%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG059+1 : 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 : n018.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 12:35:19 PM UTC 2026
% Result : Theorem 2.58s 1.35s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 73 ( 35 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 81 ( 36 ~; 25 |; 18 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(f17,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
& sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
fof(f52,axiom,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(f54,axiom,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(f55,axiom,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(f58,conjecture,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f59,negated_conjecture,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,plain,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(flattening,[],[f59]) ).
fof(f93,plain,
! [X0,X1] :
( ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
& sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f94,plain,
! [X0,X1] :
( ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
& sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f93]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f116]) ).
fof(f151,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f155,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f156,plain,
xN = sdtasdt0(xR,xS),
inference(cnf_transformation,[],[f55]) ).
fof(f157,plain,
aScalar0(xN),
inference(cnf_transformation,[],[f55]) ).
fof(f160,plain,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(cnf_transformation,[],[f60]) ).
fof(f180,plain,
! [X0,X1] :
( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f207,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f355,plain,
( smndt0(xN) != smndt0(sdtasdt0(xS,xR))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(superposition,[],[f160,f180]) ).
fof(f368,plain,
( smndt0(xN) != smndt0(sdtasdt0(xS,xR))
| ~ aScalar0(xR) ),
inference(forward_subsumption_resolution,[],[f355,f155]) ).
fof(f374,plain,
smndt0(xN) != smndt0(sdtasdt0(xS,xR)),
inference(forward_subsumption_resolution,[],[f368,f151]) ).
fof(f439,plain,
! [X0] :
( smndt0(xN) != smndt0(sdtasdt0(xR,xS))
| ~ aScalar0(xR)
| ~ aScalar0(xS)
| ~ aScalar0(X0) ),
inference(superposition,[],[f374,f207]) ).
fof(f458,plain,
! [X0] :
( smndt0(xN) != smndt0(sdtasdt0(xR,xS))
| ~ aScalar0(xS)
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f439,f151]) ).
fof(f482,plain,
! [X0] :
( smndt0(xN) != smndt0(sdtasdt0(xR,xS))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f458,f155]) ).
fof(f496,plain,
! [X0] :
( smndt0(xN) != smndt0(xN)
| ~ aScalar0(X0) ),
inference(forward_demodulation,[],[f482,f156]) ).
fof(f497,plain,
! [X0] : ~ aScalar0(X0),
inference(trivial_inequality_removal,[],[f496]) ).
fof(f517,plain,
$false,
inference(resolution,[],[f497,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG059+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.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 23:05:54 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.58/1.35 % (2838404)Detected formulas, will run a generic FOF schedule.
% 2.58/1.35 % (2838413)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=261918818:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.35 % (2838413)First to succeed.
% 2.58/1.35 % (2838413)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2838404"
% 2.58/1.35 % (2838410)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=1673220909:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.35 % (2838412)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1301821443:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.35 % (2838411)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=3024762790:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.35 % (2838409)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=4016772252:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.35 % (2838415)dis-21_1_sil=8000:lcm=predicate:random_seed=2527130825: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)
% 2.58/1.35 % (2838414)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3059059210:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.35 % (2838414)Also succeeded, but the first one will report.
% 2.58/1.35 % (2838412)Instruction limit reached!
% 2.58/1.35 % (2838412)------------------------------
% 2.58/1.35 % (2838412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.35 % (2838412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.35 % (2838412)CaDiCaL version: 2.1.3
% 2.58/1.35 % (2838412)Termination reason: Instruction limit
% 2.58/1.35 % (2838412)Termination phase: Saturation
% 2.58/1.35 % (2838412)Time elapsed: 0.067 s
% 2.58/1.35 % (2838412)Peak memory usage: 89 MB
% 2.58/1.35 % (2838412)Instructions burned: 110 (million)
% 2.58/1.35 % (2838415)Instruction limit reached!
% 2.58/1.35 % (2838415)------------------------------
% 2.58/1.35 % (2838415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.35 % (2838415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.35 % (2838415)CaDiCaL version: 2.1.3
% 2.58/1.35 % (2838415)Termination reason: Instruction limit
% 2.58/1.35 % (2838415)Termination phase: Saturation
% 2.58/1.35 % (2838415)Time elapsed: 0.078 s
% 2.58/1.35 % (2838415)Peak memory usage: 90 MB
% 2.58/1.35 % (2838415)Instructions burned: 131 (million)
% 2.58/1.35 % (2838413)Refutation found. Thanks to Tanya!
% 2.58/1.35 % SZS status Theorem for theBenchmark
% 2.58/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.35 % (2838413)------------------------------
% 2.58/1.35 % (2838413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.35 % (2838413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.35 % (2838413)CaDiCaL version: 2.1.3
% 2.58/1.35 % (2838413)Termination reason: Refutation
% 2.58/1.35 % (2838413)Time elapsed: 0.005 s
% 2.58/1.35 % (2838413)Peak memory usage: 88 MB
% 2.58/1.35 % (2838413)Instructions burned: 12 (million)
% 2.58/1.35 % (2838413)------------------------------
% 2.58/1.35 % (2838413)------------------------------
% 2.58/1.35 % (2838404)Success in time 0.28 s
% 2.58/1.35 % Vampire exiting
%------------------------------------------------------------------------------