%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM465+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 : n005.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 12:24:25 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 23 unt; 5 def)
% Number of atoms : 195 ( 55 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 192 ( 76 ~; 83 |; 20 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X0 != sz00
& X1 != X2
& sdtlseqdt0(X1,X2) )
=> ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
fof(f28,axiom,
( xm != sz00
=> sdtlseqdt0(sz10,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1007) ).
fof(f29,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f45,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f46,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f61,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f70]) ).
fof(f74,plain,
( sdtlseqdt0(sz10,xm)
| sz00 = xm ),
inference(ennf_transformation,[],[f28]) ).
fof(f75,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f78,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f88,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f106,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f120,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f121,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f122,plain,
( sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
sz00 != xm,
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f75]) ).
fof(f130,plain,
~ aNaturalNumber0(sz00),
inference(consistent_polarity_flipping,[],[f76]) ).
fof(f131,plain,
~ aNaturalNumber0(sz10),
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f140,plain,
! [X0] :
( aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f143,plain,
! [X0] :
( aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f159,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| aNaturalNumber0(X0) ),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(X1)
| aNaturalNumber0(X0)
| aNaturalNumber0(X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f173,plain,
~ aNaturalNumber0(xm),
inference(consistent_polarity_flipping,[],[f121]) ).
fof(f174,plain,
~ aNaturalNumber0(xn),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f177,definition,
( spl1_1
<=> sdtlseqdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f179,plain,
( sdtlseqdt0(sz10,xm)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f181,definition,
( spl1_2
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f184,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f122,f181,f177]) ).
fof(f185,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f123,f181]) ).
fof(f197,plain,
xn = sdtasdt0(xn,sz10),
inference(resolution,[],[f140,f174]) ).
fof(f208,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[],[f143,f173]) ).
fof(f338,definition,
( spl1_3
<=> sz10 = xm ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f340,plain,
( sz10 = xm
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f398,definition,
( spl1_5
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f399,plain,
( sz00 != xn
| spl1_5 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f400,plain,
( sz00 = xn
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f683,plain,
( ~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm))
| ~ spl1_5 ),
inference(superposition,[],[f124,f400]) ).
fof(f760,plain,
( ! [X0] :
( aNaturalNumber0(sz10)
| aNaturalNumber0(X0)
| aNaturalNumber0(xm)
| sz10 = xm
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl1_1 ),
inference(resolution,[],[f169,f179]) ).
fof(f776,plain,
( ! [X0] :
( aNaturalNumber0(X0)
| aNaturalNumber0(xm)
| sz10 = xm
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f760,f131]) ).
fof(f778,plain,
( ! [X0] :
( aNaturalNumber0(X0)
| sz10 = xm
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f776,f173]) ).
fof(f781,definition,
( spl1_11
<=> ! [X0] :
( aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| sz00 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f782,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| aNaturalNumber0(X0)
| sz00 = X0 )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f783,plain,
( spl1_3
| spl1_11
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f778,f177,f781,f338]) ).
fof(f784,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,sz10))
| ~ spl1_3 ),
inference(superposition,[],[f124,f340]) ).
fof(f799,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ spl1_3 ),
inference(forward_demodulation,[],[f784,f197]) ).
fof(f864,plain,
( ~ sdtlseqdt0(sz00,sz00)
| ~ spl1_5 ),
inference(superposition,[],[f683,f208]) ).
fof(f868,plain,
( aNaturalNumber0(sz00)
| ~ spl1_5 ),
inference(resolution,[],[f864,f159]) ).
fof(f869,plain,
( $false
| ~ spl1_5 ),
inference(forward_subsumption_resolution,[],[f868,f130]) ).
fof(f870,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[],[f869]) ).
fof(f2052,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| aNaturalNumber0(xn)
| sz00 = xn
| ~ spl1_11 ),
inference(superposition,[],[f782,f197]) ).
fof(f2055,plain,
( aNaturalNumber0(xn)
| sz00 = xn
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f2052,f124]) ).
fof(f2059,plain,
( sz00 = xn
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f2055,f174]) ).
fof(f2063,plain,
( $false
| spl1_5
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f2059,f399]) ).
fof(f2064,plain,
( spl1_5
| ~ spl1_11 ),
inference(avatar_contradiction_clause,[],[f2063]) ).
fof(f2067,plain,
( aNaturalNumber0(xn)
| ~ spl1_3 ),
inference(resolution,[],[f799,f159]) ).
fof(f2068,plain,
( $false
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f2067,f174]) ).
fof(f2069,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f2068]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f184]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f185]) ).
cnf(s11,plain,
( ~ spl1_1
| spl1_3
| spl1_11 ),
inference(sat_conversion,[],[f783]) ).
cnf(s14,plain,
~ spl1_5,
inference(sat_conversion,[],[f870]) ).
cnf(s19,plain,
( spl1_5
| ~ spl1_11 ),
inference(sat_conversion,[],[f2064]) ).
cnf(s20,plain,
~ spl1_3,
inference(sat_conversion,[],[f2069]) ).
cnf(s21,plain,
~ spl1_11,
inference(rat,[],[s19,s14]) ).
cnf(s27,plain,
~ spl1_1,
inference(rat,[],[s11,s21,s20]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s1,s2,s27]) ).
fof(f2070,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM465+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:03:13 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.50 % (131765)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (131776)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2929010913:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (131771)% WARNING: option uhcvi not known.
% 0.16/0.50 % (131775)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2576432107:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (131770)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=517787782_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (131771)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2681813412:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (131772)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1046199774:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (131773)dis+10_1_sil=32000:sp=arity:random_seed=879612935:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (131774)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3617803572:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % TRYING [4]
% 0.16/0.50 % TRYING [5]
% 0.16/0.50 % (131771) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-131765-131771"...
% 0.16/0.50 % (131771)...printing done.
% 0.16/0.50 % (131776)Instruction limit reached!
% 0.16/0.50 % (131776)------------------------------
% 0.16/0.50 % (131776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (131776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (131776)CaDiCaL version: 2.1.3
% 0.16/0.50 % (131776)Termination reason: Instruction limit
% 0.16/0.50 % (131776)Termination phase: Saturation
% 0.16/0.50 % (131776)Time elapsed: 0.052 s
% 0.16/0.50 % (131776)Peak memory usage: 14 MB
% 0.16/0.50 % (131776)Instructions burned: 161 (million)
% 0.16/0.50 % (131771)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (131771)------------------------------
% 0.16/0.50 % (131771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (131771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (131771)CaDiCaL version: 2.1.3
% 0.16/0.50 % (131771)Termination reason: Refutation
% 0.16/0.50 % (131771)Time elapsed: 0.043 s
% 0.16/0.50 % (131771)Peak memory usage: 13 MB
% 0.16/0.50 % (131771)Instructions burned: 74 (million)
% 0.16/0.50 % (131765)Success in time 0.08 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------