%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG061+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 : n009.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 2.68s 1.35s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 110 ( 39 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 51 ~; 41 |; 21 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 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 : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(f52,axiom,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(f54,axiom,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(f55,axiom,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(f58,axiom,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(f59,axiom,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2180) ).
fof(f60,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f61,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(negated_conjecture,[status(cth)],[f60]) ).
fof(f62,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(flattening,[],[f61]) ).
fof(f80,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f81,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f80]) ).
fof(f103,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(f104,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,[],[f103]) ).
fof(f106,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f113,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(f114,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,[],[f113]) ).
fof(f159,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f163,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f165,plain,
aScalar0(xN),
inference(cnf_transformation,[],[f55]) ).
fof(f169,plain,
smndt0(xN) = sdtasdt0(smndt0(xS),xR),
inference(cnf_transformation,[],[f58]) ).
fof(f171,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(cnf_transformation,[],[f59]) ).
fof(f172,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(cnf_transformation,[],[f62]) ).
fof(f178,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f198,plain,
! [X0,X1] :
( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f208,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f215,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f430,plain,
( smndt0(xN) = smndt0(sdtasdt0(xS,xR))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(superposition,[],[f169,f198]) ).
fof(f445,plain,
( smndt0(xN) = smndt0(sdtasdt0(xS,xR))
| ~ aScalar0(xR) ),
inference(forward_subsumption_resolution,[],[f430,f163]) ).
fof(f453,plain,
smndt0(xN) = smndt0(sdtasdt0(xS,xR)),
inference(forward_subsumption_resolution,[],[f445,f159]) ).
fof(f462,plain,
( ~ aScalar0(sdtasdt0(xS,xR))
| aScalar0(smndt0(xN)) ),
inference(superposition,[],[f208,f453]) ).
fof(f504,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(resolution,[],[f462,f178]) ).
fof(f505,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(xR) ),
inference(forward_subsumption_resolution,[],[f504,f163]) ).
fof(f506,plain,
aScalar0(smndt0(xN)),
inference(forward_subsumption_resolution,[],[f505,f159]) ).
fof(f621,plain,
! [X0] :
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(X0) ),
inference(superposition,[],[f172,f215]) ).
fof(f637,plain,
! [X0] :
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f621,f506]) ).
fof(f1311,plain,
! [X0] :
( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(X0) ),
inference(superposition,[],[f637,f171]) ).
fof(f1320,plain,
! [X0] :
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(X0) ),
inference(trivial_inequality_removal,[],[f1311]) ).
fof(f1326,plain,
! [X0] :
( ~ aScalar0(X0)
| ~ aScalar0(xS)
| ~ aScalar0(xS) ),
inference(resolution,[],[f1320,f178]) ).
fof(f1328,plain,
! [X0] :
( ~ aScalar0(X0)
| ~ aScalar0(xS) ),
inference(duplicate_literal_removal,[],[f1326]) ).
fof(f1329,plain,
! [X0] : ~ aScalar0(X0),
inference(forward_subsumption_resolution,[],[f1328,f163]) ).
fof(f1458,plain,
$false,
inference(resolution,[],[f1329,f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG061+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 23:04:00 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.68/1.35 % (2510364)Detected formulas, will run a generic FOF schedule.
% 2.68/1.35 % (2510373)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4034852781:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.35 % (2510373)First to succeed.
% 2.68/1.35 % (2510373)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2510364"
% 2.68/1.35 % (2510369)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=3252716749:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.35 % (2510372)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1539237720:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.35 % (2510371)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=590141560:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.35 % (2510375)dis-21_1_sil=8000:lcm=predicate:random_seed=1500868095: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)
% 2.68/1.35 % (2510370)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=879992568:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.35 % (2510374)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2410745892:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.35 % (2510372)Instruction limit reached!
% 2.68/1.35 % (2510372)------------------------------
% 2.68/1.35 % (2510372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (2510372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (2510372)CaDiCaL version: 2.1.3
% 2.68/1.35 % (2510372)Termination reason: Instruction limit
% 2.68/1.35 % (2510372)Termination phase: Saturation
% 2.68/1.35 % (2510372)Time elapsed: 0.059 s
% 2.68/1.35 % (2510372)Peak memory usage: 89 MB
% 2.68/1.35 % (2510372)Instructions burned: 111 (million)
% 2.68/1.35 % (2510375)Instruction limit reached!
% 2.68/1.35 % (2510375)------------------------------
% 2.68/1.35 % (2510375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (2510375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (2510375)CaDiCaL version: 2.1.3
% 2.68/1.35 % (2510375)Termination reason: Instruction limit
% 2.68/1.35 % (2510375)Termination phase: Saturation
% 2.68/1.35 % (2510375)Time elapsed: 0.076 s
% 2.68/1.35 % (2510375)Peak memory usage: 89 MB
% 2.68/1.35 % (2510375)Instructions burned: 130 (million)
% 2.68/1.35 % (2510374)Instruction limit reached!
% 2.68/1.35 % (2510374)------------------------------
% 2.68/1.35 % (2510374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (2510374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (2510374)CaDiCaL version: 2.1.3
% 2.68/1.35 % (2510374)Termination reason: Instruction limit
% 2.68/1.35 % (2510374)Termination phase: Saturation
% 2.68/1.35 % (2510374)Time elapsed: 0.090 s
% 2.68/1.35 % (2510374)Peak memory usage: 90 MB
% 2.68/1.35 % (2510374)Instructions burned: 140 (million)
% 2.68/1.35 % (2510373)Refutation found. Thanks to Tanya!
% 2.68/1.35 % SZS status Theorem for theBenchmark
% 2.68/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.35 % (2510373)------------------------------
% 2.68/1.35 % (2510373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (2510373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (2510373)CaDiCaL version: 2.1.3
% 2.68/1.35 % (2510373)Termination reason: Refutation
% 2.68/1.35 % (2510373)Time elapsed: 0.014 s
% 2.68/1.35 % (2510373)Peak memory usage: 88 MB
% 2.68/1.35 % (2510373)Instructions burned: 42 (million)
% 2.68/1.35 % (2510373)------------------------------
% 2.68/1.35 % (2510373)------------------------------
% 2.68/1.35 % (2510364)Success in time 0.295 s
% 2.68/1.35 % Vampire exiting
%------------------------------------------------------------------------------