%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG061+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 : 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 3.86s 1.54s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 79 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 92 ( 43 ~; 32 |; 14 &)
% ( 0 <=>; 3 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mArith) ).
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(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/sandbox/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/sandbox/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(f78,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f79,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f78]) ).
fof(f98,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f105,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(f106,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,[],[f105]) ).
fof(f157,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f159,plain,
aScalar0(xN),
inference(cnf_transformation,[],[f55]) ).
fof(f165,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(f166,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(f172,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f196,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f203,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f550,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(smndt0(xN))
| ~ aScalar0(X0) ),
inference(superposition,[],[f166,f203]) ).
fof(f1271,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(smndt0(xN))
| ~ aScalar0(X0) ),
inference(superposition,[],[f550,f165]) ).
fof(f1280,plain,
! [X0] :
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(X0) ),
inference(trivial_inequality_removal,[],[f1271]) ).
fof(f1282,plain,
! [X0] :
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(X0)
| ~ aScalar0(xS)
| ~ aScalar0(xS) ),
inference(resolution,[],[f1280,f172]) ).
fof(f1284,plain,
! [X0] :
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(X0)
| ~ aScalar0(xS) ),
inference(duplicate_literal_removal,[],[f1282]) ).
fof(f1285,plain,
! [X0] :
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f1284,f157]) ).
fof(f1288,plain,
! [X0] :
( ~ aScalar0(X0)
| ~ aScalar0(xN) ),
inference(resolution,[],[f1285,f196]) ).
fof(f1290,plain,
! [X0] : ~ aScalar0(X0),
inference(forward_subsumption_resolution,[],[f1288,f159]) ).
fof(f1422,plain,
$false,
inference(resolution,[],[f1290,f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG061+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n010.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 23:04:32 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 3.86/1.54 % (1408561)Detected formulas, will run a generic FOF schedule.
% 3.86/1.54 % (1408568)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=560587521:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.86/1.54 % (1408570)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2306367959:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.86/1.54 % (1408572)dis-21_1_sil=8000:lcm=predicate:random_seed=4068532263: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)
% 3.86/1.54 % (1408566)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=3262245985:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.86/1.54 % (1408567)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=2753756306:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.86/1.54 % (1408569)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=456275274:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.86/1.54 % (1408571)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2208884311:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.86/1.54 % (1408570)First to succeed.
% 3.86/1.54 % (1408570)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1408561"
% 3.86/1.54 % (1408569)Instruction limit reached!
% 3.86/1.54 % (1408569)------------------------------
% 3.86/1.54 % (1408569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.54 % (1408569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.54 % (1408569)CaDiCaL version: 2.1.3
% 3.86/1.54 % (1408569)Termination reason: Instruction limit
% 3.86/1.54 % (1408569)Termination phase: Saturation
% 3.86/1.54 % (1408569)Time elapsed: 0.057 s
% 3.86/1.54 % (1408569)Peak memory usage: 89 MB
% 3.86/1.54 % (1408569)Instructions burned: 110 (million)
% 3.86/1.54 % (1408572)Instruction limit reached!
% 3.86/1.54 % (1408572)------------------------------
% 3.86/1.54 % (1408572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.54 % (1408572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.54 % (1408572)CaDiCaL version: 2.1.3
% 3.86/1.54 % (1408572)Termination reason: Instruction limit
% 3.86/1.54 % (1408572)Termination phase: Saturation
% 3.86/1.54 % (1408572)Time elapsed: 0.069 s
% 3.86/1.54 % (1408572)Peak memory usage: 89 MB
% 3.86/1.54 % (1408572)Instructions burned: 131 (million)
% 3.86/1.54 % (1408571)Instruction limit reached!
% 3.86/1.54 % (1408571)------------------------------
% 3.86/1.54 % (1408571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.54 % (1408571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.54 % (1408571)CaDiCaL version: 2.1.3
% 3.86/1.54 % (1408571)Termination reason: Instruction limit
% 3.86/1.54 % (1408571)Termination phase: Saturation
% 3.86/1.54 % (1408571)Time elapsed: 0.089 s
% 3.86/1.54 % (1408571)Peak memory usage: 90 MB
% 3.86/1.54 % (1408571)Instructions burned: 140 (million)
% 3.86/1.54 % (1408580)lrs+10_1_sil=8000:sp=occurrence:random_seed=904802022:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.86/1.54 % (1408581)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4037490146:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.86/1.54 % (1408570)Refutation found. Thanks to Tanya!
% 3.86/1.54 % SZS status Theorem for theBenchmark
% 3.86/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.54 % (1408570)------------------------------
% 3.86/1.54 % (1408570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.54 % (1408570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.54 % (1408570)CaDiCaL version: 2.1.3
% 3.86/1.54 % (1408570)Termination reason: Refutation
% 3.86/1.54 % (1408570)Time elapsed: 0.025 s
% 3.86/1.54 % (1408570)Peak memory usage: 88 MB
% 3.86/1.54 % (1408570)Instructions burned: 42 (million)
% 3.86/1.54 % (1408570)------------------------------
% 3.86/1.54 % (1408570)------------------------------
% 3.86/1.54 % (1408561)Success in time 0.463 s
% 3.86/1.54 % Vampire exiting
%------------------------------------------------------------------------------