%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG045+1 : 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 12:35:16 PM UTC 2026
% Result : Theorem 3.44s 1.34s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 54 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 32 ~; 21 |; 8 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(f16,axiom,
( aScalar0(xx)
& aScalar0(xy)
& aScalar0(xu)
& aScalar0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__674) ).
fof(f17,axiom,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__733) ).
fof(f18,conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(flattening,[],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f22]) ).
fof(f30,plain,
aScalar0(xv),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
aScalar0(xu),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
aScalar0(xy),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
aScalar0(xx),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f211,plain,
( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtasdt0(xy,sdtpldt0(xu,xv)))
| ~ aScalar0(xy)
| ~ aScalar0(xu)
| ~ aScalar0(xv) ),
inference(superposition,[],[f35,f37]) ).
fof(f233,plain,
( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtasdt0(xy,sdtpldt0(xu,xv)))
| ~ aScalar0(xu)
| ~ aScalar0(xv) ),
inference(forward_subsumption_resolution,[],[f211,f32]) ).
fof(f246,plain,
( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtasdt0(xy,sdtpldt0(xu,xv)))
| ~ aScalar0(xv) ),
inference(forward_subsumption_resolution,[],[f233,f31]) ).
fof(f251,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(forward_subsumption_resolution,[],[f246,f30]) ).
fof(f254,plain,
( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv)))
| ~ aScalar0(xx)
| ~ aScalar0(xu)
| ~ aScalar0(xv) ),
inference(superposition,[],[f251,f37]) ).
fof(f258,plain,
( ~ aScalar0(xx)
| ~ aScalar0(xu)
| ~ aScalar0(xv) ),
inference(forward_subsumption_resolution,[],[f254,f34]) ).
fof(f259,plain,
( ~ aScalar0(xu)
| ~ aScalar0(xv) ),
inference(forward_subsumption_resolution,[],[f258,f33]) ).
fof(f260,plain,
~ aScalar0(xv),
inference(forward_subsumption_resolution,[],[f259,f31]) ).
fof(f261,plain,
$false,
inference(forward_subsumption_resolution,[],[f260,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:02:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.44/1.34 % (2507911)Detected formulas, will run a generic FOF schedule.
% 3.44/1.34 % (2507926)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=643940314:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.34 % (2507930)dis-21_1_sil=8000:lcm=predicate:random_seed=1598935096: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)
% 3.44/1.34 % (2507924)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=4157651640:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.34 % (2507928)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2507266843:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.34 % (2507925)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=1390110088:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.34 % (2507927)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2465883785:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.34 % (2507929)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2307785990:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.34 % (2507930)Refutation not found, incomplete strategy
% 3.44/1.34 % (2507930)------------------------------
% 3.44/1.34 % (2507930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.34 % (2507930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.34 % (2507930)CaDiCaL version: 2.1.3
% 3.44/1.34 % (2507930)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.34 % (2507930)Time elapsed: 0.002 s
% 3.44/1.34 % (2507930)Peak memory usage: 88 MB
% 3.44/1.34 % (2507930)Instructions burned: 2 (million)
% 3.44/1.34 % (2507928)First to succeed.
% 3.44/1.34 % (2507928)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2507911"
% 3.44/1.34 % (2507927)Also succeeded, but the first one will report.
% 3.44/1.34 % (2507929)Instruction limit reached!
% 3.44/1.34 % (2507929)------------------------------
% 3.44/1.34 % (2507929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.34 % (2507929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.34 % (2507929)CaDiCaL version: 2.1.3
% 3.44/1.34 % (2507929)Termination reason: Instruction limit
% 3.44/1.34 % (2507929)Termination phase: Saturation
% 3.44/1.34 % (2507929)Time elapsed: 0.088 s
% 3.44/1.34 % (2507929)Peak memory usage: 90 MB
% 3.44/1.34 % (2507929)Instructions burned: 139 (million)
% 3.44/1.34 % (2507938)lrs+10_1_sil=8000:sp=occurrence:random_seed=2247833643:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.44/1.34 % (2507930)------------------------------
% 3.44/1.34 % (2507930)------------------------------
% 3.44/1.34 % (2507928)Refutation found. Thanks to Tanya!
% 3.44/1.34 % SZS status Theorem for theBenchmark
% 3.44/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.34 % (2507928)------------------------------
% 3.44/1.34 % (2507928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.34 % (2507928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.34 % (2507928)CaDiCaL version: 2.1.3
% 3.44/1.34 % (2507928)Termination reason: Refutation
% 3.44/1.34 % (2507928)Time elapsed: 0.006 s
% 3.44/1.34 % (2507928)Peak memory usage: 88 MB
% 3.44/1.34 % (2507928)Instructions burned: 8 (million)
% 3.44/1.34 % (2507928)------------------------------
% 3.44/1.34 % (2507928)------------------------------
% 3.44/1.34 % (2507911)Success in time 0.408 s
% 3.44/1.34 % Vampire exiting
%------------------------------------------------------------------------------