%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n019.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 01:20:21 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 99 ( 33 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 101 ( 31 ~; 26 |; 36 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 32 ( 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
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(f108,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f108]) ).
fof(f143,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(f144,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,[],[f143]) ).
fof(f164,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f197,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,[],[f144]) ).
fof(f198,plain,
( n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index))
& leq(n0,sK31)
& leq(sK31,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,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f205,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f207,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f289,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f309,plain,
! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f312,plain,
n1 = sum(n0,n4,a_select3(q,pv10,tptp_sum_index)),
inference(cnf_transformation,[],[f198]) ).
fof(f313,plain,
leq(sK31,pv10),
inference(cnf_transformation,[],[f198]) ).
fof(f314,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f315,plain,
n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index)),
inference(cnf_transformation,[],[f198]) ).
fof(f355,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f207,f289]) ).
fof(f376,plain,
! [X1] :
( ~ leq(X1,minus(pv10,n1))
| ~ leq(n0,X1)
| n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) ),
inference(definition_unfolding,[],[f309,f289]) ).
fof(f463,plain,
! [X0] :
( ~ leq(n0,X0)
| ~ gt(pv10,X0)
| n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index)) ),
inference(resolution,[],[f355,f376]) ).
fof(f495,plain,
( ~ gt(pv10,sK31)
| n1 = sum(n0,n4,a_select3(q,sK31,tptp_sum_index)) ),
inference(resolution,[],[f463,f314]) ).
fof(f498,plain,
~ gt(pv10,sK31),
inference(forward_subsumption_resolution,[],[f495,f315]) ).
fof(f738,plain,
( gt(pv10,sK31)
| pv10 = sK31 ),
inference(resolution,[],[f205,f313]) ).
fof(f739,plain,
pv10 = sK31,
inference(forward_subsumption_resolution,[],[f738,f498]) ).
fof(f761,plain,
n1 != sum(n0,n4,a_select3(q,pv10,tptp_sum_index)),
inference(superposition,[],[f315,f739]) ).
fof(f764,plain,
$false,
inference(forward_subsumption_resolution,[],[f761,f312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV161+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 10:03:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.20/0.28 % (3899792)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3899798)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3899798)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3802942113:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3899799)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=895929346:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3899797)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2405604498_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (3899800)dis+10_1_sil=32000:sp=arity:random_seed=3269827399:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (3899801)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2587185086:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (3899802)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2917027599:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (3899800) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3899792-3899800"...
% 0.20/0.28 % (3899800)...printing done.
% 0.20/0.28 % (3899803)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3622542646:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (3899800)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3899800)------------------------------
% 0.20/0.28 % (3899800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3899800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3899800)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3899800)Termination reason: Refutation
% 0.20/0.28 % (3899800)Time elapsed: 0.014 s
% 0.20/0.28 % (3899800)Peak memory usage: 12 MB
% 0.20/0.28 % (3899800)Instructions burned: 23 (million)
% 0.20/0.28 % (3899792)Success in time 0.058 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------