%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV161+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 01:08:16 PM UTC 2026
% Result : Theorem 2.68s 1.16s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 22 unt; 3 def)
% Number of atoms : 132 ( 36 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 126 ( 45 ~; 35 |; 36 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f53,conjecture,
( ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,pv10) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0011) ).
fof(f54,negated_conjecture,
~ ( ( sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,pv10) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f89,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
fof(f91,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(f94,plain,
( ? [X1] :
( n1 != sum(n0,n4,a_select3(q,X1,tptp_sum_index))
& leq(n0,X1)
& leq(X1,pv10) )
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X1] :
( n1 != sum(n0,n4,a_select3(q,X1,tptp_sum_index))
& leq(n0,X1)
& leq(X1,pv10) )
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f99,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
( ? [X0] :
( n1 != sum(n0,n4,a_select3(q,X0,tptp_sum_index))
& leq(n0,X0)
& leq(X0,pv10) )
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(rectify,[],[f95]) ).
fof(f108,plain,
( n1 != sum(n0,n4,a_select3(q,sK0,tptp_sum_index))
& leq(n0,sK0)
& leq(sK0,pv10)
& sum(n0,n4,a_select3(q,pv10,tptp_sum_index)) = n1
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f110,plain,
! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f113,plain,
n1 = sum(n0,n4,a_select3(q,pv10,tptp_sum_index)),
inference(cnf_transformation,[],[f108]) ).
fof(f114,plain,
leq(sK0,pv10),
inference(cnf_transformation,[],[f108]) ).
fof(f115,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f116,plain,
n1 != sum(n0,n4,a_select3(q,sK0,tptp_sum_index)),
inference(cnf_transformation,[],[f108]) ).
fof(f120,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f122,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f127,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f130,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f89]) ).
fof(f143,definition,
~ sP1(n1),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f144,plain,
sP1(sum(n0,n4,a_select3(q,sK0,tptp_sum_index))),
inference(inequality_splitting,[],[f116,f143]) ).
fof(f145,plain,
~ sP1(succ(n0)),
inference(forward_demodulation,[],[f143,f127]) ).
fof(f146,plain,
! [X1] :
( n1 = sum(n0,succ(succ(succ(succ(n0)))),a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ),
inference(forward_demodulation,[],[f110,f130]) ).
fof(f147,plain,
n1 = sum(n0,succ(succ(succ(succ(n0)))),a_select3(q,pv10,tptp_sum_index)),
inference(forward_demodulation,[],[f113,f130]) ).
fof(f148,plain,
sP1(sum(n0,succ(succ(succ(succ(n0)))),a_select3(q,sK0,tptp_sum_index))),
inference(forward_demodulation,[],[f144,f130]) ).
fof(f149,plain,
! [X1] :
( succ(n0) = sum(n0,succ(succ(succ(succ(n0)))),a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ),
inference(forward_demodulation,[],[f146,f127]) ).
fof(f150,plain,
succ(n0) = sum(n0,succ(succ(succ(succ(n0)))),a_select3(q,pv10,tptp_sum_index)),
inference(forward_demodulation,[],[f147,f127]) ).
fof(f213,plain,
( gt(pv10,sK0)
| pv10 = sK0 ),
inference(resolution,[],[f114,f122]) ).
fof(f227,definition,
( spl2_14
<=> pv10 = sK0 ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f229,plain,
( pv10 = sK0
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f231,definition,
( spl2_15
<=> gt(pv10,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f233,plain,
( gt(pv10,sK0)
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f234,plain,
( spl2_14
| spl2_15 ),
inference(avatar_split_clause,[],[f213,f231,f227]) ).
fof(f262,plain,
( sP1(succ(n0))
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10)) ),
inference(superposition,[],[f148,f149]) ).
fof(f263,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10)) ),
inference(forward_subsumption_resolution,[],[f262,f145]) ).
fof(f264,plain,
~ leq(sK0,pred(pv10)),
inference(forward_subsumption_resolution,[],[f263,f115]) ).
fof(f267,plain,
( sP1(sum(n0,succ(succ(succ(succ(n0)))),a_select3(q,pv10,tptp_sum_index)))
| ~ spl2_14 ),
inference(superposition,[],[f148,f229]) ).
fof(f270,plain,
( sP1(succ(n0))
| ~ spl2_14 ),
inference(forward_demodulation,[],[f267,f150]) ).
fof(f271,plain,
( $false
| ~ spl2_14 ),
inference(forward_subsumption_resolution,[],[f270,f145]) ).
fof(f272,plain,
~ spl2_14,
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f320,plain,
~ gt(pv10,sK0),
inference(resolution,[],[f264,f120]) ).
fof(f322,plain,
( $false
| ~ spl2_15 ),
inference(forward_subsumption_resolution,[],[f320,f233]) ).
fof(f323,plain,
~ spl2_15,
inference(avatar_contradiction_clause,[],[f322]) ).
cnf(s7,plain,
( spl2_14
| spl2_15 ),
inference(sat_conversion,[],[f234]) ).
cnf(s8,plain,
~ spl2_14,
inference(sat_conversion,[],[f272]) ).
cnf(s13,plain,
~ spl2_15,
inference(sat_conversion,[],[f323]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s7,s13,s8]) ).
fof(f324,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV161+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n014.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Mon Sep 28 10:03:01 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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 % (1680402)Detected formulas, will run a generic FOF schedule.
% 2.68/1.16 % (1680410)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1010988430:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.16 % (1680410)First to succeed.
% 2.68/1.16 % (1680410)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1680402"
% 2.68/1.16 % (1680411)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3940584620:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.16 % (1680412)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4222167724:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.16 % (1680407)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=1934488629:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.16 % (1680413)dis-21_1_sil=8000:lcm=predicate:random_seed=2889664667: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 % (1680408)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=3588005790:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.16 % (1680409)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=2751096283:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.16 % (1680411)Also succeeded, but the first one will report.
% 2.68/1.16 % (1680412)Also succeeded, but the first one will report.
% 2.68/1.16 % (1680413)Instruction limit reached!
% 2.68/1.16 % (1680413)------------------------------
% 2.68/1.16 % (1680413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (1680413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (1680413)CaDiCaL version: 2.1.3
% 2.68/1.16 % (1680413)Termination reason: Instruction limit
% 2.68/1.16 % (1680413)Termination phase: Saturation
% 2.68/1.16 % (1680413)Time elapsed: 0.067 s
% 2.68/1.16 % (1680413)Peak memory usage: 89 MB
% 2.68/1.16 % (1680413)Instructions burned: 129 (million)
% 2.68/1.16 % (1680410)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 % (1680410)------------------------------
% 2.68/1.16 % (1680410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (1680410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (1680410)CaDiCaL version: 2.1.3
% 2.68/1.16 % (1680410)Termination reason: Refutation
% 2.68/1.16 % (1680410)Time elapsed: 0.003 s
% 2.68/1.16 % (1680410)Peak memory usage: 90 MB
% 2.68/1.16 % (1680410)Instructions burned: 6 (million)
% 2.68/1.16 % (1680410)------------------------------
% 2.68/1.16 % (1680410)------------------------------
% 2.68/1.16 % (1680402)Success in time 0.289 s
% 2.68/1.16 % Vampire exiting
%------------------------------------------------------------------------------