%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM835+1 : 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 : n026.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 12:25:50 PM UTC 2026
% Result : Theorem 0.19s 10.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 11 unt; 2 def)
% Number of atoms : 87 ( 56 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 91 ( 36 ~; 38 |; 14 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 44 ( 0 sgn 32 !; 12 ?)
% 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(f21,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(f41,plain,
( ! [X0] : vd165 != vplus(vd151,X0)
& ! [X1] : vd151 != vplus(vd165,X1)
& vd165 != vd151 ),
inference(ennf_transformation,[],[f2]) ).
fof(f83,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| ? [X2] : X0 = vplus(X1,X2)
| ? [X3] : X1 = vplus(X0,X3)
| ~ m(X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f84,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| ? [X2] : X0 = vplus(X1,X2)
| ? [X3] : X1 = vplus(X0,X3)
| ~ m(X1) ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| ? [X4] : vplus(X1,X4) = X0
| ? [X5] : vplus(X0,X5) = X1
| ~ m(X1) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| vplus(X1,sK1(X0,X1)) = X0
| vplus(X0,sK2(X0,X1)) = X1
| ~ m(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X0,X1)),skolemize(X5,sK2(X0,X1))],[f85]) ).
fof(f87,plain,
vd165 != vd151,
inference(cnf_transformation,[],[f41]) ).
fof(f88,plain,
! [X1] : vd151 != vplus(vd165,X1),
inference(cnf_transformation,[],[f41]) ).
fof(f89,plain,
! [X0] : vd165 != vplus(vd151,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f113,plain,
! [X0,X1] :
( X0 = X1
| vplus(X1,sK1(X0,X1)) = X0
| vplus(X0,sK2(X0,X1)) = X1
| ~ m(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f116,plain,
! [X0,X1] :
( m(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f169,plain,
! [X1] : m(X1),
inference(equality_resolution,[],[f116]) ).
fof(f189,definition,
( spl3_3
<=> vd165 = vd151 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f191,plain,
( vd165 != vd151
| spl3_3 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f233,definition,
( spl3_12
<=> ! [X0] : vd165 != vplus(vd151,X0) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f234,plain,
( ! [X0] : vd165 != vplus(vd151,X0)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f87,f189]) ).
fof(f237,plain,
spl3_12,
inference(avatar_split_clause,[],[f89,f233]) ).
fof(f408,plain,
! [X0,X1] :
( vplus(X1,sK1(X0,X1)) = X0
| vplus(X0,sK2(X0,X1)) = X1
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f113,f169]) ).
fof(f420,plain,
! [X0] :
( vd151 != X0
| vd165 = vplus(X0,sK2(X0,vd165))
| vd165 = X0 ),
inference(superposition,[],[f88,f408]) ).
fof(f462,plain,
( vd165 = vplus(vd151,sK2(vd151,vd165))
| vd165 = vd151 ),
inference(equality_resolution,[],[f420]) ).
fof(f463,plain,
( vd165 = vd151
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f462,f234]) ).
fof(f464,plain,
( $false
| spl3_3
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f463,f191]) ).
fof(f465,plain,
( spl3_3
| ~ spl3_12 ),
inference(avatar_contradiction_clause,[],[f464]) ).
cnf(s12,plain,
~ spl3_3,
inference(sat_conversion,[],[f236]) ).
cnf(s13,plain,
spl3_12,
inference(sat_conversion,[],[f237]) ).
cnf(s15,plain,
( spl3_3
| ~ spl3_12 ),
inference(sat_conversion,[],[f465]) ).
cnf(s16,plain,
spl3_3,
inference(rat,[],[s15,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s12,s16]) ).
fof(f466,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/10.43 % Computer : n026.cluster.edu
% 0.13/10.43 % Model : x86_64 x86_64
% 0.13/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.43 % Memory : 8046.5625MB
% 0.13/10.43 % OS : Linux 6.8.0-71-generic
% 0.13/10.43 % CPULimit : 300
% 0.13/10.43 % WCLimit : 300
% 0.13/10.44 % DateTime : Sun Sep 27 21:32:07 UTC 2026
% 0.13/10.44 % CPUTime :
% 0.13/10.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/10.49 Running first-order model finding
% 0.13/10.49 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
% 0.19/10.54 % (3222863)Will run a generic schedule for satisfiability detection.
% 0.19/10.54 % (3222871)dis+10_1_sil=32000:sp=arity:random_seed=3095688738:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/10.54 % (3222874)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=217116245:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/10.54 % (3222869)% WARNING: option uhcvi not known.
% 0.19/10.54 % (3222868)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=837131399_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/10.54 % (3222869)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2472346232:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/10.54 % (3222870)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1540124091:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/10.54 % (3222871) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3222863-3222871"...
% 0.19/10.54 % (3222871)...printing done.
% 0.19/10.54 % TRYING [1]
% 0.19/10.54 % (3222871)Refutation found. Thanks to Tanya!
% 0.19/10.54 % SZS status Theorem for theBenchmark
% 0.19/10.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/10.54 % (3222871)------------------------------
% 0.19/10.54 % (3222871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/10.54 % (3222871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/10.54 % (3222871)CaDiCaL version: 2.1.3
% 0.19/10.54 % (3222871)Termination reason: Refutation
% 0.19/10.54 % (3222871)Time elapsed: 0.010 s
% 0.19/10.54 % (3222871)Peak memory usage: 13 MB
% 0.19/10.54 % (3222871)Instructions burned: 13 (million)
% 0.19/10.54 % (3222863)Success in time 0.041 s
% 0.19/10.54 % Vampire exiting
%------------------------------------------------------------------------------