%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM477+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:24:28 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 16 unt; 2 def)
% Number of atoms : 134 ( 32 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 62 ~; 59 |; 15 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f35,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494) ).
fof(f36,axiom,
( doDivides0(xm,xn)
& xn != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494_04) ).
fof(f37,conjecture,
sdtlseqdt0(xm,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f38,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f41,plain,
~ sdtlseqdt0(xm,xn),
inference(flattening,[],[f38]) ).
fof(f57,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f85,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f86,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f88,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f87]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f88]) ).
fof(f103,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f103]) ).
fof(f121,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f57]) ).
fof(f152,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f153,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f154,plain,
! [X0,X1] :
( aNaturalNumber0(sK1(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f162,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f35]) ).
fof(f163,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f35]) ).
fof(f164,plain,
sz00 != xn,
inference(cnf_transformation,[],[f36]) ).
fof(f165,plain,
doDivides0(xm,xn),
inference(cnf_transformation,[],[f36]) ).
fof(f166,plain,
~ sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f41]) ).
fof(f200,plain,
sz00 = sdtasdt0(xm,sz00),
inference(resolution,[],[f121,f163]) ).
fof(f414,plain,
( xn = sdtasdt0(xm,sK1(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f153,f165]) ).
fof(f423,plain,
( xn = sdtasdt0(xm,sK1(xm,xn))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f414,f163]) ).
fof(f425,plain,
xn = sdtasdt0(xm,sK1(xm,xn)),
inference(forward_subsumption_resolution,[],[f423,f162]) ).
fof(f1115,plain,
( sdtlseqdt0(xm,xn)
| sz00 = sK1(xm,xn)
| ~ aNaturalNumber0(sK1(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f152,f425]) ).
fof(f1117,plain,
( sz00 = sK1(xm,xn)
| ~ aNaturalNumber0(sK1(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1115,f166]) ).
fof(f1124,plain,
( sz00 = sK1(xm,xn)
| ~ aNaturalNumber0(sK1(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f1117,f163]) ).
fof(f1126,definition,
( spl2_11
<=> aNaturalNumber0(sK1(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f1128,plain,
( ~ aNaturalNumber0(sK1(xm,xn))
| spl2_11 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1130,definition,
( spl2_12
<=> sz00 = sK1(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f1132,plain,
( sz00 = sK1(xm,xn)
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f1148,plain,
( ~ spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f1124,f1130,f1126]) ).
fof(f1154,plain,
( ~ doDivides0(xm,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl2_11 ),
inference(resolution,[],[f1128,f154]) ).
fof(f1155,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f1154,f165]) ).
fof(f1156,plain,
( ~ aNaturalNumber0(xn)
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f1155,f163]) ).
fof(f1157,plain,
( $false
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f1156,f162]) ).
fof(f1158,plain,
spl2_11,
inference(avatar_contradiction_clause,[],[f1157]) ).
fof(f1264,plain,
( xn = sdtasdt0(xm,sz00)
| ~ spl2_12 ),
inference(superposition,[],[f425,f1132]) ).
fof(f1266,plain,
( sz00 = xn
| ~ spl2_12 ),
inference(forward_demodulation,[],[f1264,f200]) ).
fof(f1267,plain,
( $false
| ~ spl2_12 ),
inference(forward_subsumption_resolution,[],[f1266,f164]) ).
fof(f1268,plain,
~ spl2_12,
inference(avatar_contradiction_clause,[],[f1267]) ).
cnf(s15,plain,
( ~ spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s18,plain,
spl2_11,
inference(sat_conversion,[],[f1158]) ).
cnf(s21,plain,
~ spl2_12,
inference(sat_conversion,[],[f1268]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s15,s21,s18]) ).
fof(f1269,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM477+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n019.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 20:05:49 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.17/0.51 % (3374486)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (3374491)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2778179490_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % TRYING [1]
% 0.17/0.51 % TRYING [2]
% 0.17/0.51 % TRYING [3]
% 0.17/0.51 % (3374492)% WARNING: option uhcvi not known.
% 0.17/0.51 % TRYING [4]
% 0.17/0.51 % (3374494)dis+10_1_sil=32000:sp=arity:random_seed=592006688:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (3374492)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3812867201:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (3374493)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2616685908:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (3374495)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=74242129:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (3374496)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3613857842:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (3374497)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3167505744:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % TRYING [5]
% 0.17/0.51 % (3374494) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3374486-3374494"...
% 0.17/0.51 % (3374494)...printing done.
% 0.17/0.51 % (3374494)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Theorem for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (3374494)------------------------------
% 0.17/0.51 % (3374494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (3374494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (3374494)CaDiCaL version: 2.1.3
% 0.17/0.51 % (3374494)Termination reason: Refutation
% 0.17/0.51 % (3374494)Time elapsed: 0.023 s
% 0.17/0.51 % (3374494)Peak memory usage: 13 MB
% 0.17/0.51 % (3374494)Instructions burned: 39 (million)
% 0.17/0.51 % (3374486)Success in time 0.062 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------