%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG103+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 : n017.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 12:35:32 PM UTC 2026
% Result : Theorem 2.75s 1.35s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 47 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 46 ( 22 ~; 16 |; 7 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f40,axiom,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).
fof(f41,axiom,
( aElement0(xv)
& sdtasdt0(xc,xv) = xy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1979) ).
fof(f42,conjecture,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f45,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(flattening,[],[f43]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f56]) ).
fof(f73,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
xx = sdtasdt0(xc,xu),
inference(cnf_transformation,[],[f40]) ).
fof(f82,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
xy = sdtasdt0(xc,xv),
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f45]) ).
fof(f97,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f411,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(X0,xv)) = sdtpldt0(sdtasdt0(xc,X0),xy)
| ~ aElement0(xc)
| ~ aElement0(X0)
| ~ aElement0(xv) ),
inference(superposition,[],[f97,f83]) ).
fof(f448,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(X0,xv)) = sdtpldt0(sdtasdt0(xc,X0),xy)
| ~ aElement0(X0)
| ~ aElement0(xv) ),
inference(forward_subsumption_resolution,[],[f411,f73]) ).
fof(f474,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(X0,xv)) = sdtpldt0(sdtasdt0(xc,X0),xy)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f448,f84]) ).
fof(f1447,plain,
( sdtpldt0(xx,xy) != sdtpldt0(sdtasdt0(xc,xu),xy)
| ~ aElement0(xu) ),
inference(superposition,[],[f85,f474]) ).
fof(f1473,plain,
sdtpldt0(xx,xy) != sdtpldt0(sdtasdt0(xc,xu),xy),
inference(forward_subsumption_resolution,[],[f1447,f82]) ).
fof(f1478,plain,
sdtpldt0(xx,xy) != sdtpldt0(xx,xy),
inference(forward_demodulation,[],[f1473,f81]) ).
fof(f1479,plain,
$false,
inference(trivial_inequality_removal,[],[f1478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 23:11:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.75/1.35 % (3060560)Detected formulas, will run a generic FOF schedule.
% 2.75/1.35 % (3060569)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3468830695:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.35 % (3060569)First to succeed.
% 2.75/1.35 % (3060569)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3060560"
% 2.75/1.35 % (3060566)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=2124811601:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.35 % (3060568)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2208617863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.35 % (3060571)dis-21_1_sil=8000:lcm=predicate:random_seed=3699114186: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)
% 2.75/1.35 % (3060565)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=3887122331:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.35 % (3060567)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=3700123249:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.35 % (3060570)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1417018309:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.35 % (3060568)Also succeeded, but the first one will report.
% 2.75/1.35 % (3060571)Instruction limit reached!
% 2.75/1.35 % (3060571)------------------------------
% 2.75/1.35 % (3060571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (3060571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (3060571)CaDiCaL version: 2.1.3
% 2.75/1.35 % (3060571)Termination reason: Instruction limit
% 2.75/1.35 % (3060571)Termination phase: Saturation
% 2.75/1.35 % (3060571)Time elapsed: 0.073 s
% 2.75/1.35 % (3060571)Peak memory usage: 89 MB
% 2.75/1.35 % (3060571)Instructions burned: 130 (million)
% 2.75/1.35 % (3060570)Instruction limit reached!
% 2.75/1.35 % (3060570)------------------------------
% 2.75/1.35 % (3060570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (3060570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (3060570)CaDiCaL version: 2.1.3
% 2.75/1.35 % (3060570)Termination reason: Instruction limit
% 2.75/1.35 % (3060570)Termination phase: Saturation
% 2.75/1.35 % (3060570)Time elapsed: 0.087 s
% 2.75/1.35 % (3060570)Peak memory usage: 90 MB
% 2.75/1.35 % (3060570)Instructions burned: 141 (million)
% 2.75/1.35 % (3060569)Refutation found. Thanks to Tanya!
% 2.75/1.35 % SZS status Theorem for theBenchmark
% 2.75/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.35 % (3060569)------------------------------
% 2.75/1.35 % (3060569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (3060569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (3060569)CaDiCaL version: 2.1.3
% 2.75/1.35 % (3060569)Termination reason: Refutation
% 2.75/1.35 % (3060569)Time elapsed: 0.014 s
% 2.75/1.35 % (3060569)Peak memory usage: 88 MB
% 2.75/1.35 % (3060569)Instructions burned: 40 (million)
% 2.75/1.35 % (3060569)------------------------------
% 2.75/1.35 % (3060569)------------------------------
% 2.75/1.35 % (3060560)Success in time 0.305 s
% 2.75/1.35 % Vampire exiting
%------------------------------------------------------------------------------