%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM427+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 : n006.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 12:24:16 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 117 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 59 ~; 52 |; 14 &)
% ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
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(f21,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
fof(f23,axiom,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
fof(f24,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__767) ).
fof(f25,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f26,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(flattening,[],[f26]) ).
fof(f29,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f32]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f52]) ).
fof(f58,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f60,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f83,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
sz00 != xq,
inference(cnf_transformation,[],[f21]) ).
fof(f87,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f21]) ).
fof(f88,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f21]) ).
fof(f89,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f21]) ).
fof(f92,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f23]) ).
fof(f93,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[],[f24]) ).
fof(f94,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[],[f27]) ).
fof(f96,plain,
! [X2,X1] :
( ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f78]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sz00 = X2 ),
inference(consistent_polarity_flipping,[],[f83]) ).
fof(f101,plain,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(consistent_polarity_flipping,[],[f94]) ).
fof(f212,plain,
! [X2,X1] :
( aDivisorOf0(X1,sdtasdt0(X1,X2))
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(forward_subsumption_resolution,[],[f96,f60]) ).
fof(f299,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sz00 = xq ),
inference(resolution,[],[f98,f101]) ).
fof(f300,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f299,f87]) ).
fof(f301,plain,
( ~ aInteger0(xb)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f300,f89]) ).
fof(f302,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f301,f88]) ).
fof(f303,plain,
~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))),
inference(forward_subsumption_resolution,[],[f302,f86]) ).
fof(f304,plain,
~ aDivisorOf0(xq,sdtasdt0(xq,smndt0(xn))),
inference(forward_demodulation,[],[f303,f93]) ).
fof(f305,plain,
( sz00 = xq
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) ),
inference(resolution,[],[f304,f212]) ).
fof(f306,plain,
( ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) ),
inference(forward_subsumption_resolution,[],[f305,f86]) ).
fof(f307,plain,
~ aInteger0(smndt0(xn)),
inference(forward_subsumption_resolution,[],[f306,f87]) ).
fof(f308,plain,
~ aInteger0(xn),
inference(resolution,[],[f307,f58]) ).
fof(f309,plain,
$false,
inference(forward_subsumption_resolution,[],[f308,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 19:51:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.44 % (3276722)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (3276728)% WARNING: option uhcvi not known.
% 0.11/0.44 % (3276728)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=145276386:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % (3276730)dis+10_1_sil=32000:sp=arity:random_seed=3550743711:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (3276727)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3474119818_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % (3276729)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=284828256:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (3276731)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3384947286:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (3276732)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2951198650:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (3276733)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1069003224:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (3276728) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3276722-3276728"...
% 0.11/0.44 % TRYING [1]
% 0.11/0.44 % TRYING [2]
% 0.11/0.44 % (3276728)...printing done.
% 0.11/0.44 % (3276728)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (3276728)------------------------------
% 0.11/0.44 % (3276728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (3276728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (3276728)CaDiCaL version: 2.1.3
% 0.11/0.44 % (3276728)Termination reason: Refutation
% 0.11/0.44 % (3276728)Time elapsed: 0.004 s
% 0.11/0.44 % (3276728)Peak memory usage: 12 MB
% 0.11/0.44 % (3276728)Instructions burned: 10 (million)
% 0.11/0.44 % (3276722)Success in time 0.039 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------