%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG046+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 : n014.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 12:35:16 PM UTC 2026
% Result : Theorem 5.84s 1.79s
% Output : Refutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 74 ( 43 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 63 ( 22 ~; 19 |; 19 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( sdtpldt0(X0,sz0z00) = X0
& sdtpldt0(sz0z00,X0) = X0
& sdtasdt0(X0,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X0) = sz0z00
& sdtpldt0(X0,smndt0(X0)) = sz0z00
& sdtpldt0(smndt0(X0),X0) = sz0z00
& smndt0(smndt0(X0)) = X0
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).
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(f18,axiom,
( aScalar0(xx)
& aScalar0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f19,conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(flattening,[],[f20]) ).
fof(f23,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(f24,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,[],[f23]) ).
fof(f31,plain,
! [X0] :
( ( sdtpldt0(X0,sz0z00) = X0
& sdtpldt0(sz0z00,X0) = X0
& sdtasdt0(X0,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X0) = sz0z00
& sdtpldt0(X0,smndt0(X0)) = sz0z00
& sdtpldt0(smndt0(X0),X0) = sz0z00
& smndt0(smndt0(X0)) = X0
& smndt0(sz0z00) = sz0z00 )
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f34,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
aScalar0(xy),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
aScalar0(xx),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f50,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(smndt0(X0)) = X0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f58,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f81,plain,
xy = smndt0(smndt0(xy)),
inference(resolution,[],[f50,f37]) ).
fof(f150,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(sdtasdt0(X0,xy)) = sdtasdt0(smndt0(X0),xy) ),
inference(resolution,[],[f40,f37]) ).
fof(f156,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| smndt0(sdtasdt0(X0,smndt0(X1))) = sdtasdt0(X0,smndt0(smndt0(X1)))
| ~ aScalar0(X0) ),
inference(resolution,[],[f41,f58]) ).
fof(f158,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(sdtasdt0(X0,xy)) = sdtasdt0(X0,smndt0(xy)) ),
inference(resolution,[],[f41,f37]) ).
fof(f369,plain,
smndt0(sdtasdt0(xx,xy)) = sdtasdt0(smndt0(xx),xy),
inference(resolution,[],[f150,f38]) ).
fof(f444,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(sdtasdt0(smndt0(X0),xy)) = sdtasdt0(smndt0(X0),smndt0(xy)) ),
inference(resolution,[],[f158,f58]) ).
fof(f445,plain,
smndt0(sdtasdt0(xx,xy)) = sdtasdt0(xx,smndt0(xy)),
inference(resolution,[],[f158,f38]) ).
fof(f1191,plain,
! [X0] :
( smndt0(sdtasdt0(X0,smndt0(xy))) = sdtasdt0(X0,smndt0(smndt0(xy)))
| ~ aScalar0(X0) ),
inference(resolution,[],[f156,f37]) ).
fof(f1192,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,xy) = smndt0(sdtasdt0(X0,smndt0(xy))) ),
inference(forward_demodulation,[],[f1191,f81]) ).
fof(f1597,plain,
sdtasdt0(smndt0(xx),xy) = sdtasdt0(xx,smndt0(xy)),
inference(superposition,[],[f369,f445]) ).
fof(f4563,plain,
sdtasdt0(xx,xy) = smndt0(sdtasdt0(xx,smndt0(xy))),
inference(resolution,[],[f1192,f38]) ).
fof(f7276,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = smndt0(sdtasdt0(smndt0(xx),xy)),
inference(resolution,[],[f444,f38]) ).
fof(f7583,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = smndt0(sdtasdt0(xx,smndt0(xy))),
inference(forward_demodulation,[],[f7276,f1597]) ).
fof(f7646,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
inference(forward_demodulation,[],[f7583,f4563]) ).
fof(f7652,plain,
$false,
inference(forward_subsumption_resolution,[],[f7646,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG046+1 : 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 : n014.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:02:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 5.84/1.79 % (1274600)Detected formulas, will run a generic FOF schedule.
% 5.84/1.79 % (1274608)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2846896541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.84/1.79 % (1274608)Refutation not found, incomplete strategy
% 5.84/1.79 % (1274608)------------------------------
% 5.84/1.79 % (1274608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274608)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274608)Termination reason: Refutation not found, incomplete strategy
% 5.84/1.79 % (1274608)Time elapsed: 0.001 s
% 5.84/1.79 % (1274608)Peak memory usage: 88 MB
% 5.84/1.79 % (1274610)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=276324582:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.84/1.79 % (1274606)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=3368991505:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.84/1.79 % (1274605)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=486683789:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.84/1.79 % (1274611)dis-21_1_sil=8000:lcm=predicate:random_seed=2473238003: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)
% 5.84/1.79 % (1274609)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3779340047:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.84/1.79 % (1274607)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=110961849:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.84/1.79 % (1274611)Refutation not found, incomplete strategy
% 5.84/1.79 % (1274611)------------------------------
% 5.84/1.79 % (1274611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274611)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274611)Termination reason: Refutation not found, incomplete strategy
% 5.84/1.79 % (1274611)Time elapsed: 0.002 s
% 5.84/1.79 % (1274611)Peak memory usage: 88 MB
% 5.84/1.79 % (1274611)Instructions burned: 2 (million)
% 5.84/1.79 % (1274609)Instruction limit reached!
% 5.84/1.79 % (1274609)------------------------------
% 5.84/1.79 % (1274609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274609)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274609)Termination reason: Instruction limit
% 5.84/1.79 % (1274609)Termination phase: Saturation
% 5.84/1.79 % (1274609)Time elapsed: 0.061 s
% 5.84/1.79 % (1274609)Peak memory usage: 88 MB
% 5.84/1.79 % (1274609)Instructions burned: 121 (million)
% 5.84/1.79 % (1274610)Instruction limit reached!
% 5.84/1.79 % (1274610)------------------------------
% 5.84/1.79 % (1274610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274610)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274610)Termination reason: Instruction limit
% 5.84/1.79 % (1274610)Termination phase: Saturation
% 5.84/1.79 % (1274610)Time elapsed: 0.085 s
% 5.84/1.79 % (1274610)Peak memory usage: 89 MB
% 5.84/1.79 % (1274610)Instructions burned: 139 (million)
% 5.84/1.79 % (1274608)------------------------------
% 5.84/1.79 % (1274608)------------------------------
% 5.84/1.79 % (1274619)lrs+10_1_sil=8000:sp=occurrence:random_seed=1727674731:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.84/1.79 % (1274620)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3462939709:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.84/1.79 % (1274621)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1964431624:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.84/1.79 % (1274611)------------------------------
% 5.84/1.79 % (1274611)------------------------------
% 5.84/1.79 % (1274620)Instruction limit reached!
% 5.84/1.79 % (1274620)------------------------------
% 5.84/1.79 % (1274620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274620)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274620)Termination reason: Instruction limit
% 5.84/1.79 % (1274620)Termination phase: Saturation
% 5.84/1.79 % (1274620)Time elapsed: 0.073 s
% 5.84/1.79 % (1274620)Peak memory usage: 91 MB
% 5.84/1.79 % (1274620)Instructions burned: 157 (million)
% 5.84/1.79 % (1274621)Instruction limit reached!
% 5.84/1.79 % (1274621)------------------------------
% 5.84/1.79 % (1274621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274621)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274621)Termination reason: Instruction limit
% 5.84/1.79 % (1274621)Termination phase: Saturation
% 5.84/1.79 % (1274621)Time elapsed: 0.099 s
% 5.84/1.79 % (1274621)Peak memory usage: 94 MB
% 5.84/1.79 % (1274621)Instructions burned: 328 (million)
% 5.84/1.79 % (1274619)First to succeed.
% 5.84/1.79 % (1274619)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1274600"
% 5.84/1.79 % (1274625)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2458177147:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.84/1.79 % (1274627)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=853893581:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.84/1.79 % (1274626)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1574073357:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.84/1.79 % (1274626)Refutation not found, incomplete strategy
% 5.84/1.79 % (1274626)------------------------------
% 5.84/1.79 % (1274626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274626)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274626)Termination reason: Refutation not found, incomplete strategy
% 5.84/1.79 % (1274626)Time elapsed: 0.002 s
% 5.84/1.79 % (1274626)Peak memory usage: 88 MB
% 5.84/1.79 % (1274626)Instructions burned: 1 (million)
% 5.84/1.79 % (1274625)Instruction limit reached!
% 5.84/1.79 % (1274625)------------------------------
% 5.84/1.79 % (1274625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274625)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274625)Termination reason: Instruction limit
% 5.84/1.79 % (1274625)Termination phase: Saturation
% 5.84/1.79 % (1274625)Time elapsed: 0.119 s
% 5.84/1.79 % (1274625)Peak memory usage: 94 MB
% 5.84/1.79 % (1274625)Instructions burned: 250 (million)
% 5.84/1.79 % (1274619)Refutation found. Thanks to Tanya!
% 5.84/1.79 % SZS status Theorem for theBenchmark
% 5.84/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 5.84/1.79 % (1274619)------------------------------
% 5.84/1.79 % (1274619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.84/1.79 % (1274619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.79 % (1274619)CaDiCaL version: 2.1.3
% 5.84/1.79 % (1274619)Termination reason: Refutation
% 5.84/1.79 % (1274619)Time elapsed: 0.162 s
% 5.84/1.79 % (1274619)Peak memory usage: 93 MB
% 5.84/1.79 % (1274619)Instructions burned: 289 (million)
% 5.84/1.79 % (1274619)------------------------------
% 5.84/1.79 % (1274619)------------------------------
% 5.84/1.79 % (1274600)Success in time 0.75 s
% 5.84/1.79 % Vampire exiting
%------------------------------------------------------------------------------