%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:15:19 PM UTC 2026
% Result : Theorem 3.10s 1.10s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 18 unt; 1 def)
% Number of atoms : 91 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 26 ~; 15 |; 36 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f33,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xl,X0) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,conjecture,
( xl != sz00
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ( xl != sz00
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
inference(rectify,[],[f34]) ).
fof(f39,plain,
( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& xl != sz00 ),
inference(ennf_transformation,[],[f36]) ).
fof(f40,plain,
( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& xl != sz00 ),
inference(flattening,[],[f39]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f64]) ).
fof(f75,plain,
( aNaturalNumber0(sK0)
& xm = sdtasdt0(xl,sK0)
& doDivides0(xl,xm)
& aNaturalNumber0(sK1)
& xn = sdtasdt0(xl,sK1)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f37]) ).
fof(f86,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f33]) ).
fof(f88,plain,
xn = sdtasdt0(xl,sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f91,plain,
xm = sdtasdt0(xl,sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f94,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f40]) ).
fof(f95,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f40]) ).
fof(f96,plain,
xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
inference(cnf_transformation,[],[f40]) ).
fof(f97,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(cnf_transformation,[],[f40]) ).
fof(f98,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(cnf_transformation,[],[f40]) ).
fof(f124,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f133,definition,
~ sP4(sdtpldt0(xm,xn)),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f134,plain,
sP4(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))),
inference(inequality_splitting,[],[f98,f133]) ).
fof(f262,plain,
( sP4(sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(superposition,[],[f134,f124]) ).
fof(f263,plain,
( sP4(sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(forward_subsumption_resolution,[],[f262,f86]) ).
fof(f264,plain,
( sP4(sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))))
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(forward_subsumption_resolution,[],[f263,f95]) ).
fof(f265,plain,
sP4(sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl)))),
inference(forward_subsumption_resolution,[],[f264,f97]) ).
fof(f266,plain,
sP4(sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),xn)),
inference(forward_demodulation,[],[f265,f96]) ).
fof(f267,plain,
sP4(sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sK1))),
inference(forward_demodulation,[],[f266,f88]) ).
fof(f294,plain,
sP4(sdtpldt0(xm,sdtasdt0(xl,sK1))),
inference(forward_demodulation,[],[f267,f94]) ).
fof(f295,plain,
sP4(sdtpldt0(sdtasdt0(xl,sK0),sdtasdt0(xl,sK1))),
inference(forward_demodulation,[],[f294,f91]) ).
fof(f369,plain,
~ sP4(sdtpldt0(xm,sdtasdt0(xl,sK1))),
inference(superposition,[],[f133,f88]) ).
fof(f372,plain,
~ sP4(sdtpldt0(sdtasdt0(xl,sK0),sdtasdt0(xl,sK1))),
inference(forward_demodulation,[],[f369,f91]) ).
fof(f375,plain,
$false,
inference(forward_subsumption_resolution,[],[f372,f295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.04/0.36 % CPULimit : 300
% 0.04/0.36 % WCLimit : 300
% 0.04/0.36 % DateTime : Sun Sep 27 20:04:00 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.10/1.09 % (2723130)Detected formulas, will run a generic FOF schedule.
% 3.10/1.09 % (2723140)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=167444251:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.10/1.09 % (2723139)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2014762440:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.10/1.09 % (2723141)dis-21_1_sil=8000:lcm=predicate:random_seed=3056147444: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)
% 3.10/1.09 % (2723135)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=792134191:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.10/1.09 % (2723138)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3614935027:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.10/1.09 % (2723136)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=1225771634:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.10/1.09 % (2723137)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=3196559705:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.10/1.09 % (2723138)First to succeed.
% 3.10/1.09 % (2723138)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2723130"
% 3.10/1.09 % (2723139)Also succeeded, but the first one will report.
% 3.10/1.09 % (2723140)Instruction limit reached!
% 3.10/1.09 % (2723140)------------------------------
% 3.10/1.09 % (2723140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.09 % (2723140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.09 % (2723140)CaDiCaL version: 2.1.3
% 3.10/1.09 % (2723140)Termination reason: Instruction limit
% 3.10/1.09 % (2723140)Termination phase: Saturation
% 3.10/1.09 % (2723140)Time elapsed: 0.045 s
% 3.10/1.09 % (2723140)Peak memory usage: 90 MB
% 3.10/1.09 % (2723140)Instructions burned: 140 (million)
% 3.10/1.10 % (2723141)Instruction limit reached!
% 3.10/1.10 % (2723141)------------------------------
% 3.10/1.10 % (2723141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.10 % (2723141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.10 % (2723141)CaDiCaL version: 2.1.3
% 3.10/1.10 % (2723141)Termination reason: Instruction limit
% 3.10/1.10 % (2723141)Termination phase: Saturation
% 3.10/1.10 % (2723141)Time elapsed: 0.082 s
% 3.10/1.10 % (2723141)Peak memory usage: 91 MB
% 3.10/1.10 % (2723141)Instructions burned: 130 (million)
% 3.10/1.10 % (2723149)lrs+10_1_sil=8000:sp=occurrence:random_seed=4124233586:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.10/1.10 % (2723150)lrs+10_1_sil=32000:urr=on:br=off:random_seed=812340537:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.10/1.10 % (2723149)Instruction limit reached!
% 3.10/1.10 % (2723149)------------------------------
% 3.10/1.10 % (2723149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.10 % (2723149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.10 % (2723149)CaDiCaL version: 2.1.3
% 3.10/1.10 % (2723149)Termination reason: Instruction limit
% 3.10/1.10 % (2723149)Termination phase: Saturation
% 3.10/1.10 % (2723149)Time elapsed: 0.090 s
% 3.10/1.10 % (2723149)Peak memory usage: 92 MB
% 3.10/1.10 % (2723149)Instructions burned: 287 (million)
% 3.10/1.10 % (2723138)Refutation found. Thanks to Tanya!
% 3.10/1.10 % SZS status Theorem for theBenchmark
% 3.10/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.10/1.10 % (2723138)------------------------------
% 3.10/1.10 % (2723138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.10 % (2723138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.10 % (2723138)CaDiCaL version: 2.1.3
% 3.10/1.10 % (2723138)Termination reason: Refutation
% 3.10/1.10 % (2723138)Time elapsed: 0.007 s
% 3.10/1.10 % (2723138)Peak memory usage: 89 MB
% 3.10/1.10 % (2723138)Instructions burned: 10 (million)
% 3.10/1.10 % (2723138)------------------------------
% 3.10/1.10 % (2723138)------------------------------
% 3.10/1.10 % (2723130)Success in time 0.402 s
% 3.10/1.10 % Vampire exiting
%------------------------------------------------------------------------------