%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:25:51 PM UTC 2026
% Result : Theorem 0.19s 0.72s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 11 unt; 2 def)
% Number of atoms : 55 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 20 ~; 22 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] : vd165 = vplus(vd151,X0)
| ? [X1] : vd151 = vplus(vd165,X1)
| vd151 = vd165 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).
fof(f2,negated_conjecture,
~ ( ? [X0] : vd165 = vplus(vd151,X0)
| ? [X1] : vd151 = vplus(vd165,X1)
| vd151 = vd165 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f18,axiom,
! [X0,X1] :
( m(X1)
<=> ( X0 = X1
| ? [X2] : X0 = vplus(X1,X2)
| ? [X3] : X1 = vplus(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
fof(f26,plain,
( ! [X0] : vd165 != vplus(vd151,X0)
& ! [X1] : vd151 != vplus(vd165,X1)
& vd165 != vd151 ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
vd165 != vd151,
inference(cnf_transformation,[],[f26]) ).
fof(f53,plain,
! [X1] : vd151 != vplus(vd165,X1),
inference(cnf_transformation,[],[f26]) ).
fof(f54,plain,
! [X0] : vd165 != vplus(vd151,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1
| ~ m(X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f73,plain,
! [X0,X1] :
( X0 != X1
| m(X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f101,plain,
! [X1] : m(X1),
inference(equality_resolution,[],[f73]) ).
fof(f109,definition,
( spl2_2
<=> vd165 = vd151 ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f111,plain,
( vd165 != vd151
| spl2_2 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f149,definition,
( spl2_10
<=> ! [X0] : vd165 != vplus(vd151,X0) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f150,plain,
( ! [X0] : vd165 != vplus(vd151,X0)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f52,f109]) ).
fof(f153,plain,
spl2_10,
inference(avatar_split_clause,[],[f54,f149]) ).
fof(f204,plain,
! [X0,X1] :
( vplus(X1,sK1(X0,X1)) = X0
| vplus(X0,sK0(X0,X1)) = X1
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f70,f101]) ).
fof(f218,plain,
! [X0] :
( vd151 != X0
| vd165 = vplus(X0,sK0(X0,vd165))
| vd165 = X0 ),
inference(superposition,[],[f53,f204]) ).
fof(f234,plain,
( vd165 = vplus(vd151,sK0(vd151,vd165))
| vd165 = vd151 ),
inference(equality_resolution,[],[f218]) ).
fof(f235,plain,
( vd165 = vd151
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f234,f150]) ).
fof(f236,plain,
( $false
| spl2_2
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f235,f111]) ).
fof(f237,plain,
( spl2_2
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[],[f236]) ).
cnf(s11,plain,
~ spl2_2,
inference(sat_conversion,[],[f152]) ).
cnf(s12,plain,
spl2_10,
inference(sat_conversion,[],[f153]) ).
cnf(s13,plain,
( spl2_2
| ~ spl2_10 ),
inference(sat_conversion,[],[f237]) ).
cnf(s14,plain,
spl2_2,
inference(rat,[],[s13,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s11,s14]) ).
fof(f238,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.61 % Computer : n009.cluster.edu
% 0.15/0.61 % Model : x86_64 x86_64
% 0.15/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.61 % Memory : 8046.5625MB
% 0.15/0.61 % OS : Linux 6.8.0-71-generic
% 0.15/0.61 % CPULimit : 300
% 0.15/0.61 % WCLimit : 300
% 0.15/0.61 % DateTime : Sun Sep 27 21:29:16 UTC 2026
% 0.15/0.61 % CPUTime :
% 0.15/0.61 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.19/0.66 Running first-order model finding
% 0.19/0.66 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.72 % (2413846)Will run a generic schedule for satisfiability detection.
% 0.19/0.72 % (2413856)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3004248801:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.72 % (2413853)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3466623384:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.72 % (2413852)% WARNING: option uhcvi not known.
% 0.19/0.72 % (2413851)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1334282545_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.72 % (2413855)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4017920599:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.72 % (2413852)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=674875633:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.72 % (2413857)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=325539571:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.72 % (2413854)dis+10_1_sil=32000:sp=arity:random_seed=3025778112:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.72 % TRYING [1]
% 0.19/0.72 % TRYING [2]
% 0.19/0.72 % TRYING [3]
% 0.19/0.72 % (2413852) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2413846-2413852"...
% 0.19/0.72 % (2413854) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2413846-2413854"...
% 0.19/0.72 % (2413852)...printing done.
% 0.19/0.72 % (2413854)...printing done.
% 0.19/0.72 % (2413852)Refutation found. Thanks to Tanya!
% 0.19/0.72 % SZS status Theorem for theBenchmark
% 0.19/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.72 % (2413852)------------------------------
% 0.19/0.72 % (2413852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.72 % (2413852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.72 % (2413852)CaDiCaL version: 2.1.3
% 0.19/0.72 % (2413852)Termination reason: Refutation
% 0.19/0.72 % (2413852)Time elapsed: 0.009 s
% 0.19/0.72 % (2413852)Peak memory usage: 12 MB
% 0.19/0.72 % (2413852)Instructions burned: 7 (million)
% 0.19/0.72 % (2413846)Success in time 0.048 s
% 0.19/0.72 % Vampire exiting
%------------------------------------------------------------------------------