%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM423+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 : n002.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 12:24:15 PM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 109 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 49 ~; 47 |; 15 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(f20,axiom,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
fof(f21,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(flattening,[],[f22]) ).
fof(f35,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(ennf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f60,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f68,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f77,plain,
! [X2,X0,X1] :
( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sz00 = X2 ),
inference(cnf_transformation,[],[f49]) ).
fof(f79,plain,
sz00 != xq,
inference(cnf_transformation,[],[f20]) ).
fof(f80,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f20]) ).
fof(f81,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f82,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnf_transformation,[],[f23]) ).
fof(f84,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f72]) ).
fof(f114,plain,
sz00 = sdtasdt0(xq,sz00),
inference(resolution,[],[f68,f80]) ).
fof(f148,plain,
sz00 = sdtpldt0(xa,smndt0(xa)),
inference(resolution,[],[f60,f81]) ).
fof(f265,plain,
( aDivisorOf0(xq,sz00)
| ~ aInteger0(sz00)
| sz00 = xq
| ~ aInteger0(xq)
| ~ aInteger0(sz00) ),
inference(superposition,[],[f84,f114]) ).
fof(f266,plain,
( aDivisorOf0(xq,sz00)
| ~ aInteger0(sz00)
| sz00 = xq
| ~ aInteger0(xq) ),
inference(duplicate_literal_removal,[],[f265]) ).
fof(f275,plain,
( aDivisorOf0(xq,sz00)
| sz00 = xq
| ~ aInteger0(xq) ),
inference(forward_subsumption_resolution,[],[f266,f50]) ).
fof(f284,plain,
( aDivisorOf0(xq,sz00)
| ~ aInteger0(xq) ),
inference(forward_subsumption_resolution,[],[f275,f79]) ).
fof(f291,plain,
aDivisorOf0(xq,sz00),
inference(forward_subsumption_resolution,[],[f284,f80]) ).
fof(f418,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sz00 = xq ),
inference(resolution,[],[f77,f82]) ).
fof(f421,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sz00 = xq ),
inference(duplicate_literal_removal,[],[f418]) ).
fof(f423,plain,
( ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f421,f80]) ).
fof(f425,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f423,f81]) ).
fof(f427,plain,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))),
inference(forward_subsumption_resolution,[],[f425,f79]) ).
fof(f429,plain,
~ aDivisorOf0(xq,sz00),
inference(forward_demodulation,[],[f427,f148]) ).
fof(f432,plain,
$false,
inference(forward_subsumption_resolution,[],[f429,f291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 % Computer : n002.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 19:54:24 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.44 Running first-order model finding
% 0.12/0.45 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
% 0.19/0.50 % (3837282)Will run a generic schedule for satisfiability detection.
% 0.19/0.50 % (3837292)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1638487331:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.50 % (3837288)% WARNING: option uhcvi not known.
% 0.19/0.50 % (3837287)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2766356537_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.50 % (3837288)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2071352844:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.50 % (3837289)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3265638607:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.50 % (3837293)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=569274897:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.50 % (3837290)dis+10_1_sil=32000:sp=arity:random_seed=25098557:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.50 % (3837291)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3304666038:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.50 % TRYING [1]
% 0.19/0.50 % TRYING [2]
% 0.19/0.50 % TRYING [3]
% 0.19/0.50 % TRYING [4]
% 0.19/0.50 % (3837291) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3837282-3837291"...
% 0.19/0.50 % (3837291)...printing done.
% 0.19/0.50 % (3837291)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (3837291)------------------------------
% 0.19/0.50 % (3837291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.50 % (3837291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.50 % (3837291)CaDiCaL version: 2.1.3
% 0.19/0.50 % (3837291)Termination reason: Refutation
% 0.19/0.50 % (3837291)Time elapsed: 0.010 s
% 0.19/0.50 % (3837291)Peak memory usage: 12 MB
% 0.19/0.50 % (3837291)Instructions burned: 16 (million)
% 0.19/0.50 % (3837282)Success in time 0.045 s
% 0.19/0.50 % Vampire exiting
%------------------------------------------------------------------------------