%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 0.15s 0.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 19 unt; 5 def)
% Number of atoms : 194 ( 57 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 208 ( 87 ~; 79 |; 29 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(f28,axiom,
( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sz10,X0) = xm )
& sdtlseqdt0(sz10,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1007) ).
fof(f29,conjecture,
( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = sdtasdt0(xn,xm) )
| 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,
( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sz10,X0) = xm )
& sdtlseqdt0(sz10,xm) )
| sz00 = xm ),
inference(ennf_transformation,[],[f28]) ).
fof(f75,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f79,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f89,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f45]) ).
fof(f90,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f107,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f118,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(cnf_transformation,[],[f71]) ).
fof(f121,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f122,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f125,plain,
( sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(cnf_transformation,[],[f74]) ).
fof(f127,plain,
sz00 != xm,
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f76]) ).
fof(f140,definition,
( spl2_2
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f150,definition,
( spl2_4
<=> sdtlseqdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f152,plain,
( sdtlseqdt0(sz10,xm)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f125,f140,f150]) ).
fof(f154,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f127,f140]) ).
fof(f173,plain,
xn = sdtasdt0(xn,sz10),
inference(resolution,[],[f89,f121]) ).
fof(f177,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[],[f90,f122]) ).
fof(f266,definition,
( spl2_9
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f267,plain,
( sz00 != xn
| spl2_9 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( sz00 = xn
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f284,definition,
( spl2_11
<=> sz10 = xm ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f286,plain,
( sz10 = xm
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f296,plain,
( ~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm))
| ~ spl2_9 ),
inference(superposition,[],[f128,f268]) ).
fof(f408,plain,
( ~ sdtlseqdt0(sz00,sz00)
| ~ spl2_9 ),
inference(superposition,[],[f296,f177]) ).
fof(f409,plain,
( ~ aNaturalNumber0(sz00)
| ~ spl2_9 ),
inference(resolution,[],[f408,f107]) ).
fof(f410,plain,
( $false
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f409,f77]) ).
fof(f411,plain,
~ spl2_9,
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f500,plain,
( ! [X0] :
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sz10 = xm
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl2_4 ),
inference(resolution,[],[f118,f152]) ).
fof(f549,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sz10 = xm
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f500,f79]) ).
fof(f552,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz10 = xm
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f549,f122]) ).
fof(f562,definition,
( spl2_20
<=> ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| sz00 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f563,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| sz00 = X0 )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f564,plain,
( spl2_11
| spl2_20
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f552,f150,f562,f284]) ).
fof(f617,plain,
( xn = sdtasdt0(xn,xm)
| ~ spl2_11 ),
inference(forward_demodulation,[],[f173,f286]) ).
fof(f1375,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ spl2_11 ),
inference(superposition,[],[f128,f617]) ).
fof(f1379,plain,
( ~ aNaturalNumber0(xn)
| ~ spl2_11 ),
inference(resolution,[],[f1375,f107]) ).
fof(f1380,plain,
( $false
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f1379,f121]) ).
fof(f1381,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[],[f1380]) ).
fof(f2708,plain,
( sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))
| sz00 = xn
| ~ spl2_20 ),
inference(resolution,[],[f563,f121]) ).
fof(f2717,plain,
( sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))
| spl2_9
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f2708,f267]) ).
fof(f2761,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| spl2_9
| ~ spl2_20 ),
inference(forward_demodulation,[],[f2717,f173]) ).
fof(f2764,plain,
( $false
| spl2_9
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f2761,f128]) ).
fof(f2765,plain,
( spl2_9
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f2764]) ).
cnf(s3,plain,
( spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f153]) ).
cnf(s4,plain,
~ spl2_2,
inference(sat_conversion,[],[f154]) ).
cnf(s10,plain,
~ spl2_9,
inference(sat_conversion,[],[f411]) ).
cnf(s16,plain,
( ~ spl2_4
| spl2_11
| spl2_20 ),
inference(sat_conversion,[],[f564]) ).
cnf(s36,plain,
~ spl2_11,
inference(sat_conversion,[],[f1381]) ).
cnf(s153,plain,
( spl2_9
| ~ spl2_20 ),
inference(sat_conversion,[],[f2765]) ).
cnf(s157,plain,
( ~ spl2_4
| spl2_20 ),
inference(rat,[],[s16,s36]) ).
cnf(s161,plain,
~ spl2_20,
inference(rat,[],[s153,s10]) ).
cnf(s162,plain,
~ spl2_4,
inference(rat,[],[s157,s161]) ).
cnf(s164,plain,
$false,
inference(rat,[],[s3,s162,s4]) ).
fof(f2767,plain,
$false,
inference(avatar_sat_refutation,[],[s164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:03:45 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.15/0.51 % (2722730)Will run a generic schedule for satisfiability detection.
% 0.15/0.51 % (2722738)dis+10_1_sil=32000:sp=arity:random_seed=2727240239:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.51 % (2722736)% WARNING: option uhcvi not known.
% 0.15/0.51 % (2722736)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3151153515:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.51 % (2722735)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1507494387_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.51 % (2722737)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2630890586:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.51 % (2722739)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=717679934:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.51 % (2722741)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3798716344:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.51 % (2722740)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4063450071:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.51 % TRYING [1]
% 0.15/0.51 % TRYING [2]
% 0.15/0.51 % TRYING [3]
% 0.15/0.51 % TRYING [4]
% 0.15/0.51 % (2722738)Instruction limit reached!
% 0.15/0.51 % (2722738)------------------------------
% 0.15/0.51 % (2722738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.51 % (2722738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.51 % (2722738)CaDiCaL version: 2.1.3
% 0.15/0.51 % (2722738)Termination reason: Instruction limit
% 0.15/0.51 % (2722738)Termination phase: Saturation
% 0.15/0.51 % (2722738)Time elapsed: 0.033 s
% 0.15/0.51 % (2722738)Peak memory usage: 12 MB
% 0.15/0.51 % (2722738)Instructions burned: 105 (million)
% 0.15/0.51 % TRYING [5]
% 0.15/0.51 % (2722749)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2857947449:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.15/0.51 % TRYING [1]
% 0.15/0.51 % TRYING [2]
% 0.15/0.51 % TRYING [3]
% 0.15/0.51 % (2722736) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2722730-2722736"...
% 0.15/0.51 % TRYING [4]
% 0.15/0.51 % (2722736)...printing done.
% 0.15/0.51 % (2722736)Refutation found. Thanks to Tanya!
% 0.15/0.51 % SZS status Theorem for theBenchmark
% 0.15/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.51 % (2722736)------------------------------
% 0.15/0.51 % (2722736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.51 % (2722736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.51 % (2722736)CaDiCaL version: 2.1.3
% 0.15/0.51 % (2722736)Termination reason: Refutation
% 0.15/0.51 % (2722736)Time elapsed: 0.045 s
% 0.15/0.51 % (2722736)Peak memory usage: 14 MB
% 0.15/0.51 % (2722736)Instructions burned: 70 (million)
% 0.15/0.51 % (2722730)Success in time 0.079 s
% 0.15/0.51 % Vampire exiting
%------------------------------------------------------------------------------