%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV163+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 01:08:17 PM UTC 2026
% Result : Theorem 2.54s 0.83s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 19 unt; 3 def)
% Number of atoms : 133 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 124 ( 45 ~; 35 |; 31 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
=> leq(X0,succ(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
fof(f42,axiom,
! [X0,X1] :
( leq(succ(X0),succ(X1))
<=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
fof(f53,conjecture,
( ( 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,tptp_minus_1) )
=> a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0013) ).
fof(f54,negated_conjecture,
~ ( ( 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,tptp_minus_1) )
=> a_select3(q,pv10,X1) = divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f85,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f110,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f143,plain,
( ? [X1] :
( a_select3(q,pv10,X1) != divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(n0,X1)
& leq(X1,tptp_minus_1) )
& 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(f144,plain,
( ? [X1] :
( a_select3(q,pv10,X1) != divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(n0,X1)
& leq(X1,tptp_minus_1) )
& 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,[],[f143]) ).
fof(f149,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f150,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f149]) ).
fof(f165,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f194,plain,
! [X0,X1] :
( ( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) )
& ( leq(X0,X1)
| ~ leq(succ(X0),succ(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f197,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(n0,X0)
& leq(X0,tptp_minus_1) )
& 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,[],[f144]) ).
fof(f198,plain,
( a_select3(q,pv10,sK31) != divide(sqrt(times(minus(a_select3(center,sK31,n0),a_select2(x,pv10)),minus(a_select3(center,sK31,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(n0,sK31)
& leq(sK31,tptp_minus_1)
& 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,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f201,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f209,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f210,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f278,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f290,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f293,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| leq(succ(X0),succ(X1)) ),
inference(cnf_transformation,[],[f194]) ).
fof(f312,plain,
leq(sK31,tptp_minus_1),
inference(cnf_transformation,[],[f198]) ).
fof(f313,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f345,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| n0 = X0 ),
inference(cnf_transformation,[],[f150]) ).
fof(f367,plain,
tptp_minus_1 = pred(n0),
inference(superposition,[],[f290,f278]) ).
fof(f406,plain,
! [X0] :
( gt(n0,X0)
| ~ leq(X0,tptp_minus_1) ),
inference(superposition,[],[f210,f278]) ).
fof(f552,plain,
leq(succ(sK31),succ(tptp_minus_1)),
inference(resolution,[],[f293,f312]) ).
fof(f553,plain,
leq(succ(sK31),n0),
inference(forward_demodulation,[],[f552,f278]) ).
fof(f828,definition,
( spl32_26
<=> leq(n0,tptp_minus_1) ),
introduced(definition,[new_symbols(definition,[spl32_26])],[avatar_definition]) ).
fof(f858,plain,
( ~ leq(n0,succ(sK31))
| n0 = succ(sK31) ),
inference(resolution,[],[f345,f553]) ).
fof(f864,definition,
( spl32_27
<=> n0 = succ(sK31) ),
introduced(definition,[new_symbols(definition,[spl32_27])],[avatar_definition]) ).
fof(f866,plain,
( n0 = succ(sK31)
| ~ spl32_27 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f868,definition,
( spl32_28
<=> leq(n0,succ(sK31)) ),
introduced(definition,[new_symbols(definition,[spl32_28])],[avatar_definition]) ).
fof(f870,plain,
( ~ leq(n0,succ(sK31))
| spl32_28 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f871,plain,
( spl32_27
| ~ spl32_28 ),
inference(avatar_split_clause,[],[f858,f868,f864]) ).
fof(f1798,plain,
~ leq(n0,tptp_minus_1),
inference(resolution,[],[f406,f201]) ).
fof(f2354,plain,
( ~ leq(n0,sK31)
| spl32_28 ),
inference(resolution,[],[f870,f209]) ).
fof(f2360,plain,
( $false
| spl32_28 ),
inference(forward_subsumption_resolution,[],[f2354,f313]) ).
fof(f2361,plain,
spl32_28,
inference(avatar_contradiction_clause,[],[f2360]) ).
fof(f2370,plain,
( sK31 = pred(n0)
| ~ spl32_27 ),
inference(superposition,[],[f290,f866]) ).
fof(f2386,plain,
( tptp_minus_1 = sK31
| ~ spl32_27 ),
inference(forward_demodulation,[],[f2370,f367]) ).
fof(f2403,plain,
~ spl32_26,
inference(avatar_split_clause,[],[f1798,f828]) ).
fof(f2438,plain,
( leq(n0,tptp_minus_1)
| ~ spl32_27 ),
inference(superposition,[],[f313,f2386]) ).
fof(f2446,plain,
( spl32_26
| ~ spl32_27 ),
inference(avatar_split_clause,[],[f2438,f864,f828]) ).
cnf(s15,plain,
( spl32_27
| ~ spl32_28 ),
inference(sat_conversion,[],[f871]) ).
cnf(s68,plain,
spl32_28,
inference(sat_conversion,[],[f2361]) ).
cnf(s71,plain,
~ spl32_26,
inference(sat_conversion,[],[f2403]) ).
cnf(s73,plain,
( spl32_26
| ~ spl32_27 ),
inference(sat_conversion,[],[f2446]) ).
cnf(s74,plain,
~ spl32_27,
inference(rat,[],[s73,s71]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s15,s68,s74]) ).
fof(f2447,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV163+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n014.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 10:03:31 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.54/0.83 % (1681244)Detected formulas, will run a generic FOF schedule.
% 2.54/0.83 % (1681254)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1758659505:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/0.83 % (1681252)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=541029082:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/0.83 % (1681249)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=207418953:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/0.83 % (1681255)dis-21_1_sil=8000:lcm=predicate:random_seed=1983107962: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)
% 2.54/0.83 % (1681251)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=578179830:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/0.83 % (1681253)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3198211538:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/0.83 % (1681250)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=1359813479:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/0.83 % (1681254)First to succeed.
% 2.54/0.83 % (1681254)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1681244"
% 2.54/0.83 % (1681252)Refutation not found, incomplete strategy
% 2.54/0.83 % (1681252)------------------------------
% 2.54/0.83 % (1681252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.83 % (1681252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.83 % (1681252)CaDiCaL version: 2.1.3
% 2.54/0.83 % (1681252)Termination reason: Refutation not found, incomplete strategy
% 2.54/0.83 % (1681252)Time elapsed: 0.008 s
% 2.54/0.83 % (1681252)Peak memory usage: 88 MB
% 2.54/0.83 % (1681252)Instructions burned: 10 (million)
% 2.54/0.83 % (1681253)Also succeeded, but the first one will report.
% 2.54/0.83 % (1681255)Instruction limit reached!
% 2.54/0.83 % (1681255)------------------------------
% 2.54/0.83 % (1681255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.83 % (1681255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.83 % (1681255)CaDiCaL version: 2.1.3
% 2.54/0.83 % (1681255)Termination reason: Instruction limit
% 2.54/0.83 % (1681255)Termination phase: Saturation
% 2.54/0.83 % (1681255)Time elapsed: 0.063 s
% 2.54/0.83 % (1681255)Peak memory usage: 88 MB
% 2.54/0.83 % (1681255)Instructions burned: 130 (million)
% 2.54/0.83 % (1681254)Refutation found. Thanks to Tanya!
% 2.54/0.83 % SZS status Theorem for theBenchmark
% 2.54/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.83 % (1681254)------------------------------
% 2.54/0.83 % (1681254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.83 % (1681254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.83 % (1681254)CaDiCaL version: 2.1.3
% 2.54/0.83 % (1681254)Termination reason: Refutation
% 2.54/0.83 % (1681254)Time elapsed: 0.036 s
% 2.54/0.83 % (1681254)Peak memory usage: 91 MB
% 2.54/0.83 % (1681254)Instructions burned: 104 (million)
% 2.54/0.83 % (1681254)------------------------------
% 2.54/0.83 % (1681254)------------------------------
% 2.54/0.83 % (1681244)Success in time 0.312 s
% 2.54/0.83 % Vampire exiting
%------------------------------------------------------------------------------