%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM477+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:15:22 PM UTC 2026
% Result : Theorem 3.77s 1.52s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 83 ( 32 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 35 ~; 31 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
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(f35,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494) ).
fof(f36,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xm,X0) )
& doDivides0(xm,xn)
& xn != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494_04) ).
fof(f37,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
| sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f38,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
| sdtlseqdt0(xm,xn) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtpldt0(xm,X0) )
& ~ sdtlseqdt0(xm,xn) ),
inference(ennf_transformation,[],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f41]) ).
fof(f51,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f57,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f58,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f57]) ).
fof(f88,plain,
( aNaturalNumber0(sK0)
& xn = sdtasdt0(xm,sK0)
& doDivides0(xm,xn)
& xn != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f36]) ).
fof(f96,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f35]) ).
fof(f97,plain,
sz00 != xn,
inference(cnf_transformation,[],[f88]) ).
fof(f99,plain,
xn = sdtasdt0(xm,sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f100,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f101,plain,
~ sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f40]) ).
fof(f103,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f113,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f121,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f175,plain,
( xn = sdtasdt0(sK0,xm)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f99,f121]) ).
fof(f189,plain,
( xn = sdtasdt0(sK0,xm)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f175,f100]) ).
fof(f193,plain,
xn = sdtasdt0(sK0,xm),
inference(forward_subsumption_resolution,[],[f189,f96]) ).
fof(f232,plain,
( sdtlseqdt0(xm,xn)
| sz00 = sK0
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f103,f99]) ).
fof(f238,plain,
( sz00 = sK0
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f232,f101]) ).
fof(f240,plain,
( sz00 = sK0
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f238,f100]) ).
fof(f241,plain,
sz00 = sK0,
inference(forward_subsumption_resolution,[],[f240,f96]) ).
fof(f242,plain,
xn != sK0,
inference(superposition,[],[f97,f241]) ).
fof(f243,plain,
! [X0] :
( sK0 = sdtasdt0(sK0,X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f113,f241]) ).
fof(f262,plain,
( xn = sK0
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f193,f243]) ).
fof(f276,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[],[f262,f242]) ).
fof(f280,plain,
$false,
inference(forward_subsumption_resolution,[],[f276,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM477+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:07:42 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.77/1.52 % (890899)Detected formulas, will run a generic FOF schedule.
% 3.77/1.52 % (890910)dis-21_1_sil=8000:lcm=predicate:random_seed=3342463250:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.77/1.52 % (890910)Instruction limit reached!
% 3.77/1.52 % (890910)------------------------------
% 3.77/1.52 % (890910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (890910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (890910)CaDiCaL version: 2.1.3
% 3.77/1.52 % (890910)Termination reason: Instruction limit
% 3.77/1.52 % (890910)Termination phase: Saturation
% 3.77/1.52 % (890910)Time elapsed: 0.042 s
% 3.77/1.52 % (890910)Peak memory usage: 90 MB
% 3.77/1.52 % (890910)Instructions burned: 129 (million)
% 3.77/1.52 % (890907)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1631152506:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.77/1.52 % (890905)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=20013023:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.77/1.52 % (890909)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4242476576:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.77/1.52 % (890904)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2491587279:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.77/1.52 % (890906)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=408072216:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.77/1.52 % (890908)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3046980262:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.77/1.52 % (890908)First to succeed.
% 3.77/1.52 % (890908)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-890899"
% 3.77/1.52 % (890909)Also succeeded, but the first one will report.
% 3.77/1.52 % (890907)Also succeeded, but the first one will report.
% 3.77/1.52 % (890918)lrs+10_1_sil=8000:sp=occurrence:random_seed=3349338644:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.77/1.52 % (890918)Also succeeded, but the first one will report.
% 3.77/1.52 % (890908)Refutation found. Thanks to Tanya!
% 3.77/1.52 % SZS status Theorem for theBenchmark
% 3.77/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.52 % (890908)------------------------------
% 3.77/1.52 % (890908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.52 % (890908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.52 % (890908)CaDiCaL version: 2.1.3
% 3.77/1.52 % (890908)Termination reason: Refutation
% 3.77/1.52 % (890908)Time elapsed: 0.005 s
% 3.77/1.52 % (890908)Peak memory usage: 88 MB
% 3.77/1.52 % (890908)Instructions burned: 6 (million)
% 3.77/1.52 % (890908)------------------------------
% 3.77/1.52 % (890908)------------------------------
% 3.77/1.52 % (890899)Success in time 0.445 s
% 3.77/1.52 % Vampire exiting
%------------------------------------------------------------------------------