f244,plain,
! [X0] :
( ~ gt(X0,succ(n0))
| gt(X0,loopcounter) ),
inference(resolution,[],[f153,f123]) ).
fof(f250,plain,
( gt(loopcounter,succ(n0))
| loopcounter = succ(n0) ),
inference(resolution,[],[f154,f126]) ).
fof(f265,definition,
( spl2_19
<=> loopcounter = succ(n0) ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
fof(f267,plain,
( loopcounter = succ(n0)
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f269,definition,
( spl2_20
<=> gt(loopcounter,succ(n0)) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f271,plain,
( gt(loopcounter,succ(n0))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,plain,
( spl2_19
| spl2_20 ),
inference(avatar_split_clause,[],[f250,f269,f265]) ).
fof(f359,plain,
( gt(succ(n0),succ(n0))
| ~ spl2_19 ),
inference(superposition,[],[f153,f267]) ).
fof(f367,plain,
( $false
| ~ spl2_19 ),
inference(forward_subsumption_resolution,[],[f359,f122]) ).
fof(f368,plain,
~ spl2_19,
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f452,plain,
( gt(loopcounter,loopcounter)
| ~ spl2_20 ),
inference(resolution,[],[f244,f271]) ).
fof(f453,plain,
( $false
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f452,f122]) ).
fof(f454,plain,
~ spl2_20,
inference(avatar_contradiction_clause,[],[f453]) ).
cnf(s11,plain,
( spl2_19
| spl2_20 ),
inference(sat_conversion,[],[f272]) ).
cnf(s18,plain,
~ spl2_19,
inference(sat_conversion,[],[f368]) ).
cnf(s24,plain,
~ spl2_20,
inference(sat_conversion,[],[f454]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s11,s24,s18]) ).
fof(f459,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV181+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 10:08:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.59/1.29 % (2933992)Detected formulas, will run a generic FOF schedule.
% 3.59/1.29 % (2933999)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=3440904583:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.29 % (2934001)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1648714314:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.29 % (2933998)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=1266759336:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.29 % (2934002)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1699271172:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.29 % (2934000)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1872024062:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.29 % (2933997)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=1309152607:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.29 % (2934003)dis-21_1_sil=8000:lcm=predicate:random_seed=1455855377: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)
% 3.59/1.29 % (2934000)First to succeed.
% 3.59/1.29 % (2934000)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2933992"
% 3.59/1.29 % (2934001)Also succeeded, but the first one will report.
% 3.59/1.29 % (2934002)Also succeeded, but the first one will report.
% 3.59/1.29 % (2934003)Instruction limit reached!
% 3.59/1.29 % (2934003)------------------------------
% 3.59/1.29 % (2934003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (2934003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (2934003)CaDiCaL version: 2.1.3
% 3.59/1.29 % (2934003)Termination reason: Instruction limit
% 3.59/1.29 % (2934003)Termination phase: Saturation
% 3.59/1.29 % (2934003)Time elapsed: 0.075 s
% 3.59/1.29 % (2934003)Peak memory usage: 89 MB
% 3.59/1.29 % (2934003)Instructions burned: 129 (million)
% 3.59/1.29 % (2934011)lrs+10_1_sil=8000:sp=occurrence:random_seed=3902963008:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.59/1.29 % (2934011)Also succeeded, but the first one will report.
% 3.59/1.29 % (2934000)Refutation found. Thanks to Tanya!
% 3.59/1.29 % SZS status Theorem for theBenchmark
% 3.59/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.29 % (2934000)------------------------------
% 3.59/1.29 % (2934000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (2934000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (2934000)CaDiCaL version: 2.1.3
% 3.59/1.29 % (2934000)Termination reason: Refutation
% 3.59/1.29 % (2934000)Time elapsed: 0.008 s
% 3.59/1.29 % (2934000)Peak memory usage: 89 MB
% 3.59/1.29 % (2934000)Instructions burned: 10 (million)
% 3.59/1.29 % (2934000)------------------------------
% 3.59/1.29 % (2934000)------------------------------
% 3.59/1.29 % (2933992)Success in time 0.425 s
% 3.59/1.29 % Vampire exiting
%------------------------------------------------------------------------------