%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 01:20:22 PM UTC 2026
% Result : Theorem 0.35s 0.28s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 19 unt; 1 def)
% Number of atoms : 113 ( 25 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 104 ( 36 ~; 28 |; 30 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 16 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
=> leq(X0,succ(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_tptp_minus_1) ).
fof(f29,axiom,
! [X0] : plus(X0,n1) = succ(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
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(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0014) ).
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(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f93,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f118,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f151,plain,
( ? [X1] :
( a_select3(q,pv10,X1) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& 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(f152,plain,
( ? [X1] :
( a_select3(q,pv10,X1) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& 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,[],[f151]) ).
fof(f157,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f158,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f157]) ).
fof(f173,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f205,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& 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,[],[f152]) ).
fof(f206,plain,
( a_select3(q,pv10,sK31) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& 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)],[f205]) ).
fof(f209,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f217,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f218,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
fof(f286,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f287,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f320,plain,
leq(sK31,tptp_minus_1),
inference(cnf_transformation,[],[f206]) ).
fof(f321,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f206]) ).
fof(f361,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f373,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| leq(X0,plus(X1,n1)) ),
inference(definition_unfolding,[],[f217,f287]) ).
fof(f375,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(plus(X1,n1),X0) ),
inference(definition_unfolding,[],[f218,f287]) ).
fof(f376,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f286,f287]) ).
fof(f808,plain,
leq(sK31,plus(tptp_minus_1,n1)),
inference(resolution,[],[f373,f320]) ).
fof(f809,plain,
leq(sK31,n0),
inference(forward_demodulation,[],[f808,f376]) ).
fof(f887,plain,
gt(plus(tptp_minus_1,n1),sK31),
inference(resolution,[],[f375,f320]) ).
fof(f891,plain,
gt(n0,sK31),
inference(forward_demodulation,[],[f887,f376]) ).
fof(f1129,definition,
( spl32_19
<=> n0 = sK31 ),
introduced(definition,[new_symbols(definition,[spl32_19])],[avatar_definition]) ).
fof(f1130,plain,
( n0 != sK31
| spl32_19 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1131,plain,
( n0 = sK31
| ~ spl32_19 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1192,plain,
( n0 = sK31
| ~ leq(sK31,n0) ),
inference(resolution,[],[f361,f321]) ).
fof(f1310,plain,
( gt(n0,n0)
| ~ spl32_19 ),
inference(superposition,[],[f891,f1131]) ).
fof(f1311,plain,
( $false
| ~ spl32_19 ),
inference(forward_subsumption_resolution,[],[f1310,f209]) ).
fof(f1312,plain,
~ spl32_19,
inference(avatar_contradiction_clause,[],[f1311]) ).
fof(f1341,plain,
( ~ leq(sK31,n0)
| spl32_19 ),
inference(forward_subsumption_resolution,[],[f1192,f1130]) ).
fof(f1351,plain,
( $false
| spl32_19 ),
inference(forward_subsumption_resolution,[],[f1341,f809]) ).
fof(f1352,plain,
spl32_19,
inference(avatar_contradiction_clause,[],[f1351]) ).
cnf(s20,plain,
~ spl32_19,
inference(sat_conversion,[],[f1312]) ).
cnf(s22,plain,
spl32_19,
inference(sat_conversion,[],[f1352]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s20,s22]) ).
fof(f1353,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 10:05:40 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.28 % (3275396)Will run a generic schedule for satisfiability detection.
% 0.35/0.28 % (3275406)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1359640231:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.35/0.28 % (3275401)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=68599063_2999 on theBenchmark for (2999ds/0Mi)
% 0.35/0.28 % (3275403)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4015456587:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.35/0.28 % (3275405)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2457757174:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.35/0.28 % (3275407)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1868029231:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.35/0.28 % (3275404)dis+10_1_sil=32000:sp=arity:random_seed=3908361671:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.35/0.28 % (3275402)% WARNING: option uhcvi not known.
% 0.35/0.28 % (3275402)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2017910417:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.35/0.28 % (3275406) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3275396-3275406"...
% 0.35/0.28 % (3275406)...printing done.
% 0.35/0.28 % (3275406)Refutation found. Thanks to Tanya!
% 0.35/0.28 % SZS status Theorem for theBenchmark
% 0.35/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.28 % (3275406)------------------------------
% 0.35/0.28 % (3275406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.28 % (3275406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.28 % (3275406)CaDiCaL version: 2.1.3
% 0.35/0.28 % (3275406)Termination reason: Refutation
% 0.35/0.28 % (3275406)Time elapsed: 0.025 s
% 0.35/0.28 % (3275406)Peak memory usage: 13 MB
% 0.35/0.28 % (3275406)Instructions burned: 45 (million)
% 0.35/0.28 % (3275396)Success in time 0.057 s
% 0.35/0.28 % Vampire exiting
%------------------------------------------------------------------------------