%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG059+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 : n010.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 12:35:20 PM UTC 2026
% Result : Theorem 0.16s 1.51s
% Output : Refutation 0.16s
% 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(f101,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(f102,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,[],[f101]) ).
fof(f118,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(f119,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,[],[f118]) ).
fof(f157,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f161,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f162,plain,
xN = sdtasdt0(xR,xS),
inference(cnf_transformation,[],[f55]) ).
fof(f163,plain,
aScalar0(xN),
inference(cnf_transformation,[],[f55]) ).
fof(f166,plain,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(cnf_transformation,[],[f60]) ).
fof(f192,plain,
! [X0,X1] :
( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f213,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f433,plain,
( smndt0(xN) != smndt0(sdtasdt0(xS,xR))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(superposition,[],[f166,f192]) ).
fof(f446,plain,
( smndt0(xN) != smndt0(sdtasdt0(xS,xR))
| ~ aScalar0(xR) ),
inference(forward_subsumption_resolution,[],[f433,f161]) ).
fof(f452,plain,
smndt0(xN) != smndt0(sdtasdt0(xS,xR)),
inference(forward_subsumption_resolution,[],[f446,f157]) ).
fof(f516,plain,
! [X0] :
( smndt0(xN) != smndt0(sdtasdt0(xR,xS))
| ~ aScalar0(xR)
| ~ aScalar0(xS)
| ~ aScalar0(X0) ),
inference(superposition,[],[f452,f213]) ).
fof(f535,plain,
! [X0] :
( smndt0(xN) != smndt0(sdtasdt0(xR,xS))
| ~ aScalar0(xS)
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f516,f157]) ).
fof(f559,plain,
! [X0] :
( smndt0(xN) != smndt0(sdtasdt0(xR,xS))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f535,f161]) ).
fof(f573,plain,
! [X0] :
( smndt0(xN) != smndt0(xN)
| ~ aScalar0(X0) ),
inference(forward_demodulation,[],[f559,f162]) ).
fof(f574,plain,
! [X0] : ~ aScalar0(X0),
inference(trivial_inequality_removal,[],[f573]) ).
fof(f596,plain,
$false,
inference(resolution,[],[f574,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG059+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:04:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.16/1.51 % (1407719)Detected formulas, will run a generic FOF schedule.
% 0.16/1.51 % (1407730)dis-21_1_sil=8000:lcm=predicate:random_seed=3929367928: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)
% 0.16/1.51 % (1407728)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3104950736:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.51 % (1407725)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=4242638744:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.51 % (1407727)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3645117806:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.51 % (1407726)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=2015411547:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.51 % (1407724)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=3617458974:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.51 % (1407728)First to succeed.
% 0.16/1.51 % (1407728)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1407719"
% 0.16/1.51 % (1407729)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4154342357:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.51 % (1407730)Instruction limit reached!
% 0.16/1.51 % (1407730)------------------------------
% 0.16/1.51 % (1407730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.51 % (1407730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.51 % (1407730)CaDiCaL version: 2.1.3
% 0.16/1.51 % (1407730)Termination reason: Instruction limit
% 0.16/1.51 % (1407730)Termination phase: Saturation
% 0.16/1.51 % (1407730)Time elapsed: 0.043 s
% 0.16/1.51 % (1407730)Peak memory usage: 90 MB
% 0.16/1.51 % (1407730)Instructions burned: 130 (million)
% 0.16/1.51 % (1407729)Also succeeded, but the first one will report.
% 0.16/1.51 % (1407727)Instruction limit reached!
% 0.16/1.51 % (1407727)------------------------------
% 0.16/1.51 % (1407727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.51 % (1407727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.51 % (1407727)CaDiCaL version: 2.1.3
% 0.16/1.51 % (1407727)Termination reason: Instruction limit
% 0.16/1.51 % (1407727)Termination phase: Saturation
% 0.16/1.51 % (1407727)Time elapsed: 0.067 s
% 0.16/1.51 % (1407727)Peak memory usage: 89 MB
% 0.16/1.51 % (1407727)Instructions burned: 109 (million)
% 0.16/1.51 % (1407738)lrs+10_1_sil=8000:sp=occurrence:random_seed=3841172883:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.16/1.51 % (1407738)Also succeeded, but the first one will report.
% 0.16/1.51 % (1407739)lrs+10_1_sil=32000:urr=on:br=off:random_seed=937893887:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.16/1.51 % (1407728)Refutation found. Thanks to Tanya!
% 0.16/1.51 % SZS status Theorem for theBenchmark
% 0.16/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.51 % (1407728)------------------------------
% 0.16/1.51 % (1407728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.51 % (1407728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.51 % (1407728)CaDiCaL version: 2.1.3
% 0.16/1.51 % (1407728)Termination reason: Refutation
% 0.16/1.51 % (1407728)Time elapsed: 0.010 s
% 0.16/1.51 % (1407728)Peak memory usage: 88 MB
% 0.16/1.51 % (1407728)Instructions burned: 14 (million)
% 0.16/1.51 % (1407728)------------------------------
% 0.16/1.51 % (1407728)------------------------------
% 0.16/1.51 % (1407719)Success in time 0.444 s
% 0.16/1.51 % Vampire exiting
%------------------------------------------------------------------------------